Thomas Dick

The telescope is an optical instrument for viewing objects at a distance. Its name is compounded of two Greek words,—t??e, which signifies, at a distance, or far off, and s??pe??, to view, or to contemplate. By means of telescopes, remote objects are represented as if they were near, small apparent magnitudes are enlarged, confused objects are rendered distinct, and the invisible and obscure parts of very distant scenes are rendered perceptible and clear to the organ of vision. The telescope is justly considered as a grand and noble instrument. It is not a little surprising that it should be in the power of man to invent and construct an instrument by which objects, too remote for the unassisted eye to distinguish, should be brought within the range of distinct vision, as if they were only a few yards from our eye, and that thousands of august objects in the heavens, which had been concealed from mortals for numerous ages, should be brought within the limits of our contemplation, and be as distinctly perceived, as if we had been transported many millions of miles from the space we occupy, through the celestial regions. The celebrated Huygens remarks, in reference to this instrument, that, in his opinion, ‘the wit and industry of man has not produced any thing so noble and so worthy of his faculties as this sort of knowledge; (namely of the telescope) insomuch that if any particular person had been so diligent and sagacious as to invent this instrument from the principles of nature and geometry,—for my part, I should have thought his abilities were more than human; but the case is so far from this, that the most learned men have not yet been able sufficiently to explain the reason of the effects of this casual invention.’

The persons who constructed the first telescopes, and the exact period when they were first invented, are involved in some degree of obscurity. It does not certainly appear that such instruments were known to the ancients, although we ought not to be perfectly decisive on this point. The cabinets of the curious contain some very ancient gems, of admirable workmanship, the figures on which are so small, that they appear beautiful through a magnifying glass, but altogether confused and indistinct to the naked eye: and, therefore, it may be asked, if they cannot be viewed, how could they be wrought, without the assistance of glasses? And as some of the ancients have declared that the moon has a form like that of the earth, and has plains, hills, and valleys in it,—how could they know this—unless by mere conjecture, without the use of a telescope? And how could they have known that the Milky Way is formed by the combined rays of an infinite number of stars? For Ovid states, in reference to this zone, ‘its ground-work is of stars.’ But whatever knowledge the ancients may have possessed of the telescope or other optical glasses, it is quite evident that they never had telescopes of such size and power as those which we now possess; and that no discoveries in the heavens, such as are now brought to light, were made by any of the ancient astronomers; otherwise some allusions to them must have been found in their writings.

Among the moderns, the illustrious Friar Bacon appears to have acquired some rude ideas respecting the construction of telescopes. ‘Lenses and specula’ says he, ‘may be so figured that one object may be multiplied into many, that those which are situated at a great distance may be made to appear very near, that those which are small may be made to appear very large, and those which are obscure very plain; and we can make stars to appear wherever we will.’ From these expressions, it appears highly probable, that this philosopher was acquainted with the general principle both of telescopes and microscopes, and that he may have constructed telescopes of small magnifying power, for his own observation and amusement, although they never came into general use. He was a man of extensive learning, and made so rapid a progress in the sciences, when attending the university of Paris, that he was esteemed the glory of that seat of learning. He prosecuted his favourite study of experimental philosophy with unremitting ardour; and in this pursuit, in the course of twenty years, he expended no less than £2000 in experiments, instruments, and in procuring scarce books. In consequence of such extraordinary talents, and such astonishing progress in the sciences, in that ignorant age, he was represented, by the envy of his illiterate fraternity, as having dealings with the devil; and, under this pretence, he was restrained from reading lectures, and at length, in 1278, when sixty-four years of age, he was imprisoned in his cell, where he remained in confinement for ten years. He shone like a single bright star in a dark hemisphere—the glory of our country—and died at Oxford, in the year 1294, in the eightieth year of his age. ‘Friar Bacon,’ says the Rev. Mr. Jones, ‘may be considered as the first of English philosophers; his profound skill in mechanics, optics, astronomy, and chemistry, would make an honourable figure in the present age. But he is entitled to further praise, as he made all his studies subservient to theology, and directed all his writings, as much as could be, to the glory of God. He had the highest regard for the sacred scriptures, and was persuaded they contain the principles of all true science.’

The next person who is supposed to have acquired a knowledge of telescopes, was Joannes Baptista Porta, of Naples, who flourished in the sixteenth century. He discovered the Camera Obscura—the knowledge of which might naturally have led to the invention of the telescope; but it does not appear that he ever constructed such an instrument. Des Cartes considers James Metius, a Dutchman, as the first constructor of a telescope, and says, that ‘as he was amusing himself with making mirrors and burning-glasses, he casually thought of looking through two of his lenses at a time, and found that distant objects appeared very large and distinct.’ Others say that this great discovery was first made by John Lippersheim, a maker of spectacles at Middleburg, or rather by his children, who were diverting themselves with looking through two glasses at a time, and placing them at different distances from each other. But Borellus, who wrote a book ‘on the invention of the telescope,’ gives this honour to Zacharias Jansen, another spectacle-maker in the same town, who, he says, made the first telescope in 1590. Jansen was a diligent inquirer into nature, and, being engaged in such pursuits, he was trying what use could be made of lenses for those purposes, when he fortunately hit upon the construction. Having found the arrangement of glasses which produced the effect desired, he enclosed them in a tube, and ran with his instrument to prince Maurice, who, immediately conceiving that it might be of use to him in his wars, desired the author to keep it a secret. Such are the rude conceptions and selfish views of princely warriors, who would apply every invention in their power for the destruction of mankind. But the telescope was soon destined to more noble and honourable achievements. Jansen, it is said, directed his instrument towards celestial objects, and distinctly saw the spots on the surface of the moon, and discovered many new stars, particularly seven pretty considerable ones in the Great Bear. His son Joannes is said to have noted the lucid circle near the lower limb of the moon, now named Tycho, from whence several bright rays seem to dart in different directions. In viewing Jupiter, he perceived two, sometimes three, and at the most four small stars, a little above or below him, and thought that they performed revolutions around him. This was, probably, the first observation of the satellites of Jupiter, though the person who made it was not aware of the importance of his discovery.17

It is not improbable that different persons about Middleburgh hit upon the invention, in different modes, about the same time. Lippersheim seems to have made his first rude telescope by adjusting two glasses on a board, and supporting them on brass circles.18 Other workmen, particularly Metius and Jansen, in emulation of each other, seem to have made use of that discovery, and by the new form they gave it, made all the honour of it their own. One of them, considering the effects of light as injurious to distinctness, placed the glasses in a tube blackened within. The other, still more cautious, placed the same glasses within tubes capable of sliding one in another, both to vary the prospects, by lengthening the instrument, according to the pleasure of the observer, and to render it portable and commodious. Thus, it is probable that different persons had a share in the invention, and jointly contributed to its improvement. At any rate, it is undoubtedly to the Dutch that we owe the original invention. The first telescope made by Jansen, did not exceed fifteen or sixteen inches in length, and therefore its magnifying power could not have been very great.

The famous Galileo has frequently been supposed to have been the inventor of the telescope, but he acknowledges that he had not the honour of being the original inventor, having first learned from a German, that such an instrument had already been made; although, from his own account, it appears that he had actually re-invented this instrument. The following is the account, in his own words, of the circumstances which led him to construct a telescope. ‘Nearly ten months ago (namely in April or May 1609) it was reported that a certain Dutchman had made a perspective through which many distant objects appeared distinct as if they were near: several effects of this wonderful instrument were reported, which some believed and others denied: but, having it confirmed to me a few days after by a letter from the noble John Badoverie, at Paris, I applied myself to consider the reason of it, and by what means I might contrive a similar instrument, which I afterwards attained to by the doctrine of refractions. And, first, I prepared a leaden tube, to whose extremities I fitted two spectacle-glasses, both of them plain on one side, and on the other side, one of them was spherically convex, and the other concave. Then applying my eye to the concave, I saw objects appear pretty large and pretty near me. They appeared three times nearer and nine times larger in surface than to the naked eye: and soon after I made another, which represented objects about sixty times larger, and eight times nearer; and, at last, having spared no labour nor expense, I made an instrument so excellent, as to show things almost a thousand times larger, and above thirty times nearer, than to the naked eye.’ In another part of his writings, Galileo informs us that ‘he was at Venice when he heard of Prince Maurice’s instrument, but nothing of its construction; that the first night, after he returned to Padua, he solved the problem, and made his instrument the next day; and soon after, presented it to the Doge at Venice, who, to do him honour for his grand invention, gave him the ducal letters which settled him for life in his lectureship at Padua; and the Republic, on the twenty-fifth of August in the same year (1610) more than tripled his salary as professor.’

The following is the account which this philosopher gives of the process of reasoning, which led him to the construction of a telescope:—‘I argued in the following manner. The contrivance consists either of one glass or more—one is not sufficient, since it must be either convex, concave, or plane; the last does not produce any sensible alteration in objects, the concave diminishes them; it is true that the convex magnifies, but it renders them confused and indistinct; consequently one glass is insufficient to produce the desired effect. Proceeding to consider two glasses, and bearing in mind that the plane glass causes no change, I determined that the instrument could not consist of the combination of a plane glass with either of the other two. I therefore applied myself to make experiments on combinations of the two other kinds; and thus obtained that of which I was in search.’ If the true inventor is the person who makes the discovery by reasoning and reflection, by tracing facts and principles to their consequences, and by applying his invention to important purposes, then, Galileo may be considered as the real inventor of the telescope. No sooner had he constructed this instrument—before he had seen any similar one—than he directed his tube to the celestial regions, and his unwearied diligence and ardour were soon rewarded by a series of new and splendid discoveries. He descried the four satellites of Jupiter, and marked the periods of their revolutions; he discovered the phases of Venus, and thus was enabled to adduce a new proof of the Copernican system, and to remove an objection that had been brought against it. He traced on the lunar orb, a resemblance to the structure of the earth, and plainly perceived the outlines of mountains and vales, casting their shadows over different parts of its surface. He observed, that when Mars was in quadrature, his figure varied slightly from a perfect circle; and that Saturn consisted of a triple body, having a small globe on each side—which deception was owing to the imperfect power of his telescope, which was insufficient to show him that the phenomenon was in reality a ring. In viewing the sun, he discovered large dark spots on the surface of that luminary, by which he ascertained that that mighty orb performed a revolution round its axis. He brought to view multitudes of stars imperceptible to the naked eye, and ascertained that those nebulous appearances in the heavens which constitute the Milky Way, consist of a vast collection of minute stars, too closely compacted together to produce an impression on our unassisted vision.

The results of Galileo’s observations were given to the world in a small work, entitled ‘Nuncius Sidereus,’ or, ‘News from the starry regions,’ which produced an extraordinary sensation among the learned. These discoveries soon spread throughout Europe, and were incessantly talked of, and were the cause of much speculation and debate among the circles of philosophers. Many doubted; many positively refused to believe so novel and unlooked-for announcements, because they ran counter to the philosophy of Aristotle, and all the preconceived notions which then prevailed in the learned world. It is curious, and may be instructive, to consider to what a length of absurdity, ignorance and prejudice carried many of those who made pretensions to learning and science. Some tried to reason against the facts alleged to be discovered, others contented themselves, and endeavoured to satisfy others, with the simple assertion that such things were not, and could not possibly be; and the manner in which they supported themselves in their incredulity was truly ridiculous. ‘O my dear Kepler,’ says Galileo in a letter to that astronomer, ‘how I wish we could have one hearty laugh together. Here at Padua is the principal professor of philosophy, whom I have repeatedly and urgently requested to look at the moon and planets through my glass, which he pertinaciously refuses to do, lest his opinions should be overturned. Why are you not here? what shouts of laughter we should have at this glorious folly! and to hear the professor of philosophy at Pisa labouring with the Grand Duke with logical arguments, as if with magical incantations, to charm the new planets out of the sky.’ Another opponent of Galileo, one Christmann, says in a book he published, ‘We are not to think that Jupiter has four satellites given him by nature, in order, by revolving round him, to immortalize the Medici who first had notice of the observation. These are the dreams of idle men, who love ludicrous ideas better than our laborious and industrious correction of the heavens. Nature abhors so horrible a chaos; and to the truly wise, such vanity is detestable.’ One Martin Horky, a would-be philosopher, declared to Kepler, ‘I will never concede his four new planets to that Italian from Padua, though I should die for it;’ and he followed up this declaration, by publishing a book against Galileo, in which he examines four principal questions respecting the alleged planets; 1. Whether they exist? 2. What they are? 3. What they are like? 4. Why they are? The first question is soon disposed of by declaring positively that he has examined the heavens with Galileo’s own glass, and that no such thing as a satellite about Jupiter exists. To the second, he declares solemnly that he does not more surely know, that he has a soul in his body than that reflected rays are the sole cause of Galileo’s erroneous observations. In regard to the third question, he says, that these planets are like the smallest fly compared to an elephant; and finally, concludes on the fourth, that the only use of them is to gratify Galileo’s ‘thirst of gold,’ and to afford himself a subject of discussion. Kepler, in a letter to Galileo, when alluding to Horky, says, ‘He begged so hard to be forgiven, that I have taken him again into favour upon this preliminary condition—that I am to show him Jupiter’s satellites, AND HE IS TO SEE THEM, and own that they are there.’

The following is a specimen of the reasoning of certain pretended philosophers of that age against the discoveries of Galileo. Sizzi, a Florentine astronomer, reasons in this strain: ‘There are seven windows given to animals in the domicile of the head, through which the air is admitted to the rest of the tabernacle of the body to enlighten, to warm and to nourish it; two nostrils, two eyes, two ears, and a mouth; so in the heavens, or the great world, there are two favourable stars, two unpropitious, two luminaries, and Mercury alone undecided and indifferent. From which and many other similar phenomena in nature, such as the seven metals, &c., we gather that the number of planets is necessarily seven. Moreover, the satellites are invisible to the naked eye, and therefore can exert no influence on the earth, and therefore would be useless, and therefore do not exist. Besides, as well the Jews as other ancient nations have adopted the division of the week into seven days, and have named them from the seven planets. Now, if we increase the number of the planets, this whole system falls to the ground.’ The opinions which then prevailed in regard to Galileo’s observations on the moon, were such as the following:—Some thought that the dark shades on the moon’s surface arose from the interposition of opaque bodies floating between her and the sun, which prevent his light from reaching those parts; others imagined that, on account of her vicinity to the earth, she was partly tainted with the imperfections of our terrestrial and elementary nature, and was not of that entirely pure and refined substance of which the more remote heavens consist: and a third party looked on her as a vast mirror, and maintained that the dark parts of her surface were the reflected images of our earthly forests and mountains.

Such learned nonsense is a disgrace to our species, and to the rational faculties with which man is endowed, and exhibits, in a most ludicrous manner, the imbecility and prejudice of those who made bold pretensions to erudition and philosophy. The statement of such facts, however, may be instructive, if they tend to guard us against those prejudices and pre-conceived opinions, which prevent the mind from the cordial reception of truth, and from the admission of improvements in society which run counter to long-established customs. For the same principles and prejudices, though in a different form, still operate in society and retard the improvement of the social state, the march of science, and the progress of Christianity. How ridiculous is it for a man, calling himself a philosopher, to be afraid to look through a glass to an existing object in the heavens, lest it should endanger his previous opinions! And how foolish is it to resist any improvement or reformation in society, because it does not exactly accord with existing opinions, and with ‘the wisdom of our ancestors.’

It is not a little surprising, that Galileo should have first hit on that construction of a telescope which goes by his name, and which was formed with a concave glass next the eye. This construction of a telescope is more difficult to be understood, in theory, than one which is composed solely of convex glasses; and its field of view is comparatively very small, so that it is almost useless when attempted to be made of a great length. In the present day, we cannot help wondering that Galileo and other astronomers, should have made such discoveries as they did with such an instrument, the use of which must have required a great degree of patience and address. Galileo’s best telescope, which he constructed ‘with great trouble and expense,’ magnified the diameters of objects only thirty-three times; but its length is not stated—which would depend upon the focal distance of the concave eye-glass. If the eye-glass was two inches focus, the length of the instrument would be five feet four inches; if it was only one inch, the length would be two feet eight inches, which is the least we can allow to it—the object-glass being thirty-three inches focus, and the eye-glass placed an inch within this focus. With this telescope, Galileo discovered the satellites of Jupiter, the crescent of Venus, and the other celestial objects to which we have already alluded. The telescopes made in Holland, are supposed to have been constructed solely of convex glasses, on the principle of the astronomical telescope; and, if so, Galileo’s telescope was in reality a new invention.

Certain other claimants of the invention of the telescope, have appeared, besides those already mentioned. Francis Fontana, in his ‘celestial observations,’ says, that he was assured by a Mr. Hardy, advocate of the parliament of Paris, a person of great learning and undoubted integrity, that on the death of his father, there was found among his things an old tube, by which distant objects were distinctly seen, and that it was of a date long prior to the telescope lately invented, and had been kept by him as a secret. Mr. Leonard Digges, a gentleman who lived near Bristol, in the seventeenth century, and was possessed of great and various knowledge, positively asserts in his ‘Stratoticos,’ and in another work, that his father, a military gentleman, had an instrument which he used in the field, by which he could bring distant objects near, and could know a man at the distance of three miles. Mr. Thomas Digges, in the preface to his ‘Pantometria,’ published in 1591, declares, “My father, by his continual painful practices, assisted by demonstrations mathematical, was able, and sundry times hath by proportional glasses, duly situate in convenient angles, not only discovered things far off, read letters, numbered pieces of money, with the very coin and superscription thereof, cast by some of his friends of purpose, upon downs in open fields, but also, seven miles off, declared what hath been done that instant, in private places. He hath also, sundry times, by the sun-beams, fired powder and discharged ordnance half a mile and more distant, and many other matters far more strange and rare, of which there are yet living divers witnesses.”

It is by no means unlikely, that persons accustomed to reflection, and imbued with a certain degree of curiosity, when handling spectacle-glasses, and amusing themselves with their magnifying powers and other properties, might sometimes hit upon the construction of a telescope; as it only requires two lenses of different focal distances to be held at a certain distance from each other, in order to show distant objects magnified. Nay, even one lens, of a long focal distance, is sufficient to constitute a telescope of a moderate magnifying power, as I shall show in the sequel. But such instruments, when they happened to be constructed accidentally, appear to have been kept as secrets, and confined to the cabinets of the curious, so that they never came into general use; and as their magnifying power would probably be comparatively small, the appearance of the heavenly bodies would not be much enlarged by such instruments—nor is it likely that they would be often directed to the heavens. On the whole, therefore, we may conclude that the period when instruments of this description came into general use, and were applied to useful purposes, was when Galileo constructed his first telescopes.

CHAPTER II.

OF THE CAMERA OBSCURA.

Before proceeding to a particular description of the different kinds of telescopes, I shall first give a brief description of the Camera Obscura, as the phenomena exhibited by this instrument tend to illustrate the principle of a refracting telescope.

The term Camera Obscura literally signifies a darkened vault or roof; and hence it came to denote a chamber, or box, or any other place made dark for the purpose of optical experiments. The camera obscura, though a simple, is yet a very curious and noble contrivance; as it naturally and clearly explains the manner in which vision is performed, and the principle of the telescope, and entertains the spectator with a most exquisite picture of surrounding objects, painted in the most accurate proportions and colours by the hand of nature. The manner of exhibiting the pictures of objects in a dark room is as follows:—In one of the window-shutters of a room which commands a good prospect of objects not very distant, a circular hole should be cut of four or five inches diameter. In this hole an instrument should be placed, called a Scioptric ball, which has three parts, a frame, a ball, and a lens. The ball has a circular hole cut through the middle, in which the lens is fixed, and its use is, to turn every way so as to take in a view of objects on every side. The chamber should be made perfectly dark; and a white screen, or a large sheet of elephant paper, should be placed opposite to the lens, and in its focus, to receive the image. If then, the objects without be strongly enlightened by the sun, there will be a beautiful living picture of the scene delineated on the white screen, where every object is beheld in its proportions, and with its colours even more vivid than life; green objects appear in the picture more intensely green, and yellow, blue, red or white flowers appear much more beautiful in the picture than in nature; if the lens be a good one, and the room perfectly dark, the perspective is seen in perfection. The lights and shadows are not only perfectly just, but also greatly heightened; and, what is peculiar to this delineation, and which no other picture or painting can exhibit—the motions of all the objects are exactly expressed in the picture; the boughs of the trees wave, the leaves quiver, the smoke ascends in a waving form, the people walk, the children at their sports leap and run, the horse and cart move along, the ships sail, the clouds soar and shift their aspects, and all as natural as in the real objects; the motions being somewhat quicker, as they are performed in a more contracted scene.

These are the inimitable perfections of a picture, drawn by the rays of light as the only pencil in nature’s hand, and which are finished in a moment; for no sensible interval elapses before the painting is completed, when the ground on which it is painted is prepared and adjusted. In comparison of such a picture, the finest productions of the most celebrated artists, the proportions of Raphael, the natural tints and colouring of Titian, and the shadowing of the Venetians, are but coarse and sorry daubings, when set in competition with what nature can exhibit by the rays of light passing through a single lens. The Camera obscura is at the same time the painter’s assistant, and the painter’s reproach. From the picture it forms he receives his best instructions, and is shown what he should endeavour to attain; and hence, too, he learns the imperfections of his art, and what it is impossible for him to imitate. As a proof of this, the picture formed in the dark chamber will bear to be magnified to a great extent, without defacing its beauty, or injuring the fineness of its parts; but the finest painted landscape, if viewed through a high magnifier will appear only as a coarse daubing.

The following scheme will illustrate what has been now stated respecting the dark chamber. EF represents a darkened room, in the side of which, IK, is made the circular hole V, in which, on the inside, is fixed the scioptric ball. At some considerable distance from this hole is exhibited a landscape of houses, trees, and other objects, ABCD, which are opposite to the window. The rays which flow from the different objects which compose this landscape, to the lens at V, and which pass through it, are converged to their respective foci, on the opposite wall of the chamber HG or on a white moveable screen placed in the focus of the lens, where they all combine to paint a lively and beautiful picture of the range of objects directly opposite, and on each side, so far as the lens can take in.

Though I have said, that a scioptric ball and socket are expedient to be used in the above experiment, yet where such an instrument is not at hand, the lens may be placed in a short tube made of pasteboard or any other material, and fixed in the hole made in the window shutter. The only imperfection attending this method is, that the lens can exhibit those objects only which lie directly opposite the window.

figure 37.

Some may be disposed to consider it as an imperfection in this picture, that all the objects appear in an inverted position; as they must necessarily do, according to what we formerly stated respecting the properties of convex lenses, (p. 72). There are, however, different modes of viewing the picture as if it were erect. For, if we stand before the picture, and hold a common mirror against our breast at an acute angle with the picture, and look down upon it, we shall see all the images of the objects as if restored to their erect position; and by the reflection of the mirror, the picture will receive such a lustre as will make it still more delightful. Or, if a large concave mirror were placed before the picture at such a distance, that its image may appear before the mirror, it will then appear erect and pendulous in the air in the front of the mirror. Or, if the image be received on a frame of paper, we may stand behind the frame, with our face towards the window, and look down upon the objects, when they will appear as if erect.

The experiment of the Camera Obscura may serve to explain and illustrate the nature of a common refracting telescope. Let us suppose, that the lens in the window-shutter represents the object-glass of a refracting telescope. This glass forms an image in its focus, which is in every respect an exact picture or representation of the objects before it; and consequently the same idea is formed in the mind, of the nature, form, magnitude, and colour of the object—whether the eye at the centre of the glass views the object itself, or the image formed in its focus. For, as formerly stated, the object and its image are both seen under the same angles by the eye placed at the centre of the lens. Without such an image as is formed in the camera obscura—depicted either in the tube of a telescope or in the eye itself—no telescope could possibly be formed. If we now suppose that, behind the image formed in the dark chamber, we apply a convex lens of a short focal distance to view that image, then the image will be seen distinctly, in the same manner as we view common objects, such as a leaf or a flower, with a magnifying glass; consequently, the object itself will be seen distinct and magnified. And, as the same image is nearer to one lens than the other, it will subtend a larger angle at the nearest lens, and of course, will appear larger than through the other, and consequently the object will be seen magnified in proportion. For example, let us suppose the lens in the camera obscura, or the object lens of a telescope, to be five feet, or sixty inches focal distance, at this distance from the glass, an image of the distant objects opposite to it will be formed. If now, we place a small lens two inches focal distance beyond this point, or five feet two inches from the object-glass, the objects, when viewed through the small lens, will appear considerably magnified, and apparently much nearer than to the naked eye. The degree of magnifying power is in proportion to the focal distances of the two glasses; that is, in the present case, in the proportion of two inches, the focus of the small lens, to sixty inches, the focus of the object lens. Divide sixty by two, the quotient is thirty, which gives the magnifying power of such a telescope, that is, it represents objects thirty times nearer, or under an angle thirty times larger than to the naked eye. If the eye-glass, instead of being two inches, were only one and a half inch focus, the magnifying power would be in the proportion of one and a half to sixty, or forty times. If the eye-glass were three inches focus, the magnifying power would be twenty times; and so on, with regard to other proportions. In all cases, where a telescope is composed of only two convex lenses, the magnifying power is determined, by dividing the focal distance of the object-glass, by the focal distance of the eye-glass, and the quotient expresses the number of times the object is magnified, in length and breadth. This and various other particulars, will be more fully illustrated in the sequel.

In performing experiments with the camera obscura in a darkened chamber, it is requisite that the following particulars be attended to:—1. That the lens be well figured, and free from any veins or blemishes that might distort the picture. 2. That it be placed directly against the object whose image we wish to see distinctly delineated. 3. The lens should be of a proper size both as to its breadth and focal distance. It should not be less than three or four feet focal distance, otherwise the picture will be too small, and the parts of objects too minute to be distinctly perceived; nor should it exceed fifteen or eighteen feet, as in this case the picture will be faint, and of course not so pleasing. The best medium as to focal distance, is from five to eight or ten feet. The aperture, too, or breadth of the glass, should not be too small, otherwise the image will be obscure, and the minute parts of it invisible for want of a sufficient quantity of light. A lens of six feet focal distance, for example, will require an aperture of at least two inches. Lenses of a shorter focal distance require less apertures, and those of a longer focal distance larger. But if the aperture be too large, the image will be confused, and indistinct, by the admission of too much light. 4. We should never attempt to exhibit the images of objects, unless when the sun is shining and strongly illuminating the objects, except in the case of very near objects placed in a good light. As one of the greatest beauties, in the phenomena of the dark chamber, consists in the exquisite appearance and contrast of light and shadows, nothing of this kind can be perceived but from objects directly illuminated by the sun. 5. A south window should never be used in the forenoon, as the sun cannot then enlighten the north side of an object; and besides, his rays would be apt to shine upon the lens, which would make the picture appear with a confused lustre. An east window is best in the afternoon, and a western in the morning; but a north window is in most cases to be preferred, especially in the forenoon, when the sun is shining with his greatest strength and splendour. In general, that window ought to be used which looks to the quarter opposite to that in which the sun is shining.

The picture should be received upon a very white surface, as the finest and whitest paper, or a painted cloth, bordered with black; as white bodies reflect most copiously the incident rays, while black surfaces absorb them. If the screen could be bent into the concave segment of a sphere, of which the focal distance of the double convex lens which is used, is the radius, the parts of the picture adjacent to the extremities would appear most distinct. Sir D. Brewster informs us that, having tried a number of white substances of different degrees of smoothness, and several metallic surfaces, on which to receive the image, he happened to receive the picture on the silvered back of a looking-glass, and was surprised at the brilliancy and distinctness with which external objects were represented. To remove the spherical protuberances of the tin foil, he ground the surface very carefully with a bed of hones which he had used for working the plane specula of Newtonian telescopes. By this operation, which may be performed without injuring the other side of the mirror, he obtained a surface finely adapted for the reception of images. The minute parts of the landscape were formed with so much precision, and the brilliancy of colouring was so uncommonly fine, as to equal, if not exceed the images that are formed in the air by means of concave specula.

The following additional circumstances may be stated respecting the phenomena exhibited in the dark chamber. A more critical idea may be formed of any movement in the picture here presented than from observing the motion of the object itself. For instance, a man walking in a picture appears to have an undulating motion, or to rise up and down every step he takes, and the hands seem to move almost exactly like a pendulum; whereas scarcely any thing of this kind is observed in the man himself, as viewed by the naked eye. Again, if an object be placed just twice the focal distance from the lens without the room, the image will be formed at the same distance from the lens within the room, and consequently will be equal in magnitude to the object itself. The recognition of this principle may be of use to those concerned in drawing, and who may wish, at any time, to form a picture of the exact size of the object. If the object be placed further from the lens than twice its focal length, the image will be less than the object. If it be placed nearer, the image will be greater than the life. In regard to immoveable objects, such as houses, gardens, trees, &c., we may form the images of so many different sizes, by means of different lenses, the shorter focus making the lesser picture, and the longer focal distance the largest.

The experiments with the camera obscura, may likewise serve to illustrate the nature of vision, and the functions of the human eye. The frame or socket of the scioptric ball may represent the orbit of the natural eye. The ball, which turns every way, resembles the globe of the eye, moveable in its orbit. The hole in the ball may represent the pupil of the eye; the convex lens corresponds to the crystalline humour, which is shaped like a lens, and contributes to form the images of objects on the inner part of the eye. The dark chamber itself, is somewhat similar to the internal part of the eye, which is lined all around, and under the retina, with a membrane, over which is spread a mucous of a very black colour. The white wall or frame of white paper to receive the picture of objects, is a fair representation of the retina of the eye, on which all the images of external objects are depicted. Such are some of the general points of resemblance between the apparatus connected with the dark chamber, and the organ of vision; but the human eye is an organ of such exquisite construction, and composed of such a number and variety of delicate parts, that it cannot be adequately represented by any artificial contrivance.

The darkened chamber is frequently exhibited in a manner somewhat different from what we have above described, as in the following scheme, (fig. 38) which is termed the revolving camera obscura. In this construction, KH represents a plane mirror or metallic reflector, placed at half a right angle to the convex lens HI, by which, rays proceeding from objects situated in the direction O are reflected to the lens, which forms an image of the objects on a round white table at T, around which several spectators may stand, and view the picture, as delineated on a horizontal plane. The reflector, along with its case, is capable of being turned round, by means of a simple apparatus connected with it, so as to take in, in succession, all the objects which compose the surrounding scene. But as the image here is received on a flat surface, the rays fm, en, will have to diverge farther than the central rays dc; and hence the representation of the object, near the sides, will be somewhat distorted; to remedy which, the image should be received on a concave surface, as ab or PS. This is the general plan of those Camera Obscuras, fitted up in large wooden tents, which are frequently exhibited in our large cities, and removed occasionally from one town to another. Were an instrument of this kind fitted up on a small scale, a hole might be made in one of the sides, as at E, where the eye could be applied to view the picture. The focal distances of the lenses used in large instruments of this kind, are generally from eight to twelve feet, in which case they produce a telescopic effect upon distant objects, so as to make them appear nearer than when viewed with the naked eye.

figure 38.

figure 39.

The camera obscura is frequently constructed in a portable form, so as to be carried about for the purpose of delineating landscapes. The following is a brief description of the instrument in this form. AC is a convex lens placed near the end of a tube or drawer, which is moveable in the side of a square box, within which is a plane mirror DE, reclining backward in an angle of forty-five degrees from the perpendicular pn. The pencils of rays flowing from the object OB, and passing through the convex lens—instead of proceeding forward and forming the image HI, are reflected upward by the mirror, and meet in points as FG, at the same distance at which they would have met at H and I, if they had not been intercepted by the mirror. At FG, the image of the object OB is received either on a piece of oiled paper, or more frequently on a plane unpolished glass, placed in the horizontal situation FG, which receives the images of all objects, opposite to the lens, and on which, or on an oiled paper placed upon it, their outlines may be traced by a pencil. The moveable tube on which the lens is fixed, serves to adjust the focus for near and distant objects, till their images appear distinctly painted on the horizontal glass at FG. Above is shown the most common form of the box of this kind of Camera Obscura. A is the position of the lens, BC, the position of the mirror, D, the plane unpolished glass on which the images are depicted, GH a moveable top or screen to prevent the light from injuring the picture, and EF, the moveable tube.

figure 40.

The Daguerreotype.—An important, and somewhat surprising discovery has lately been made, in relation to the picture formed by the Camera Obscura. It is found, that the images formed by this instrument are capable of being indelibly fixed on certain surfaces previously prepared for the purpose, so that the picture is rendered permanent. When a Camera is presented to any object or landscape strongly illuminated by the sun, and the prepared ground for receiving the image is adjusted, and a certain time allowed to elapse till the rays of light produce their due effect, in a few minutes or even seconds, a picture of the objects opposite to the lens is indelibly impressed upon the prepared plate, in all the accurate proportions and perspective, which distinguish the images formed in a dark chamber—which representations may be hung up in apartments, along with other paintings and engravings; and will likely retain their beauty and lustre for many years. These are pictures of nature’s own workmanship finished in an extremely short space of time, and with the most exquisite delicacy and accuracy. The effect is evidently owing to certain chemical properties in the rays of light; and opens a new field for experiment and investigation to the philosopher. The only defect in the picture is, that it is not coloured; but, in the progress of experiments on this subject, it is not unlikely that even this object may be accomplished, in which case, we should be able to obtain the most accurate landscapes and representations of all objects, which can possibly be formed. This art or discovery goes by the name of the Daguerreotype from M. Daguerre, a Frenchman, who is supposed to have been the first discoverer, and who received a large premium from the French government for disclosing the process, and making the discovery public. Several improvements and modifications, in reference to the preparation of the plates, have been made since the discovery was first announced, about the beginning of 1839; and the pictures formed on this principle, are frequently distinguished by the name of Photogenic drawings; and are now exhibited at most of our public scientific institutions.

This new science or art, has been distinguished by different names. It was first called Photography, from two Greek words, signifying writing by light: it was afterwards called the art of Photogenic Drawing, or drawing produced by light. M. Daguerre gave it the name of Heliography, or writing by the sun, all which appellatives are derived from the Greek, and are expressive, in some degree, of the nature of the process. We shall, however, make use of the term Daguerreotype, derived from the name of the inventor.

As it does not fall within our plan to give any minute descriptions of the Daguerreotype process, we shall just give a few general hints in reference to it, referring those who wish for particular details, to the separate treatises which have been published respecting it. The first thing necessary to be attended to in this art is, the preparation of the plate on which the drawing is to be made. The plate consists of a thin leaf of copper, plated with silver; both metals together, not being thicker than a card. The object of the copper is simply to support the silver, which must be the purest that can be procured. But though the copper should be no thicker than to serve the purpose of support, it is necessary that it should be so thick as to prevent the plate from being warped, which would produce a distortion of the images traced upon it. This plate must be polished;—and for this purpose, the following articles are required—a phial of olive oil—some very fine cotton—pumice-powder, ground till it is almost impalpable, and tied up in a piece of fine muslin, thin enough to let the powder pass through without touching the plate when the bag is shaken. A little nitric acid diluted with sixteen times, by measure, its own quantity of water—a frame of wire on which to place the plate, when being heated—a spirit lamp to make the plate hot—a small box with inclined sides within, and having a lid to shut it up close—and a square board large enough to hold the drawing, and having catches at the side to keep it steady.

To the above prerequisites, a good Camera Obscura is, of course, essentially necessary. This instrument should be large enough to admit the plate of the largest drawing intended to be taken. The lens which forms the image of the object, should, if possible, be achromatic, and of a considerable diameter. In an excellent instrument of this description, now before me, the lens is an achromatic, about 3 inches diameter, but capable of being contracted to a smaller aperture. Its focal distance is about 17 inches; and the box, exclusive of the tube which contains the lens, is 15 inches long, 13½ inches broad, and 11 inches deep. It forms a beautiful and well-defined picture of every well-enlightened object to which it is directed.

Before the plate is placed in the camera, there are certain operations to be performed. 1. The surface of the plate should be made perfectly smooth, or highly polished. For this purpose, it must be laid flat, with the silver side upwards, upon several folds of paper for a bedding; and having been well polished in the usual way, the surface must be powdered equally and carefully with fine pumice enclosed in the muslin bag. Then taking a little cotton wool, dipped in olive oil, it must be rubbed over the plate with rounding strokes, and then crossing them by others which commence at right angles with the first. This process must be repeated frequently, changing the cotton, and renewing the pumice powder every time. A small portion of cotton must now be moistened with the diluted nitric acid, and applied equally to the whole surface. The next thing to be done is to make the plate thoroughly and equally hot, by holding the plate with a pair of pincers, by the corner, over a charcoal fire, and when the plate is sufficiently hot, a white coating will be observed on the silver, which indicates that that part of the operation is finished. An even cold surface is next wanted, such as a metallic plate cooled almost to the freezing point by muriate of soda, and to this the heated plate must be suddenly transferred.

2. The next operation is to give the plate a coating of Iodine. This is accomplished by fixing the plate upon a board, and then putting it into a box containing a little dish with iodine divided into small pieces, with its face downward, and supported with small brackets at the corners. In this position, the plate must remain till it assume a full gold colour, through the condensation of the iodine on its surface—which process should be conducted in a darkened apartment. The requisite time for the condensation of the iodine varies from five minutes to half an hour. When this process is satisfactorily accomplished, the plate should be immediately fixed in a frame with catches and bands, and placed in the Camera; and the transference from one receptacle to another should be made as quickly as possible, and with only so much light as will enable the operator to see what he is doing.

3. The next operation is to obtain the drawing. Having placed the Camera in front of the scene to be represented, and the lens being adjusted to the proper focus, the ground-glass of the Camera is withdrawn, and the prepared plate is substituted for it; and the whole is left till the natural images are drawn by the natural light from the object. The time necessary to leave the plate for a complete delineation of the objects, depends upon the intensity of the light. Objects in the shade will require more time for their delineation than those in the broad light. The full clear light of the south of Europe, Spain, Italy, and particularly, the more glowing brilliancy of tropical countries, will effect the object much more speedily than the duller luminosity of a northern clime. Some hours of the day are likewise more favourable than others. Daguerre states, that ‘the most favourable, is from 7 A.M. to 3 o’clock P.M., and that a drawing could be effected in Paris in 3 or 4 minutes, in June and July, which would require 5 or 6, in May and August, and 7 or 8 in April and September.’ In the progress of this art, at the present time, portraits and other objects are frequently delineated in the course of a few seconds.

4. Immediately after removing the plate from the Camera, it is next placed over the vapour of mercury, which is placed in a cup at the bottom of a box, and a spirit lamp applied to its bottom, till the temperature rise to 140 of Fahrenheit. This process is intended to bring out the image, which is not visible when withdrawn from the Camera; but in the course of a few minutes a faint tracery will begin to appear, and in a very short time the figure will be clearly developed.

5. The next operation is to fix the impression. In order to this, the coating on which the design was impressed must be removed, to preserve it from being decomposed by the rays of light. For this purpose, the plate is placed in a trough containing common water, plunging, and withdrawing it immediately, and then plunging it into a solution of salt and water, till the yellow coating has disappeared.

Such is a very brief sketch of the photogenic processes of Daguerre. Other substances, however, more easily prepared, have been recommended by Mr. Talbot, F.R.S., who appears, about the same time, to have invented a process somewhat similar to that of Daguerre. The following are his directions for the preparation of Photogenic Paper.

The paper is to be dipped into a solution of salt in water, in the proportion of half an ounce of salt to half a pint of water. Let the superfluous moisture drain off, and then, laying the paper upon a clean cloth, dab it gently with a napkin, so as to prevent the salt collecting in one spot more than another. The paper is then to be pinned down by two of its corners on a drawing board, by means of common pins, and one side washed or wetted with the Photogenic fluid, using the brush prepared for that purpose, and taking care to distribute it equally. Next dry the paper as rapidly as you can at the fire, and it will be fit for use for most purposes. If, when the paper is exposed to the sun’s rays, it should assume an irregular tint, a very thin extra wash of the fluid will render the colour uniform, and at the same time somewhat darker. Should it be required to make a more sensitive description of paper, after the first application of the fluid, the solution of salt should be applied, and the paper dried at the fire. Apply a second wash of the fluid, and dry it at the fire again: employ the salt a third time, dry it,—and one application more of the fluid will, when dried, have made the paper extremely sensitive. When slips of such papers, differently prepared, are exposed to the action of day light, those which are soonest affected by the light, by becoming dark, are the best prepared.

When photogenic drawings are finished in a perfect way, the designs then taken on the plate or paper are exceedingly beautiful and correct, and will bear to be inspected with a considerable magnifying power, so that the most minute portions of the objects delineated may be distinctly perceived. We have seen portraits, finished in this way by a London artist, with an accuracy which the best miniature painter could never attempt—every feature being so distinct, as to bear being viewed with a deep magnifier. And in landscapes and buildings, such is the delicacy and accuracy of such representations, that the marks of the chisel and the crevices in the stones may frequently be seen by applying a magnifying lens to the picture; so that we may justly exclaim, in the words of the Poet: ‘Who can paint like nature!.’ That LIGHT—which is the first-born of Deity, which pervades all space, and illuminates all worlds—in the twinkling of an eye, and with an accuracy which no art can imitate, depicts every object in its exact form and proportions, superior to every thing that human genius can produce.

The Photogenic art, in its progress, will doubtless be productive of many highly interesting and beneficial effects. It affords us the power of representing, by an accurate and rapid process, all the grand and beautiful objects connected with our globe—the landscapes peculiar to every country—the lofty ranges of mountains which distinguish Alpine regions—the noble edifices which art has reared—the monumental remains of antiquity—and every other object which it would be interesting for human beings to contemplate; so that in the course of time, the general scenery of our world, in its prominent parts, might be exhibited to almost every eye. The commission of the French Chambers, when referring to this art, has the following remark, ‘To copy the millions upon millions of hieroglyphics which cover even the exterior of the great monuments of Thebes and Memphis, of Carnac, &c., would require scores of years and legions of designers. By the assistance of the Daguerreotype, a single man could finish that immense work.’—This instrument lays down objects, which the visual organs of man would overlook, or might be unable to perceive, with the same minuteness and nicety, that it delineates the most prominent features of a landscape. The time-stained excrescences on a tree, the blades of grass, the leaf of a rose, the neglected weed, the moss on the summit of a lofty tower, and similar objects, are traced with the same accuracy as the larger objects in the surrounding scene.

It is not improbable, likewise, that this art (still in its infancy) when it approximates to perfection, may enable us to take representations of the sublime objects in the heavens. The sun affords sufficient light for this purpose; and there appears no insurmountable obstacle in taking, in this way, a highly magnified picture of that luminary, which shall be capable of being again magnified by a powerful microscope. It is by no means improbable, from experiments that have hitherto been made, that we may obtain an accurate delineation of the lunar world from the moon herself. The plated disks prepared by Daguerre receive impressions from the action of the lunar rays to such an extent as permits the hope that photographic charts of the moon may soon be obtained; and, if so, they will excel in accuracy all the delineations of this orb that have hitherto been obtained; and if they should bear a microscopic power, objects may be perceived on the lunar surface which have hitherto been invisible. Nor is it impossible that the planets Venus, Mars, Jupiter and Saturn, may be delineated in this way, and objects discovered which cannot be descried by means of the telescope. It might perhaps be considered as beyond the bounds of probability to expect that even distant NebulÆ, might thus be fixed, and a delineation of their objects produced which shall be capable of being magnified by microscopes. But we ought to consider that the art is yet only in its infancy—that plates of a more delicate nature than those hitherto used, may yet be prepared, and that other properties of light may yet be discovered, which shall facilitate such designs. For, we ought now to set no boundaries to the discoveries of science, and to the practical applications of scientific discovery which genius and art may accomplish.

In short, this invention leads to the conclusion, that we have not yet discovered all the wonderful properties of that Luminous Agent which pervades the universe, and which unveils to us its beauties and sublimities—and that thousands of admirable objects and agencies may yet be disclosed to our view through the medium of light, as philosophical investigators advance in their researches and discoveries. In the present instance, as well as in many others, it evidently appears, that the Creator intends, in the course of his providence, by means of scientific researches, gradually to open to the view of the inhabitants of our world the wonders, the beauties and the sublimities of his vast creation, to manifest his infinite wisdom, and his superabundant goodness, and to raise our souls to the contemplation and the love of Him who is the original source of all that is glorious and beneficent in the scene of nature.

CHAPTER III.

ON THE OPTICAL ANGLE, AND THE APPARENT MAGNITUDE OF OBJECTS.

In order to understand the principle on which telescopes represent distant objects as magnified, it may be expedient to explain what is meant by the angle of vision, and the apparent magnitudes under which different objects appear, and the same object, when placed at different distances.

figure 40*.

The optical angle is the angle contained under two right lines drawn from the extreme points of an object to the eye. Thus AEB or CED (fig. 40*.) is the optical or visual angle, or the angle under which the object AB or CD, appears to the eye at E. These two objects, being at different distances, are seen under the same angle, although CD is evidently larger than AB. On the retina of the eye, their images are exactly of the same size, and so is the still larger object FG.

figure 41.

The apparent magnitude of objects denotes their magnitude as they appear to us, in contradistinction from their real or true magnitude, and it is measured by the visual angle; for whatever objects are seen under the same or equal angles appear equal, however different their real magnitudes. If a half-crown or half-dollar be placed at about 120 yards from the eye, it is just perceptible as a visible point, and its apparent magnitude, or the angle under which it is seen, is very small. At the distance of thirty or forty yards, its bulk appears sensibly increased, and we perceive it to be a round body; at the distance of six or eight yards, we can see the king or queen’s head engraved upon it; and at the distance of eight or ten inches from the eye it will appear so large, that it will seem to cover a large building placed within the distance of a quarter of a mile, in other words, the apparent magnitude of the half-crown held at such a distance, will more than equal that of such a building, in the picture on the retina, owing to the increase of the optical angle. If we suppose A (fig. 41.) to represent the apparent size of the half-crown at nine yards distance, then we say it is seen under the small angle FED. B will represent its apparent magnitude at 4½ yards distant under the angle HEG, and the circle C, its apparent magnitude at 3 yards distant, under the large angle KEI.

figure 42.

This may be otherwise illustrated by the following figure. Let AB (fig. 42.) be an object viewed directly by the eye QR. From each extremity A and B draw the lines AN,BM, intersecting each other in the crystalline humour in I: then is AIB the optical angle which is the measure of the apparent magnitude or length of the object AB. From an inspection of this figure, it will evidently appear that the apparent magnitudes of objects will vary according to their distances. Thus AB, CD, EF, the real magnitudes of which are unequal, may be situated at such distances from the eye, as to have their apparent magnitudes all equal, and occupying the same space on the retina MN, as here represented. In like manner, objects of equal magnitude, placed at unequal distances, will appear unequal. The objects AB and GH which are equal, being situated at different distances from the eye, GH will appear under the large angle TIV, or as large as an object TV, situated at the same place as the object AB, while AB appears under the smaller angle AIB. Therefore the object GH is apparently greater than the object AB, though it is only equal to it. Hence it appears that we have no certain standard of the true magnitude of objects, by our visual perception abstractly considered, but only of the proportions of magnitude.

In reference to apparent magnitudes, we scarcely ever judge any object to be so great or so small as it appears to be, or that there is so great a disparity in the visible magnitude of two equal bodies at different distances from the eye. Thus, for example, suppose two men, each six feet 3 inches high, to stand directly before us, one at the distance of a pole, or 5½ yards, and the other at the distance of 100 poles, or 550 yards—we should observe a considerable difference in their apparent size, but we should scarcely suppose, at first sight, that the one nearest the eye appeared a hundred times greater than the other, or that, while the nearest one appeared 6 feet 3 inches high, the remote one appeared only about three fourths of an inch. Yet such is in reality the case; and not only so, but the visible bulk or area of the one is to that of the other, as the square of these numbers, namely as 10,000 to 1; the man nearest us presenting to the eye a magnitude or surface ten thousand times greater than that of the other. Again, suppose two chairs standing in a large room, the one 21 feet distance from us, and the other 3 feet—the one nearest us will appear 7 times larger both in length and breadth, than the more distant one, and consequently, its visible area 49 times greater. If I hold up my finger at 9 inches distant from my eye, it seems to cover a large town a mile and a half in extent, situated at 3 miles distant; consequently, the apparent magnitude of my finger, at 9 inches distant from the organ of vision, is greater than that of the large town at 3 miles distance, and forms a larger picture on the retina of the eye. When I stand at the distance of a foot from my window, and look through one of the panes to a village less than a quarter of a mile distant, I see, through that pane, nearly the whole extent of the village, comprehending two or three hundred houses; consequently, the apparent magnitude of the pane is equal to nearly the extent of the village, and all the buildings it contains do not appear larger than the pane of glass in the window, otherwise, the houses and other objects which compose the village could not be seen through that single pane. For, if we suppose a line drawn from one end of the village, passing through the one side of the pane, and another line drawn from the other end, and passing through the other side of the pane to the eye, these lines would form the optical angle under which the pane of glass and the village appears. If the pane of glass be fourteen inches broad, and the length of the village 2640 yards, or half a mile—this last lineal extent is 6,788 times greater than the other, and yet they have the same apparent magnitude in the case supposed.

Hence we may learn the absurdity and futility of attempting to describe the extent of spaces in the heavens, by saying, that a certain phenomenon was two or three feet or yards distant from another, or that the tail of a comet appeared several yards in length. Such representations can convey no definite ideas in relation to such magnitudes, unless it be specified at what distance from the eye, the foot or yard is supposed to be placed. If a rod, a yard in length, be held at nine inches from the eye, it will subtend an angle, or cover a space in the heavens, equal to more than one fourth of the circumference of the sky, or about one hundred degrees. If it be eighteen inches from the eye, it will cover a space equal to fifty degrees; if at three feet, twenty-five degrees, and so on in proportion to the distance from the eye; so that we can form no correct conceptions of apparent spaces or distances in the heavens, when we are merely told that two stars, for example, appear to be three yards distant from each other. The only definite measure we can use, in such cases, is that of degrees. The sun and moon are about half a degree in apparent diameter, and the distance between the extreme stars in Orion’s belt, three degrees, which measures being made familiar to the eye, may be applied to other spaces of the heavens, and an approximate idea conveyed of the relative distances of objects in the sky.

From what has been stated above, it is evident that the magnitude of objects may be considered in different points of view. The true dimensions of an object, considered in itself, give what is called its real or absolute magnitude; and the opening of the visual angle determines the apparent magnitude. The real magnitude, therefore, is a constant quantity; but the apparent magnitude varies continually with the distance, real or imaginary; and therefore, if we always judged of the dimensions of an object from its apparent magnitude, every thing around us would, in this respect, be undergoing very sensible variations, which might lead us into strange and serious mistakes. A fly, near enough to the eye, might appear under an angle as great as an elephant at the distance of twenty feet, and the one be mistaken for the other. A giant eight feet high, seen at the distance of twenty-four feet, would not appear taller than a child two feet in height, at the distance of six feet; for both would be seen nearly under the same angle. But our experience generally prevents us from being deceived by such illusions. By the help of touch, and by making allowance for the different distances at which we see particular objects, we learn to correct the ideas we might otherwise form from attending to the optical angle alone, especially in the case of objects that are near us. By the sense of touch we acquire an impression of the distance of an object; this impression combines itself with that of the apparent magnitude, so that the impression which represents to us the real magnitude is the product of these two elements. When the objects, however, are at a great distance, it is more difficult to form a correct estimate of their true magnitudes. The visual angles are so small, that they prevent comparison; and the estimated bulks of the objects depend in a great measure upon the apparent magnitudes; and thus an object situated at a great distance, appears to us much smaller than it is in reality. We also estimate objects to be nearer or farther distant according as they are more or less clear, and our perception of them more or less distinct and well defined; and likewise, when several objects intervene between us and the object we are particularly observing. We make a sort of addition of all the estimated distances of intermediate objects, in order to form a total distance of the remote object, which in this case appears to be farther off than if the intervening space were unoccupied. It is generally estimated that no terrestrial object can be distinctly perceived, if the visual angle it subtends be less than one minute of a degree; and that most objects become indistinct, when the angle they subtend at the pupil of the eye is less than six minutes.

We have deemed it expedient to introduce the above remarks on the apparent magnitude of objects, because the principal use of a telescope is to increase the angle of vision, or to represent objects under a larger angle than that under which they appear to the naked eye, so as to render the view of distant objects more distinct, and to exhibit to the organ of vision those objects which would otherwise be invisible. A telescope may be said to enlarge an object just as many times as the angle under which the instrument represents it, is greater than that under which it appears to the unassisted eye. Thus the moon appears to the naked eye under an angle of about half a degree; consequently a telescope magnifies 60 times if it represents that orb under an angle of 30 degrees; and if it magnified 180 times, it would exhibit the moon under an angle of 90 degrees, which would make her appear to fill half of the visible heavens, or the space which intervenes from the horizon to the zenith.

CHAPTER IV.

ON THE DIFFERENT KINDS OF REFRACTING TELESCOPES.

There are two kinds of telescopes, corresponding to two modes of vision, namely, those which perform their office by refraction through lenses, and those which magnify distant objects by reflection from mirrors. The telescope which is constructed with lenses, produces its effects solely by refracted light, and is called a Dioptric, or refracting telescope. The other kind of telescope produces its effects partly by reflection, and partly by refraction, and is composed both of mirrors and lenses; but the mirrors form the principal part of the telescope; and therefore such instruments are denominated reflecting telescopes. In this chapter I shall describe the various kinds of refracting telescopes.

SECT 1.—THE GALILEAN TELESCOPE.

This telescope is named after the celebrated Galileo, who first constructed, and probably invented it in the year 1609. It consists of only two glasses, a convex glass next the object, and a concave next the eye. The convex is called the object-glass, and the concave to which the eye is applied, is called the eye-glass. Let C (fig. 43.) represent the convex object-glass, presented to any object in the direction DEI, so that the rays fall parallel upon it;—if these rays, after passing through it, were not intercepted by the concave lens K, they would pass on, and cross each other in the focus F, where an inverted image of the object would be formed. But the concave lens K, the virtual focus of which is at F, being interposed, the rays are not suffered to converge to that point, but are made less convergent,19 and enter the pupil almost parallel, as GH, and are converged by the humours of the eye to their proper foci on the retina. The object, through this telescope, is seen upright, or in its natural position, because the rays are not suffered to come to a focus, so as to form an inverted picture. The concave eye-glass is placed as far within the focus of the object-glass, as is equal to its own virtual focus; and the magnifying power is as the focal length of the object-glass to that of the eye-glass, that is, as CF to BF. Thus, suppose the focus of the object-glass to be 10 inches, and the focus of the eye-glass to be 1 inch, the magnifying power will be 10 times—which is always found by dividing the focal length of the object-glass by that of the eye-glass. The interval between the two glasses, in this case, will be 9 inches, which is the length of the telescope, and the objects seen through it will appear under an angle ten times greater than they do to the naked eye. These propositions might be proved mathematically; but the process is somewhat tedious and intricate, and might not fully be understood by general readers. I shall therefore only mention some of the general properties of this telescope, which is now seldom used, except for the purpose of opera-glasses.

figure 43

1. The focal distance of the object-glass must be greater than that of the eye-glass, otherwise it would not magnify an object: if the focal distance of the eye-glass were greater than that of the object-glass, it would diminish objects, instead of magnifying them. 2. The visible area of the object is greater, the nearer the eye is to the glass; and it depends on the diameter of the pupil of the eye, and on the breadth of the object-glass; consequently the field of view in this telescope is very small. 3. The distinctness of vision in this construction of a telescope exceeds that of almost any other. This arises from the rays of light proceeding from the object directly through the lenses, without crossing or intersecting each other; whereas in the combination of convex lenses, they intersect one another to form an image in the focus of the object-glass, and this image is magnified by the eye-glass with all its imperfections and distortions. The thinness of the centre of the concave lens also contributes to distinctness. 4. Although the field of view in this telescope is very small, yet where no other telescope can be procured, it might be made of such a length as to show the spots on the Sun, the crescent of Venus, the satellites of Jupiter, and the ring of Saturn; and, requiring only two glasses, it is the cheapest of all telescopes. It has been found that an object-lens 5 feet focal distance, will bear a concave eye-glass of only 1 inch focal distance, and will consequently magnify the diameters of the planets 60 times, and their surfaces 3600 times, which is sufficient to show the phenomena now stated. And, although only a small portion of the sun and moon can be seen at once, yet Jupiter and all his satellites may sometimes be seen at one view; but there is some difficulty in finding objects with such telescopes. 5. Opera-glasses, which are always of this construction, have the object-lens generally about 6 inches focus and 1 inch diameter, with a concave eye-glass of about 2 inches focus. These glasses magnify about 3 times in diameter, have a pretty large field, and produce very distinct vision. When adjusted to the eye, they are about 4 inches in length. To the object end of an opera-glass there is sometimes attached a plane mirror, placed at an angle of 45 degrees, for the purpose of viewing objects on either side of us. By this means, in a theatre or assembly, we can take a view of any person without his having the least suspicion of it, as the glass is directed in quite a different direction. The instrument with this appendage is sometimes called a Polemoscope.

SECT. 2.—THE COMMON ASTRONOMICAL REFRACTING TELESCOPE.

The astronomical telescope is the most simple construction of a telescope, composed of convex lenses only, of which there are but two essentially necessary, though a third is sometimes added to the eye-piece for the purpose of enlarging the field of view. Its construction will be easily understood from a description of the following figure. Its two essential parts are, an object-glass AD, and an eye-glass EY, so combined in a tube that the focus F of the object-glass is exactly coincident with the focus of the eye-glass. Let OB (fig. 44.) represent a distant object, from which rays nearly parallel proceed to the object-lens AD. The rays passing through this lens will cross at F, and form an image of the object at IM. This image forms as it were an object to the eye-glass EY, which is of a short focal distance, and the eye is thus enabled to contemplate the object as if it were brought much nearer than it is in reality. For the rays, which after crossing proceed in a divergent state, fall upon the lens EY, as if they proceeded from a real object situated at F. All that is effected therefore, by such a telescope is, to form an image of a distant object by means of the object-lens, and then to give the eye such assistance as is necessary for viewing that image as near as possible, so that the angle it shall subtend at the eye shall be very large compared with the angle which the object itself would subtend in the same situation.

figure 44.

Here it may be expedient to explain, 1. how this arrangement of glasses shows distant objects distinctly, and 2. the reason why objects appear magnified when seen through it. As to the first particular, it may be proved as follows:—The rays OA and BD, which are parallel before they fall upon the object-glass, are by this glass refracted and united at its focus: In order, then, to distinct vision, the eye-glass must re-establish the parallelism of the rays,—which is effected by placing the eye-glass so that its focus may be at F, and consequently the rays will proceed from it parallel to each other and fall upon the eye in that direction. For distinct vision is produced by parallel rays. 2. The reason why the object appears magnified will appear, if we consider that, if the eye viewed the object from the centre of the object-glass, it would see it under the angle OCB; let OC and BC then be produced to the focus of the glass, they will then limit the image IM formed in the focus. If then, two parallel rays are supposed to proceed to the eye-glass EY, they will be converged to its focus H, and the eye will see the image under the angle EHY. The apparent magnitude of the object, therefore, as seen by the naked eye, is to the magnitude of the image as seen through the telescope, as OCB to EHY, or as the distance CF to the distance FG, in other words, as the focal length of the object-glass to that of the eye-glass.

It is obvious from the figure, that, through this telescope, all objects will appear inverted; since the object OB is depicted by the object-glass in an inverted position at IM, and in this position is viewed by the eye-glass EY; and, therefore this kind of telescope is not well adapted for viewing terrestrial objects, since it exhibits the tops of trees, houses, and other objects as undermost, and the heads of people as pointing downwards. But this circumstance is of no consequence with respect to the heavenly bodies, since they are round, and it can make little difference to an observer which side of a globular body appears uppermost or undermost. All astronomical refracting telescopes invert objects; but they are preferred to any other telescopes, because they have few glasses, and consequently more light. This telescope however, can be transformed into a common day telescope for land objects, by the addition of two other eye-glasses, as we shall afterwards explain; but in this case a quantity of light is lost by refraction at each lens; for there is scarcely any transparent substance that transmits all the rays of light that fall upon it.

The magnifying power of this telescope is found by dividing the focal distance of the object-glass by the focal distance of the eye-glass: the quotient gives the magnifying power, or the number of times that the object seen through the telescope, appears larger or nearer than to the naked eye. Thus, for example, if the focal distance of the object-glass be 28 inches, and the focal distance of the eye-glass 1 inch, the magnifying power will be 28 times. If we would enlarge the telescope and select an object-glass 10 feet, or 120 inches focus, an eye-glass of 2 inches focal length might be applied, and then the diameter of objects would be magnified 60 times, and their surfaces 3600 times. If we would use an object-glass of 100 feet, it would be necessary to select an eye-glass about 6 inches focus, and the magnifying power would be 200 times, equal to 1200 inches divided by 6. Since, then, the power of magnifying depends on the proportion of the focal length of the object and eye-glasses, and this proportion may be varied to any degree, it may seem strange to some that a short telescope of this kind will not answer that purpose as well as a long one. For instance, it may be asked why an object-glass of 10 feet focus, may not be made to magnify as much, as one of 100 feet focal length, by using an eye-glass of half an inch focus, in which case, the magnifying power would be 240 times? But it is to be considered, that if the power of magnifying be increased, while the length of the telescope remains the same, it is necessary to diminish the focal length of the eye-glass in the same proportion, and this cannot be done on account of the great distortion and colouring which would then appear in the image, arising both from the deep convexity of the lens and the different refrangibility of the rays of light. It is found that the length of common refracting telescopes must be increased in proportion to the square of the increase of their magnifying power; so that in order to magnify twice as much as before, with the same light and distinctness, the telescope must be lengthened four times; to magnify 3 times as much, 9 times; and to magnify four times as much, sixteen times; that is—suppose a telescope of 3 feet to magnify 33 times,—in order to procure a power four times as great, or 132 times, we must extend the telescope to the length of 48 feet, or 16 times the length of the other. Much likewise depends upon the breadth or aperture of the object-glass. If it be too small, there will not be sufficient light to illuminate the object; and if it be too large, the redundance of light will produce confusion in the image.

The following table, constructed originally by Huygens, and which I have re-calculated and corrected, shows the linear aperture, the focal distance of the eye-glass, and the magnifying power of astronomical telescopes of different lengths, which may serve as a guide to those who wish to construct telescopes of this description.

Focal distance of the object-glass.	Linear aperture of the object-glass.		Focal distance of the eye-glass.		Magnifying power.
Feet.	Inch.	Dec.	Inch.	Dec.
1	0.	545	0.	605	20
2	0.	76	0.	84	20.5
3	0.	94	1.	04	34.6
4	1.	08	1.	18	40
5	1.	21	1.	33	45
6	1.	32	1.	45	50
7	1.	43	1.	58	53
8	1.	53	1.	69	56.8
9	1.	62	1.	78	60.6
10	1.	71	1.	88	63.8
15	2.	10	2.	30	78
20	2.	43	2.	68	89.5
30	3.	00	3.	28	109
40	3.	43	3.	76	127
50	3.	84	4.	20	142
60	4.	20	4.	60	156
70	4.	55	5.	00	168
80	4.	83	5.	35	179
90	5.	15	5.	65	190
100	5.	40	5.	95	200
120	5.	90	6.	52	220

In the above table, the first column expresses the focal length of the object-glass in feet; the second column, the diameter of the aperture20 of the object-glass, the third column, the focal distance of the eye-glass, and the fourth, the magnifying power, which is found by reducing the feet in the first column to inches, and dividing by the numbers in the third column. From this table it appears that, in order to obtain a magnifying power of 168 times, by this kind of telescope, it is requisite to have an object-glass of 70 feet focal distance, and an eye-glass five inches focus, and that the aperture of the object-glass ought not to be more than about 4½ inches diameter. To obtain a power of 220 times requires a length of 120 feet.

The following is a summary view of the properties of this telescope. 1. The object is always inverted. 2. The magnifying power is always in the proportion of the focal distance of the object-glass to the eye-glass. 3. As the rays emerging from the eye-glass, should be rendered parallel for every eye, there is a small sliding tube next the eye, which should be pushed out or in till the object appears distinct. When objects are pretty near, this tube requires to be pulled out a little. These circumstances require to be attended to in all telescopes. 4. The apparent magnitude of an object is the same wherever the eye be placed, but the visible area, or field of view, is the greatest when the eye is nearly at the focal distance of the eye-glass. 5. The visual angle depends on the breadth of the eye-glass; for it is equal to the angle which the eye-glass subtends at the object-glass; but the breadth of the eye-glass cannot be increased beyond a certain limit, without producing colouring and distortion.

If the general principles on which this telescope is constructed be thoroughly understood, it will be quite easy for the reader to understand the construction of all the other kinds of telescopes, whether refracting or reflecting. A small astronomical telescope can be constructed in a few moments, provided one has at hand the following lenses:—1. A common reading-glass, eight or ten inches focal distance; 2. A common magnifying lens, such as watchmakers or botanists use, of about 1½ or 2 inches focus. Hold the reading-glass—suppose of ten inches focus—in the left hand opposite any object, and the magnifying lens of two inches focus, in the right hand near the eye, at twelve inches distance from the other in a direct line, and a telescope is formed which magnifies five times. I have frequently used this plan, when travelling, when no other telescope was at hand.

SECT. 3.—THE AERIAL TELESCOPE.

The Aerial is a refracting telescope of the kind we have now described, intended to be used without a tube in a dark night; for the use of a tube is not only to direct the glasses, but to make the place dark where the images are formed. It appears from the preceding table inserted above, that we cannot obtain a high magnifying power, with the common astronomical telescope, without making it of an extreme length, in which case the glasses are not manageable in tubes—which are either too slight and apt to bend, or too heavy and unwieldy if made of wood, iron or other strong materials. The astronomers of the seventeenth century, feeling such inconveniences in making celestial observations with long tubes, contrived a method of using the glasses without tubes. Hartsocker, an eminent optician, contrived to fix them at the top of a tree, a high wall, or the roof of a house; but the celebrated Huygens, who was not only an astronomer, but also an excellent mechanic, made considerable improvements in the method of using an object-glass without a tube. He placed it at the top of a very long pole, having previously enclosed it in a short tube, which was made to turn in all directions by means of a ball and socket. The axis of this tube he could command with a fine silken string, so as to bring it into a line with the axis of another short tube which he held in his hand, and which contained the eye-glass. The following is a more particular description of one of these telescopes. On the top of a long pole or mast ab (fig. 45), is fixed a board moveable up and down in the channel cd: e is a perpendicular arm fixed to it, and ff is a transverse board that supports the object glass enclosed in the tube i, which is raised or lowered by means of the silk cord rl; gg is an endless rope with a weight h, by which the apparatus of the object-glass is counterpoised; kl is a stick fastened to the tube i; m the ball and socket, by means of which the object-glass is moveable every way: and to keep it steady, there is a weight n suspended by a wire; l is a short wire to which the thread rl is tied; o is the tube which holds the eye-glass; q the stick fixed to this tube, s a leaden bullet, and t a spool to wind the thread on; u is pins for the thread to pass through; x the rest for the observer to lean upon, and y the lantern. Fig. 46 is an apparatus contrived by M. de la Hire for managing the object-glass; but which it would be too tedious particularly to describe. To keep off the dew from the object-glass, it was sometimes included in a pasteboard tube, made of spongy paper, to absorb the humidity of the air. And to find an object more readily, a broad annulus of white pasteboard was put over the tube that carried the eye-glass; upon which the image of the object being painted, an assistant who perceived it, might direct the tube of the eye-glass into its place.

figure 45.

fig 46.

Such was the construction of the telescopes with which Hevelius, Huygens, Cassini, and other eminent astronomers of the seventeenth century made their principal discoveries. With such telescopes, Huygens discovered the fourth satellite of Saturn, and determined that this planet was surrounded with a ring; and with the same kind of instrument Cassini detected the first, second, third, and fifth, satellites of Saturn, and made his other discoveries. When the night was very dark, they were obliged to make the object-glass visible, by means of a lantern so constructed as to throw the rays of light up to it in a parallel direction. In making such observations, they must have taken incredible pains, endured much cold and fatigue, and subjected themselves to very great labour and expense—which almost makes us wonder at the discoveries they were instrumental in bringing to light—and should make modern philosophers sensible of the obligations they are under to such men as Newton and Dollond, through whose inventions such unwieldy instruments are no longer necessary. Telescopes of the description now stated were made of all sizes, from 30 to above 120 feet in length. Divini at Rome, and Campani at Bologna, were famed as makers of the object-glasses of the long focal distance to which we have alluded, who sold them for a great price, and took every method to keep the art of making them a secret. It was with telescopes made by Campani, that Cassini made his discoveries. They were made by the express order of Louis XIV, and were of 86, 100, and 136 Paris feet in focal length. M. Auzout made one object-glass of 600 feet focus; but he was never able to manage it, so as to make any practical observations with it. Hartsocker is said to have made some of a still greater focal length. The famous aerial telescope of Huygens was 123 feet in focal length, with six inches of aperture. At his death, he bequeathed it to the Royal Society of London, in whose possession it still remains. It required a pole of more than a hundred feet high, on which to place the object-glass for general observations. It was with this glass, that Dr. Derham made the observations to which he alludes in his preface to his ‘Astro-Theology.’ When this glass was in the possession of Mr. Cavendish, it was compared with one of Mr. Dollond’s forty-six inch treble object-glass Achromatics, and the gentlemen who were present at the trial, said that ‘the Dwarf was fairly a match for the Giant.’ It magnified 218 times, and the trouble of managing it, was said to be extremely tiresome and laborious.

SECT. 4.—THE COMMON REFRACTING TELESCOPE FOR TERRESTRIAL OBJECTS.

figure 47.

This telescope is constructed on the same principle as the astronomical telescope already described, with the addition of two or three glasses. In fig. 47, OB represents a distant object, LN, the object glass, which forms the image IM in its focus, which is, of course, in an inverted position, and, if the eye were applied at the lens EE, the object would appear, exactly as through the astronomical telescope, every object being apparently turned upside down. To remedy this inconvenience, there are added two other glasses FF and GG, by which a second image is formed from the first, in the same position as the object. In order to effect this, the first of these two glasses, namely FF, is placed at twice its focal distance from the former glass EE, and the other lens GG, next the eye, is placed at the same distance from FF. For all the three glasses are supposed to be of the same focal distance. Now, the lens FF, being placed at twice the focal distance for parallel rays from EE, receives the pencils of parallel rays after they have crossed each other at X, and forms an image at i m similar to that at IM and equal to it, but contrary in position, and consequently erect; which last image is viewed by the lens GG, in the same manner as the first image IM would be viewed by the lens EE. In this case, the image IM is considered as an object to the lens FF of which it forms a picture in its focus, in a reverse position from that of the first image, and of course, in the same position as the object.

The magnifying power of this telescope is determined precisely in the same way as that of the astronomical telescope. Suppose the object-glass to be thirty inches focal distance, and each of the eye-glasses 1½ inch focal distance, the magnifying power is in the proportion of 30 to 1½, or 20 times, and the instrument is, of course, considerably longer than an astronomical telescope of the same power. The distance, in this case, between the object-glass and the first eye-glass EE is 31½ inches; the distance between EE, and the second glass FF, is 3 inches, and the distance between FF and the glass GG next the eye, 3 inches; in all 37½ inches, the whole length of the telescope. Although it is usual to make use of three eye-glasses in this telescope, yet two will cause the object to appear erect, and of the same magnitude. For suppose the middle lens FF taken away, if the first lens EE be placed at X, which is double its focal distance from the image IM, it will at the same distance X m, on the other side, form a secondary image i m equal to the primary image IM, and also in a contrary position. But such a combination of eye-glasses produces a great degree of colouring in the image, and therefore is seldom used. Even the combination now described, consisting of three lenses of equal focal distances, is now almost obsolete, and has given place to a much better arrangement consisting of four glasses, of different focal distances—which shall be afterwards described.

The following figures, 48, 49, 50 represent the manner in which the rays of light are refracted through the glasses of the telescopes we have now described. Fig. 48 represents the rays of light as they pass from the object to the eye in the Galilean telescope. After passing in a parallel direction to the object-glass, they are refracted by that glass, and undergo a slight convergence in passing towards the concave eye-glass, where they enter the eye in a parallel direction, but no image is formed previous to their entering the eye, till they arrive at the retina. Fig. 49 represents the rays as they pass through the glasses of the astronomical telescope. The rays, after entering the object-glass, proceed in a converging direction, till they arrive at its focus, about A, where an image of the object is formed; they then proceed diverging to the eye-glass, where they are rendered parallel, and enter the eye in that direction. Fig. 50 represents the rays as they converge and diverge in passing through the four glasses of the common day-telescope described above. After passing through the object-glass, they converge towards B, where the first image is formed. They then diverge towards the first eye-glass where they are rendered parallel; and passing through the second eye-glass, they again converge and form a second image at C; from which point they again diverge, and passing through the first eye-glass enter the eye in a parallel direction. If the glasses of these telescopes were fixed on long pieces of wood, at their proper distances from each other, and placed in a darkened room, when the sun is shining, the beam of the sun’s light would pass through them in the same manner as here represented.

fig. 48.	fig. 49.	fig. 50.

SECT. 5.—TELESCOPE FORMED BY A SINGLE LENS.

This is a species of telescope altogether unnoticed by optical writers, so far as I know; nor has the property of a single lens in magnifying distant objects been generally adverted to or recognised. It may not therefore be inexpedient to state a few experiments which I have made in relation to this point. When we hold a spectacle-glass of a pretty long focal distance—say, from 20 to 24 inches—close to the eye, and direct it to distant objects, they do not appear sensibly magnified. But if we hold the glass about 12 or 16 inches from our eye, we shall perceive a sensible degree of magnifying power, as if distant objects were seen at less than half the distance at which they are placed. This property of a spectacle-glass I happened to notice when a boy, and, on different occasions since that period have made several experiments on the subject, some of which I shall here relate.

With the object-glass of a common refracting telescope 4½ feet focal distance, and 2½ inches diameter, I looked at distant objects—my eye being at about 3½ feet from the lens, or about 10 or 12 inches within its focus—and it produced nearly the same effect as a telescope which magnifies the diameters of objects 5 or 6 times. With another lens 11 feet focal distance and 4 inches diameter—standing from it at the distance of about 10 feet, I obtain a magnifying power of about 12 or 14 times, which enables me to read the letters on the sign-posts of a village half a mile distant. Having some time ago procured a very large lens 26 feet focal distance, and 11½ inches diameter, I have tried with it various experiments of this kind upon different objects. Standing at the distance of about 25 feet from it, I can see distant objects through it magnified about 26 times in diameter, and consequently 676 times in surface, and remarkably clear and distinct, so that I can distinguish the hour and minute hands of a public clock in a village two miles distant. This single lens, therefore answers the purpose of an ordinary telescope with a power of 26 times. In making such experiments our eye must always be within the focus of the lens, at least 8 or 10 inches. The object will, indeed, be seen at any distance from the glass within this limit; but the magnifying power is diminished in proportion as we approach nearer to the glass. Different eyes, too, will require to place themselves at different distances, so as to obtain the greatest degree of magnifying power with distinctness, according as individuals are long or short-sighted.

This kind of telescope stands in no need of a tube, but only of a small pedestal on which it may be placed on a table, nearly at the height of the eye, and that it be capable of a motion in a perpendicular or parallel direction, to bring it in a line with the eye and the object. The principle on which the magnifying power, in this case, is produced, is materially the same as that on which the performance of the Galilean telescope depends. The eye of the observer serves instead of the concave lens in that instrument; and as the concave lens is placed as much within the focus of the object-glass, as is equal to its own focal distance, so the eye, in these experiments, must be placed at least its focal distance within the focus of the lens with which we are experimenting; and the magnifying power will be nearly in the proportion of the focal distance of the lens to the focal distance of the eye. If, for example, the focal distance of the eye, or the distance at which we see to read distinctly, be 10 inches, and the focal distance of the lens, 11 feet, the magnifying power will be as 11 feet, or 132 inches to 10, that is, about 13 times. Let A (fig. 51.) represent the lens placed on a pedestal; the rays of light passing through this lens from distant objects will converge towards a focus at F. If a person then, place his eye at E, a certain distance within the focal point, he will see distant objects magnified nearly in the proportion of the focal distance of the lens to that of the eye; and when the lens is very broad—such as the 26 feet lens mentioned above—two or three persons may look through it at once, though they will not all see the same object. I have alluded above to a lens made by M. Azout of 600 feet focal distance. Were it possible to use such a lens for distant objects, it might represent them as magnified 5 or 600 times, without the application of any eye-glass. In this way the aerial telescope of Huygens would magnify objects above 100 times, which is about half the magnifying power it produced with its eye-piece. Suppose Azout’s lens had been fitted up as a telescope, it would not have magnified above 480 times, as it would have required an eye-glass of 14 or 15 inches focal distance, whereas, without an eye-glass, it would have magnified objects considerably above 500 times. It is not unlikely that the species of telescope to which I have now adverted, constituted one of those instruments for magnifying distant objects which were said to have been in the possession of certain persons long before their invention in Holland, and by Galileo in Italy—to which I have referred in p. 182. Were this kind of telescope to be applied to the celestial bodies, it would require to be elevated upon a pole in the manner represented, fig. 45, p. 226.

figure 51.

SECT. 6.—THE ACHROMATIC TELESCOPE.

This telescope constitutes the most important and useful improvement ever made upon telescopic instruments; and, it is probable, it will, ere long, supersede the use of all other telescopes. Its importance and utility will at once appear when we consider, that a good achromatic telescope of only 4 or 5 feet in length will bear a magnifying power as great, as that of a common astronomical telescope 100 feet long, and even with a greater degree of distinctness, so that they are now come into general use both for terrestrial and celestial observations. There are, indeed, certain obstructions which prevent their being made of a very large size; but from the improvement in the manufacture of achromatic glass which is now going forward, it is to be hoped that the difficulties which have hitherto impeded the progress of opticians will soon be removed. In order to understand the nature of this telescope, it will be necessary to advert a little to the imperfections connected with common refracting telescopes.

figure 52.

The first imperfection to which I allude is this, that spherical surfaces do not refract the rays of light accurately to a point; and hence the image formed by a single convex lens is not perfectly accurate and distinct. The rays which pass near the extremities of such a lens meet in foci nearer to the lens than those which pass nearly through the centre, which may be illustrated by the following figure. Let PP (fig. 52) be a convex lens and Ee an object, the point E of which corresponds with the axis, and sends forth the rays EM, EN, EA, &c., all of which reach the surface of the glass, but in different parts. It is manifest that the ray EA which passes through the middle of the glass, suffers no refraction. The rays EM, EM, likewise, which pass through near to EA, will be converged to a focus at F, which we generally consider as the focus of the lens. But the rays EN, EN, which are nearer to the edge of the glass will be differently refracted, and will meet about G, nearer to the lens, where they will form another image Gg. Hence, it is evident, that the first image Ff, is formed only by the union of those rays which pass very near the centre of the lens; but as the rays of light proceeding from every point of an object are very numerous, there is a succession of images formed, according to the parts of the lens where they penetrate, which necessarily produces indistinctness and confusion. This is the imperfection which is distinguished by the name of spherical aberration, or the error arising from the spherical form of lenses.

The second and most important imperfection of single lenses, when used for the object-glasses of telescopes, is, that the rays of compounded light being differently refrangible, come to their respective foci at different distances from the glass; the more refrangible rays, as the violet, converging sooner than those which are less refrangible, as the red. I have had occasion to illustrate this circumstance, when treating on the colours produced by the prism, (see p. 128, and figures 32 and 33,) and it is confirmed by the experiment of a paper painted red, throwing its image, by means of a lens, at a greater distance than another paper painted blue. From such facts and experiments, it appears, that the image of a white object consists of an indefinite number of coloured images, the violet being nearest, and the red farthest from the lens, and the images of intermediate colours at intermediate distances. The aggregate, or image itself, must therefore be in some degree confused; and this confusion being much increased by the magnifying power, it is found necessary to use an eye glass of a certain limited convexity to a given object glass. Thus, an object glass of 34 inches focal length will bear an eye-glass of only 1 inch focus, and will magnify the diameters of objects 34 times; one of 50 feet focal distance will require an eye-glass of 4½ inches focus, and will magnify only 142 times; whereas, could we apply to it an eye-glass of only 1 inch focus, as in the former case, it would magnify no less than 600 times. And were we to construct an object-glass of 100 feet focal length, we should require to apply an eye-glass, not less than 6 inches focus, which would produce a power of about 200 times; so that there is no possibility of producing a great power by single lenses, without extending the telescope to an immoderate length.

Sir Isaac Newton, after having made his discoveries respecting the colours of light, considered the circumstance we have now stated as an insuperable barrier to the improvement of refracting telescopes; and therefore turned his attention to the improvement of telescopes by reflection. In the telescopes which he constructed and partly invented, the images of objects are formed by reflection from speculums or mirrors; and being free from the irregular convergency of the various coloured rays of light, will admit of a much larger aperture and the application of a much greater degree of magnifying power. The reflector which Newton constructed was only 6 inches long, but it was capable of bearing a power equal to that of a 6 feet refractor. It was a long time, however, after the invention of these telescopes before they were made of a size fitted for making celestial observations. After reflecting telescopes had been some time in use, Dollond made his famous discovery of the principle which led him to the construction of the achromatic telescope. This invention consists of a compound object glass formed of two different kinds of glass, by which both the spherical aberration and the errors arising from the different refrangibility of the rays of light are, in a great measure corrected. For the explanation of the nature of this compound object glass and of the effects it produces; it may be expedient to offer the following remarks respecting the dispersion of light and its refraction by different substances.

The dispersion of light is estimated by the variable angle formed by the red and violet rays which bound the solar spectrum;—or rather, it is the excess of the refraction of the most refrangible ray above that of the least refrangible ray. The dispersion is not proportional to the refraction—that is, the substances which have an equal mean refraction, do not disperse light in the same ratio. For example, if we make a prism with plates of glass, and fill it with oil of Cassia, and adjust its refracting angle ACB, (fig. 31, p. 127,) so that the middle of the spectrum which it forms falls exactly at the same place where the green rays of a spectrum formed by a glass prism would fall—then we shall find that the spectrum formed by the oil of Cassia prism will be two or three times longer than that of the glass prism. The oil of Cassia, therefore, is said to disperse the rays of light more than the glass, that is, to separate the extreme red and violet rays at O and P more than the mean ray at green, and to have a greater dispersive power. Sir I. Newton appears to have made use of prisms composed of different substances, yet, strange to tell, he never observed that they formed spectrums, whose lengths were different, when the refraction of the green ray was the same; but thought that the dispersion was proportional to the refraction. This error continued to be overlooked by philosophers for a considerable time, and was the cause of retarding the invention of the achromatic telescope for more than 50 years.

Dollond was among the first who detected this error. By his experiments it appears, that the different kinds of glass differ extremely with respect to the divergency of colours produced by equal refractions. He found that two prisms, one of white flint glass, whose refracting angle was about 25 degrees, and another of crown glass whose refracting angle was about 29 degrees, refracted the beam of light nearly alike; but that the divergency of colour in the white flint was considerably more than in the crown glass; so that when they were applied together, to refract contrary ways, and a beam of light transmitted through them, though the emergent continued parallel to the incident part, it was, notwithstanding, separated into component colours. From this he inferred, that, in order to render the emergent beam white, it is necessary that the refracting angle of the prism of crown glass should be increased, and by repeated experiments he discovered the exact quantity. By these means he obtained a theory in which refraction was performed without any separation or divergency of colour; and thus the way was prepared for applying the principle he had ascertained to the construction of the object glasses of refracting telescopes. For the edges of a convex and concave lens, when placed in contact with each other, may be considered as two prisms which refract contrary ways; and if the excess of refraction in the one be such as precisely to destroy the divergency of colour in the other, a colourless image will be formed. Thus, if two lenses are made of the same focal length, the one of flint glass and the other of crown, the length or diameter of the coloured image in the first will be to that produced by the crown glass, as 3 to 2 nearly. Now, if we make the focal lengths of the lenses in this proportion, that is, as 3 to 2, the coloured spectrum produced by each will be equal. But if the flint lens be concave, and the crown convex—when placed in contact—they will mutually correct each other, and a pencil of white light refracted by the compound lens will remain colourless.

figure 53.

The following figure may perhaps illustrate what has been now stated. Let LL (fig. 53.) represent a convex lens of crown glass, and ll a concave lens of flint glass. A ray of the sun S, falls at F on the convex lens which will refract it exactly as the prism ABC, whose faces touch the two surfaces of the lens at the points where the ray enters and quits it. The solar ray, SF, thus refracted by the lens LL, or prism ABC, would have formed a spectrum PT on the wall, had there been no other lens, the violet ray F crossing the axis of the lens at V, and going to the upper end P of the spectrum; and the red ray FR, going to the lower end T. But as the flint-glass lens ll, or the prism AaC which receives the rays FV, FR, at the same points, is interposed, these rays will be united at f, and form a small circle of white light; the ray SF of the sun being now refracted without colour from its primitive direction SFY into the new direction Ff. In like manner the corresponding ray SM will be refracted to f, and a white and colourless image of the sun will be there formed by the two lenses. In this combination of lenses it is obvious that the spherical aberration of the flint lens corrects to a considerable degree that of the crown-glass, and by a proper adjustment of the radii of the surfaces, it may be almost wholly removed. This error is still more completely corrected in the triple achromatic object-glass, which consists of three lenses—a concave flint lens placed between convexes of crown glass. Fig. 54 shows the double achromatic lens, and fig. 55, the triple object-glass, as they are fitted up in their cells, and placed at the object end of the telescope. In consequence of their producing a focal image free of colour they will bear a much larger aperture and a much greater magnifying power than common refracting telescopes of the same length. While a common telescope whose object-glass is 3½ feet focal distance will bear an aperture of scarcely 1 inch, the 3½ feet Achromatic will bear an aperture of 3¼ inches, and consequently transmits 10½ times the quantity of light. While the one can bear a magnifying power of only about 36 times, the other will bear a magnifying power for celestial objects of more than 200 times.

figure 54.	figure 55.

The theory of the achromatic telescope is somewhat complicated and abstruse, and would require a more lengthened investigation than my limits will permit. But what has been already stated may serve to give the reader a general idea of the principle on which it is constructed, which is all I intended. The term achromatic by which such instruments are now distinguished was first given to them by Dr. Bevis. It is compounded of two Greek words which signify, ‘free of colour.’ And, were it not that even philosophers are not altogether free of that pedantry which induces us to select Greek words which are unintelligible to the mass of mankind, they might have been contented with selecting the plain English word colourless, which is as significant and expressive as the Greek word achromatic. The crown-glass, of which the convex lenses of this telescope are made, is the same as good common window-glass; and the flint-glass is that species of glass of which wine-glasses, tumblers, decanters and similar articles are formed, and is sometimes distinguished by the name of crystal-glass. Some opticians have occasionally formed the concave lens of an achromatic object-glass from the bottom of a broken tumbler.

This telescope was invented and constructed by Mr. John Dollond, about the year 1758. When he began his researches into this subject, he was a silk weaver in Spitalfields, London. The attempt of the celebrated Euler to form a colourless telescope, by including water between two meniscus glasses, attracted his attention, and, in the year 1753, he addressed a letter to Mr. Short, the optician, which was published in the Philosophical Transactions of London, ‘concerning a mistake in Euler’s theorem for correcting the aberrations in the object glasses of refracting telescopes.’ After a great variety of experiments on the refractive and dispersive powers of different substances, he at last constructed a telescope in which an exact balance of the opposite dispersive powers of the crown and flint lenses made the colours disappear, while the predominating refraction of the crown lens disposed the achromatic rays to meet at a distant focus. In constructing such object glasses, however, he had several difficulties to encounter. In the first place, the focal distance as well as the particular surfaces must be very nicely proportioned to the densities or refractive powers of the glasses, which are very apt to vary in the same sort of glass made at different times. In the next place, the centers of the two glasses must be placed truly in the common axis of the telescope, otherwise the desired effect will be in a great measure destroyed. To these difficulties is to be added—that there are four surfaces (even in double achromatic object glasses) to be wrought perfectly spherical; and every person practised in optical operations will allow, that there must be the greatest accuracy throughout the whole work. But these and other difficulties were at length overcome by the judgment and perseverance of this ingenious artist.

It appears, however, that Dollond was not the only person who had the merit of making this discovery—a private gentleman, Mr. Chest, of Chest-hall, a considerable number of years before, having made a similar discovery, and applied it to the same purpose. This fact was ascertained in the course of a process raised against Dollond at the instance of Watkins, optician at Charing-cross, when applying for a patent. But as the other gentleman had kept his invention a secret, and Dollond had brought it forth for the benefit of the public, the decision was given in his favour. There was no evidence that Dollond borrowed the idea from his competitor, and both were, to a certain extent, entitled to the merits of the invention.

One of the greatest obstructions to the construction of large achromatic telescopes is, the difficulty of procuring large discs of flint glass of an uniform refractive density—of good colour, and free from veins. It is said that, fortunately for Mr. Dollond, this kind of glass was procurable when he began to make achromatic telescopes, though the attempts of ingenious chemists have since been exerted to make it without much success. It is also said, that the glass employed by Dollond in the fabrication of his best telescopes, was of the same melting, or made at the same time, and that, excepting this particular treasure, casually obtained, good dense glass for achromatic purposes, was always as difficult to be procured as it is now. The dispersion of the flint glass, too, is so variable, that, in forming an achromatic lens, trials on each specimen require to be made before the absolute proportional dispersion of the substances can be ascertained. It is owing, in a great measure, to these circumstances, that a large and good achromatic telescope cannot be procured unless at a very high price. Mr. Tulley of Islington—who has been long distinguished as a maker of excellent achromatic instruments—showed me, about six years ago, a rude piece of flint glass about five inches diameter, intended for the concave lens of an achromatic object glass, for which he paid eight guineas. This was before the piece of glass was either figured or polished, and, consequently, he had still to perform the delicate operation of figuring, polishing, and adjusting this concave to the convex lenses with which it was to be combined; and during the process some veins or irregularities might be detected in the flint glass which did not then appear. Some years before, he procured a disc of glass from the continent about seven or eight inches diameter, for which he paid about thirty guineas, with which an excellent telescope, twelve feet focal length, was constructed for the Astronomical Society of London. It is obvious therefore, that large achromatic telescopes must be charged at a pretty high price.

In order to stimulate ingenious chemists and opticians to make experiments on this subject, the Board of Longitude, more than half a century ago, offered a considerable reward for bringing the art of making good flint glass for optical purposes to the requisite perfection. But considerable difficulties arise in attempting improvements of this kind; as the experiments must all be tried on a very large scale, and are necessarily attended with a heavy expence. And although government has been extremely liberal in voting money for warlike purposes, and in bestowing pensions on those who stood in no need of them, it has hitherto thrown an obstruction in the way of such experiments, by the heavy duty of excise, which is rigorously exacted, whether the glass be manufactured into saleable articles or not; and has thus been instrumental in retarding the progress of improvement and discovery. It would appear that experiments of this kind have been attended with more success in France, Germany, and other places on the continent, than in Britain; as several very large achromatic telescopes have been constructed in those countries by means of flint glass which was cast for the purpose in different manufactories, and to which British artists have been considerably indebted; as the London opticians frequently purchase their largest discs of flint glass from Parisian agents. Guinaud, a continental experimenter, and who was originally a cabinet maker, appears to have had his labours in this department of art crowned with great success. Many years were employed in his experiments, and he too frequently, notwithstanding all his attention, discovered his metal to be vitiated by striÆ, spects or grains, with cometic tails. He constructed a furnace capable of melting two cwt of glass in one mass, which he sawed vertically, and polished one of the sections, in order to observe what had taken place during the fusion. From time to time, as he obtained blocks, including portions of good glass, his practice was to separate them by sawing the blocks into horizontal sections, or perpendicular to their axes. A fortunate accident conducted him to a better process. While his men were one day carrying a block of this glass, on a hand-barrow, to a saw mill which he had erected at the Fall of the Doubs, the mass slipped from its bearers, and, rolling to the bottom of a steep and rocky declivity, was broken to pieces. Guinaud having selected those fragments which appeared perfectly homogeneous, softened them in circular moulds, in such a manner, that on cooling, he obtained discs that were afterwards fit for working. To this method he adhered, and contrived a way for clearing his glass while cooling, so that the fractures should follow the most faulty parts. When flaws occurred in the large masses, they were removed by cleaving the pieces with wedges; then smelting them again in moulds, which give them the form of discs. The Astronomical Society of London have made trial of discs made by Guinaud, and have found them entirely homogeneous and free from fault. Of this ingenious artist’s flint glass, some of the largest achromatic telescopes on the continent have been constructed. But, it is more than twenty years since this experimenter took his flight from this terrestrial scene, and it is uncertain whether his process be still carried on with equal success.

Notices of some large Achromatic telescopes on the Continent and in Great Britain.

1. The Dorpat Telescope.—This is one of the largest and most expensive Refracting telescopes ever constructed. It was made by the celebrated Fraunhofer of Munich for the observatory of the Imperial University of Dorpat, and was received into the observatory by Professor Struve in the year 1825. The aperture of the object glass of this telescope is 9½ English inches, and its solar focal length about fourteen feet, the main tube being thirteen French feet exclusive of the tube which holds the eye pieces. The smallest of the four magnifying powers it possesses, is 175, and the largest 700, which, in favourable weather, is said to present the object with the utmost precision. ‘This instrument,’ says Struve, ‘was sold to us by Privy-Counsellor Von Utzchneider, the chief of the optical establishment at Munich, for 10,500 florins, (about £950 sterling), a price which only covers the expenses which the establishment incurred in making it.’ The frame work of the stand of this telescope is of oak inlaid with pieces of mahogany in an ornamental manner, and the tube is of deal veneered with mahogany and highly polished. The whole weight of the telescope and its counterpoises is supported at one point, at the common center of gravity of all its parts; and though these weigh 3000 Russian pounds, yet, we are told that this enormous telescope may be turned in every direction towards the heavens with more ease and certainty than any other hitherto in use. When the object end of the telescope is elevated to the zenith, it is sixteen feet four inches, Paris measure, above the floor, and its eye end in this position is two feet nine inches high. This instrument is mounted on an Equatorial stand, and clock work is applied to the Equatorial axis, which gives it a smooth and regular sidereal motion, which, it is said, keeps a star in the exact center of the field of view, and produces the appearance of a state of rest in the starry regions, which motion can be made solar, or even lunar, by a little change given to the place of a pointer, that is placed as an index on the dial plate. Professor Struve considers the optical powers of this telescope superior to those of SchrÖeter’s twenty-five feet reflector, from having observed s Orionis with fifteen companions, though SchrÖeter observed only twelve, that he could count with certainty. Nay, he seems disposed to place it in competition with the late Sir W. Herschel’s forty feet reflector. The finder of this telescope has a focal distance of 30 French inches, and 2-42 aperture.

2. Sir James South’s Telescope.—About the year 1829, Sir J. South, President of the London Astronomical Society, procured of M. Cauchoix of Paris, an achromatic object glass of 11²/₁₀ inches, clear aperture, and of 19 feet focal length. The flint glass employed in its construction was the manufacture of the late Guinaud le Pere, and was found to be absolutely perfect. The first observation was made with this telescope, while on a temporary stand, on Feb. 13, 1830, when Sir J. Herschel discovered with it a sixth star in the trapezium in the nebula of Orion, whose brightness was about one third of that of the fifth star discovered by Struve, which is as distinctly seen as the companion to Polaris is in a five feet achromatic. Sir James gives the following notices of the performance of this instrument on the morning of May 14, 1830. ‘At half past two, placed the 20 feet achromatic on the Georgium Sidus, saw it with a power of 346, a beautiful planetary disc; not the slightest suspicion of any ring, either perpendicular or horizontal; but the planet three hours east of the meridian, and the moon within three degrees of the planet.’ At a quarter before three, viewed Jupiter with 252 and 346, literally covered with belts, and the diameters of his satellites might have been as easily measured as himself. One came from behind the body, and the contrast of the colour with that of the planet’s limb was striking. At three o’clock viewed Mars. The contrast of light in the vicinity of the poles very decided. Several spots on his body well and strongly marked—that about the south pole seems to overtake the body of the planet, and gives an appearance not unlike that afforded by the new moon, familiarly known as ‘the old moon in the new moon’s arms.’ Saturn has been repeatedly seen with powers from 130 to 928 under circumstances the most favourable; but not any thing anomalous about the planet or its ring could even be suspected. This telescope is erected on an Equatorial stand at Sir J. South’s observatory, Kensington.

3. Captain Smyth’s Telescope in his private observatory at Bedford.—This Achromatic telescope is 8½ feet focal length, with a clear aperture of 5⁹/₁₀ inches worked by the late Mr. Tulley, Senior, from a disk purchased by Sir James South at Paris. It is considered by Captain Smyth to be the finest specimen of that eminent optician’s skill, and, it is said, will bear with distinctness, a magnifying power of 1200. Its distinctness has been proved by the clear vision it gives of the obscure nebulÆ, and of the companions of Polaris, Rigel, a LyrÆ, and the most minute double stars—-the lunar mountains, cavities and shadows under all powers—the lucid polar regions of Mars—the sharpness of the double ring of Saturn—the gibbous aspect of Venus—the shadows of Jupiter’s satellites across his body, and the splendid contrast of colours in a Hercules, ? AndromedÆ and other superb double stars.

Other large Achromatics.—Besides the above, the following, belonging to public observatories and private individuals, may be mentioned. In the Royal observatory at Greenwich, there is an Achromatic of 10 feet focal distance, having a double object glass 5 inches diameter, which was made by Mr. Peter Dollond, and the only one of that size he ever constructed. There is also a 46 inch achromatic, with a triple object glass 3¾ inches aperture, which is said to be the most perfect instrument of the kind ever produced. It was the favourite instrument of Dr. Maskelyne, late Astronomer Royal, who had a small room fitted up in the observatory for this telescope. The observatory, some years ago erected near Cambridge, is perhaps the most splendid structure of the kind in Great Britain. It is furnished with several very large achromatic telescopes on Equatorial machinery: but the Achromatic telescope, lately presented to it by the Duke of Northumberland, is undoubtedly the largest instrument of this description which is to be found in this country. The object glass is said to be 25 feet focal distance, and of a corresponding diameter, but as there was no access to this instrument at the time I visited this observatory, nearly six years ago, I am unable to give a particular description of it. In the Royal Observatory at Paris, which I visited in 1837, I noticed, among other instruments, two very large Achromatic telescopes which, measuring them rudely by the eye—I estimated to be from 15 to 18 feet long, and the aperture at the object end, from 12 to 15 inches diameter. They were the largest achromatics I had previously seen; but I could find no person in the observatory at that time, who could give me any information as to their history, or to their exact dimensions, or powers of magnifying.21

The Rev. Dr. Pearson, Treasurer to the Astronomical Society of London, is in possession of the telescope formerly alluded to, made by Mr. Tulley, of twelve feet focal distance and seven inches aperture, which is said to be a very fine one. The small star which accompanies the pole star, with a power of a 100, appears through this telescope, as distinct and steady as one of Jupiter’s satellites. With a single lens of 6 inches focus, which produced a power of 24 times, according to the testimony of an observer who noticed it—the small star appeared as it does in an achromatic of 3 inches aperture, which shows the great effect of illuminating power in such instruments. Mr. Lawson, a diligent astronomical observer in Hereford, possesses a most beautiful achromatic telescope of about 7 inches aperture, and 12 feet focal distance, which was made by one of the Dollonds, who considered it as his chief d’oeuvre. It is said to bear powers as high as 1100 or 1400; and has been fitted up with mechanism devised by Mr. Lawson himself, so as to be perfectly easy and manageable to the observer, and which displays this gentleman’s inventive talent. In several of his observations with this instrument, he is said to have had a view of some of the more minute subdivisions of the ring of Saturn. A very excellent achromatic telescope was fitted up some years ago by my worthy friend William Bridges, Esq., Blackheath. Its object glass is 5½ inches diameter, and about 5½ feet focal length. It is erected upon Equatorial machinery, and placed in a circular observatory which moves round with a slight touch of the hand. The object glass of this instrument cost about 200 Guineas, the equatorial machinery on which it is mounted cost 150 Guineas, and the circular observatory in which it is placed about 100 Guineas; in all 450 Guineas. Its powers vary from 50 to 300 times.22

Achromatic telescopes of a moderate size.

Such telescopes as I have alluded to above, are among the largest which have yet been made on the achromatic principle; they are, of course, comparatively rare, and can be afforded only at a very high price. Few of the object glasses in the telescopes to which I have referred, would be valued at less than 200 Guineas, independently of the tubes, eye pieces and other apparatus with which they are fitted up. It is so difficult to procure large discs of flint glass for optical purposes, to produce the requisite curves of the different lenses, and to combine them together with that extreme accuracy which is requisite, that when a good compound lens of this description is found perfectly achromatic, the optician must necessarily set a high value upon it; since it may happen that he may have finished half a dozen before he has got one that is nearly perfect. The more common sizes of achromatic telescopes for astronomical purposes, which are regularly sold by the London opticians, are the following:—

1. The 2½ feet Achromatic.—This telescope has an object glass 30 inches in focal length, and 2 inches clear aperture. It is generally furnished with two eye pieces, one for terrestrial objects, magnifying about 30 or 35 times, and one for celestial objects with a power of 70 or 75 times. It might be furnished with an additional astronomical eye-piece—if the object glass be a good one, so as to produce a power of 90 or 95 times. With such a telescope, the belts and satellites of Jupiter, the phases of Venus and the ring of Saturn may be perceived; but not to so much advantage as with larger telescopes. It is generally fitted up either with a mahogany or a brass tube, and is placed upon a tripod brass stand, with a universal joint which produces a horizontal and vertical motion. It is packed, along with the eye-pieces, and whatever else belongs to it, in a neat mahogany box. Its price varies, according as it is furnished with an elevating rack or other apparatus.

The following are the prices of this instrument as marked in the catalogue of Mr. Tulley, Terrett’s Court, Islington, London.

	£	s.	d.
2½ feet telescopes, brass mounted on plain pillar and claw stand, with one eye piece for astronomical purposes, and one for land objects, to vary the magnifying power, packed in a mahogany box	10	10	0
Ditto, ditto, brass mounted on pillar and claw stand, with elevating rack, 1 eye piece for astronomical purposes, and 1 for land objects, to vary the magnifying power, packed in a mahogany box	12	12	0

The following prices of the same kind of telescope are from the catalogue of Messrs. W. and, S. Jones, 30, Lower Holborn, London.

	£	s.	d.
The improved 2½ feet achromatic refractor, on a brass stand, mahogany tube, with three eye pieces, two magnifying about 40 and 50 times for terrestrial objects, and the other about 75 times for astronomical purposes, in a mahogany case	10	10	0
Ditto, ditto, the tube all brass, with three eye pieces	11	11	0
Ditto, ditto, with vertical and horizontal rack work motions	15	15	0

2. The 3½ feet Achromatic Telescope.—The object glass of this telescope is from 44 to 46 inches focal length, and 2¾ inches diameter. It is generally furnished with four eye-pieces, two for terrestrial and two for celestial objects. The lowest power for land objects is generally about 45, which affords a large field of view, and exhibits the objects with great brilliance. The other terrestrial power is usually from 65 to 70. The astronomical powers are about 80 and 130; but such a telescope should always have another eye-piece, to produce a power of 180 or 200 times, which it will bear with distinctness, in a serene state of the atmosphere, if the object glass be truly achromatic. The illuminating power in this telescope is nearly double that of the 2½ feet telescope, or in the proportion of 7, 56 to 4; and therefore it will bear about double the magnifying power with nearly equal distinctness. This telescope is fitted up in a manner somewhat similar to the former, with a tripod stand which is placed upon a table. Sometimes, however, it is mounted on a long mahogany stand which rests upon the floor, (as in fig. 58.), and is fitted with an equatorial motion; and has generally a small telescope fixed near the eye end of the large tube, called a finder, which serves to direct the telescope to a particular object in the heavens when the higher powers are applied. It is likewise eligible that it should have an elevating rack and sliding tubes, for supporting the eye end of the instrument, to keep it steady during astronomical observations, and it would be an advantage, for various purposes which shall be afterwards described, to have fitted to it a Diagonal Eye Piece magnifying 40 times or upwards.

The prices of this instrument, as marked in Mr. Tulley’s Catalogue, are as follows:—

	£	s.	d.
The 3½ feet achromatic telescope 2¾ inches aperture, on plain pillar and claw stand, 2 eye pieces for astronomical purposes, and 1 for land objects to vary the magnifying power, packed in a mahogany box	21	0	0
Ditto, ditto, with elevating rack and achromatic finder, 2 eye pieces for astronomical purposes, and 1 for day objects to vary the magnifying power, packed in a mahogany box	26	5	0

The following are the prices as marked in Messrs. W. and S. Jones’ Catalogue.

	£	s.	d.
The 3½ feet achromatic, plain mahogany tube	18	18	0
Ditto, ditto, brass tube	21	0	0
Ditto, all in brass, with rack work motions, &c.	26	5	0
Ditto, the object glass of the largest aperture, and the rack motions on an improved principle	from 37l. 16s. to 42	0	0
Ditto, fitted up with Equatorial motion, framed mahogany stand, divided altitude, and azimuth arches, or declination and right ascension circles, &c. &c.	from 60l to 80	0	0

This is the telescope which I would particularly recommend to astronomical amateurs, whose pecuniary resources do not permit them to purchase more expensive instruments. When fitted up with the eye pieces and powers already mentioned, and with a finder and elevating rack,—price 25 guineas—it will serve all the purposes of general observation. By this telescope, satisfactory views may be obtained of most of the interesting phenomena of the heavens, such as the spots of the sun—the mountains, vales, and caverns on the lunar surface—the phases of Mercury and Venus—the spots on Mars—the satellites and belts of Jupiter—the ring of Saturn—many of the more interesting nebulÆ, and most of the double stars of the second and third classes. When the object glass of this telescope is accurately figured and perfectly achromatic, a power of from 200 to 230 maybe put upon it, by which the division of Saturn’s ring might occasionally be perceived. It is more easily managed and represents objects considerably brighter than reflecting telescopes of the same price and magnifying power, and it is not so apt to be deranged as reflectors generally are. A telescope of a less size would not in general be found satisfactory for viewing the objects I have now specified, and for general astronomical purposes. It may not be improper for the information of some readers, to explain what is meant in Mr. Tulley’s catalogue, when it is stated that this instrument has ‘one eye piece for day objects, to vary the magnifying power.’ The eye piece alluded to is so constructed, that by drawing out a tube next the eye, you may increase the power at pleasure, and make it to vary, say from 40 to 80 or 100 times; so that such a construction of the terrestrial eye piece (to be afterwards explained) serves in a great measure, the purpose of separate eye-pieces. The whole length of the 3½ feet telescope, when the terrestrial eye piece is applied, is about 4½ feet from the object glass to the first eye glass.

When the aperture of the object glass of this telescope exceeds 2¾ inches its price rapidly advances.

The following is Mr. Tulley’s scale of prices, proportionate to the increase of aperture:—

	£	s.	d.
3½ feet telescopes 3¼ inches aperture, with vertical and horizontal rack work motions, achromatic finder, 3 eye pieces for astronomical purposes, and one for day objects to vary the magnifying power, packed in a mahogany box	42	0	0
Ditto, ditto, 3¾ inches diameter, mounted as above	68	5	0
Ditto, with universal Equatorial, instead of pillar and claw stand	84	0	0

Here, in the one case, the increase of half an inch in the diameter of the object-glass, adds about £16. to the expense; and in the other case no less than £26. 5s. The proportion of light in those two telescopes, compared with that of 2¾ inches aperture, is as follows:—The square of the 2¾ object-glass is 7.56; that of 3¼, 10.56, and that of the 3¾, 14.06; so that the light admitted by the 3¼ compared with the 2¾ aperture, is nearly as 10 to 7; and the light admitted by the 3¾ object-glass is nearly double that of the 2¾ aperture, and will bear nearly a proportional increase of magnifying power.

3. The 5 feet Achromatic telescope. The focal length of the object-glass of this telescope is 5 feet 3 inches, and the diameter of its aperture 3⁸/₁₀ inches. The usual magnifying powers applied to it are, for land objects 65 times; and for celestial objects, 110, 190, 250, and sometimes one or two higher powers. The quantity of light it possesses is not much larger than that of the 3½ feet telescope, with 3¾ inches aperture; but the larger focal length of this telescope is considered to be an advantage; since the longer the focus of the object-glass, the less will be its chromatic and spherical aberrations, and the larger may be the eye-glasses, and the flatter the field of view.

The following are the prices of these telescopes as marked in Mr. Tulley’s catalogue.

	£	s.	d.
5 feet telescopes 3¾ inches aperture, on an universal equatorial stand, with achromatic finder, 4 eye pieces for astronomical purposes, and 1 for day objects to vary the magnifying power, packed in a mahogany box 100 guineas to	157	10	0
7 feet ditto, 5 inches aperture, on a newly improved universal equatorial stand, 6 eye pieces for astronomical purposes, and 1 for day objects to vary the magnifying power, with achromatic finder, and Troughton’s Micrometer	207	5	0

The above are all the kinds of achromatic telescopes generally made by the London opticians. Those of the larger kind, as 5 and 7 feet telescopes, and the 3½ feet with 3¾ inches aperture, are generally made to order, and are not always to be procured. But the 2½ and 3½ feet achromatics of 2¾ inches aperture, are generally to be found ready-made at most of the optician’s shops in the metropolis. The prices of these instruments are nearly the same in most of the optician’s shops in London. Some of them demand a higher price, but few of them are ever sold lower than what has been stated above, unless in certain cases, where a discount is allowed.

figure 57.

The stands for these telescopes, and the manner in which they are fitted up for observation are represented in figures 57, 58, and 59. Fig. 57 represents either the 2½ or the 3½ feet telescopes mounted on a plain brass stand, to be placed on a table. A is the long eye-piece for land objects, and B the small eye-piece for astronomical observation, which is composed of two lenses, and represents the object in an inverted position. These eye-pieces are screwed on, as occasion requires, at E, the eye-end of the telescope. The shorter of the two astronomical eye-tubes which accompany this telescope, produces the highest magnifying power. For adjusting the telescope to distinct vision, there is a brass knob or button at a, which moves a piece of rack-work connected with the eye-tube, which must be turned either one way or the other till the object appears distinctly; and different eyes frequently require a different adjustment.

Fig. 58, represents a 5 feet telescope fitted up for astronomical observations. It is mounted on a mahogany stand, the three legs of which are made to close up together by means of the brass frame aaa, which is composed of three bars, connected with three joints in the centre, and three other joints, connected with the three mahogany bars. It is furnished with an apparatus for equatorial motions. The brass pin is made to move round in the brass socket b, and may be tightened by means of the finger screw d, when the telescope is directed nearly to the object intended to be viewed. This socket may be set perpendicular to the horizon, or to any other required angle; and the quantity of the angle is ascertained by the divided arc, and the instrument made fast in that position by the screw e. If this socket be set to the latitude of the place of observation, and the plane of this arc be turned so as to be in the plane of the meridian, the socket b being fixed to the inclination of the pole of the earth, the telescope when turned in this socket, will have an equatorial motion, so that celestial objects may be always kept in view, when this equatorial motion is performed. The two handles at k are connected with rack-work, intended to move the telescope in any required direction. The two sets of brass sliding rods ii are intended to render the telescope as steady as possible, and to elevate and depress it at pleasure, and are so constructed as to slide into each other with the utmost ease.

The Finder is placed at AE, either on the top or the left side of the tube of the telescope. When high magnifying powers are applied to any telescope, it is sometimes difficult, on account of the smallness of the field of view, to direct the main tube of the telescope to the object. But the Finder, which is a telescope with a small power, and consequently has a large field of view—when directed to any object, it is easily found, and being brought to the centre of the field, where two cross hairs intersect each other, it will then be seen in the larger telescope. B is the eye-tube for terrestrial objects, containing 4 glasses, and C, one of the astronomical eye-pieces. A socket is represented at g, containing a stained glass, which is screwed to any of the eye-pieces, to protect the eye from the glare of light, when viewing the spots of the sun. The brass nut above f, is intended for the adjustment of the eye-piece to distinct vision. The 3½ feet telescope is sometimes mounted in this form.

Fig. 59, represents a 5 or 6 feet telescope, mounted on a stand of a new construction by Dollond. It possesses the advantage of supporting the telescope in two places, which renders it extremely steady—a property of great importance when viewing celestial objects with high magnifying powers. It possesses likewise, the advantage of enabling the observer to continue seated at the same height from the floor, although the telescope be raised to any altitude—the elevation being entirely at the object end, although it may be changed from the horizon to the zenith. The frame-work is composed of bars of mahogany, and rests on three castors, two of which are made fast to their respective legs in the usual way, and the third stands under the middle of the lower horizontal bar that connects the two opposite legs, so that the frame has all the advantages of a tripod. As it becomes very inconvenient to stoop to the eye end of a telescope, when the altitude of an object is considerable, and the centre of motion at the middle of the tube, this construction of a stand serves to remedy such inconvenience.

Proportions of curvature of the lenses which form an achromatic object-glass.

As some ingenious mechanics may feel a desire to attempt the construction of a compound achromatic object-glass, I shall here state some of the proportions of curvature of the concave and convex lenses, which serve to guide opticians in their construction of achromatic instruments. These proportions are various; and even when demonstrated to be mathematically correct, it is sometimes difficult to reduce them to practice, on account of the different powers of refraction and dispersion possessed by different discs of crown and flint-glass, and of the difficulty of producing by mechanical means, the exact curves which theory requires. The following table shows the radii of curvature of the different surfaces of the lenses necessary to form a double achromatic object-glass—it being supposed that the sine of refraction in the crown-glass is as 1.528 to 1, and in the flint as 1.5735 to 1; the ratio of their dispersive powers being as 1 to 1.524. It is also assumed that the curvatures of the concave lens are as 1 to 2, that is, that the one side of this lens is ground on a tool, the radius of which is double that of the other. The 1st column expresses the compound focus of the object-glass in inches; the 2nd column states the radius of the anterior surface of the crown, and column 3rd, its posterior side. Column 4th expresses the radius of the anterior surface of the concave lens, and column 5th its posterior surface, which, it will be observed, is exactly double that of the other.

From the above table it will be seen, that to construct, for example, a 30 inch compound object-glass, the radius of the anterior side of the crown must be 7½ inches, and that of the posterior side 11.63 inches; the radius of the anterior surface of the concave 10.428, and that of the posterior 20.856 inches. It may be proper to observe, that in these computations, the radius of the anterior surface of the concave is less than the posterior side of the convex, and consequently admits of its approach, without touching in the centre—a circumstance which always requires to be guarded against in the combination of achromatic glasses. The following table shows the radii of curvature of the lenses of a triple object-glass, calculated from formula deduced by Dr. Robison of Edinburgh.

The following table contains the proportions of curvature, said to be employed by the London opticians.

From this table it appears, that the two convex lenses, have the same radii of their respective sides and that the concave flint lens has its two surfaces equally concave, so that a triple object-glass formed according to these proportions, would require only three pair of grinding tools. The following are the curves of the lenses of one of the best of Dollond’s achromatic telescopes, the focal length of the compound object-glass being 46 inches. Reckoning from the surface next the object—the radii of the crown-glass were 28 and 40 inches: the concave lens 20.9 inches, and the inner crown-glass lens, 28.4 and 28.4 inches. This telescope carried magnifying powers of from 100 to 200 times.

Although I have inserted the above tables, which might in some measure guide an ingenious artist, yet on the whole, a private amateur has little chance in succeeding in such attempts. The diversity of glasses, and the uncertainty of an unpractised workman’s producing the precise curvatures he intends, is so great, that the object-glass, for the most part, turns out different from his expectations. The great difficulty in the construction is to find the exact proportion of the dispersive powers of the crown and flint glass. The crown is pretty constant, but there are hardly two pots of flint glass which have the same dispersive power. Even if constant, it is difficult to measure it accurately; and an error in this greatly affects the instrument; because the focal distances of the lenses must be nearly as their dispersive powers. In the two preceding tables, the sine of incidence, in the crown glass, is supposed to be to the sine of refraction as 1.526 to 1; and in the flint glass, as 1.604 to 1. Opticians who make great numbers of lenses both of flint and crown glass, acquire, in time, a pretty good guess of the nature of the errors which may remain after they have finished an object-glass; and having many lenses intended to be of the same form, but unavoidably differing a little from it, they try several of the concaves with the two convexes, and finding one better than the rest, they make use of it to complete the set. In this way some of the best achromatic telescopes are frequently formed. I have sometimes found, when supplying a concave flint glass to a telescope where it happened to be wanting, that, of four or five concave lenses which appeared to be the same as to curvature and other properties, only one was found to produce a distinct and colourless image. Should any one, however, wish to attempt the construction of an achromatic lens, the best way for preventing disappointments in the result is, to procure a variety of tables of the respective curvatures founded on different conditions, and which, of course, require the surfaces of the several lenses to be of different curves. Having lenses of different radii at his command, and having glass of different refractive or dispersive powers, when one combination does not exactly suit, he may try another, and ultimately may succeed in constructing a good achromatic telescope; for, in many cases, it has been found that chance, or a happy combination of lenses by trial, has led to the formation of an excellent object-glass.

Achromatic telescopes composed of fluid lenses.

The best achromatic telescopes, when minutely examined, are found to be in some respects defective, on account of that slight degree of colour which, by the aberration of the rays, they give to objects, unless the object-glass be of small diameter. When we examine with attention a good achromatic telescope we find that it does not show white or luminous objects perfectly free from colour, their edges being tinged on one side with a claret-coloured fringe, and on the other with a green fringe. This telescope, therefore, required farther improvement, to get rid of these secondary colours, and Father Boscovich, to whom every branch of optics is much indebted, displayed much ingenuity in his attempts to attain this object. But it is to Dr. Blair, professor of astronomy in Edinburgh, that we are chiefly indebted for the first successful experiments by which this end was accomplished. By a judicious set of experiments, he proved that the quality of dispersing the rays in a greater degree than crown-glass, is not confined to a few mediums; but is possessed by a great variety of fluids, and by some of these in a most extraordinary degree. Having observed that when the extreme red and violet rays were perfectly united, the green were left out, he conceived the idea of making an achromatic concave lens which should refract the green less than the united red and violet, and an achromatic convex lens which should do the same, and as the concave lens refracted the outstanding green to the axis, while the concave one refracted them from the axis, it followed, that, by a combination of these two opposite effects, the green would be united with the red and violet.

By means of an ingenious prismatic apparatus, he examined the optical properties of a great variety of fluids. The solutions of metals and semi-metals proved in all cases more dispersive than crown glass. Some of the salts, such as sal-ammoniac, greatly increased the dispersive power of water. The marine acid disperses very considerably, and this quality increases with its strength. The most dispersive fluids were accordingly found to be those in which this acid and the metals were combined. The chemical preparation called causticum antimoniale, or butter of antimony, in its most concentrated state, when it has just attracted sufficient humidity to render it fluid, possesses the quality of dispersing the rays in an astonishing degree. The great quantity of the semi-metal retained in solution, and the highly concentrated state of the marine acid, are considered as the cause of this striking effect. Corrosive sublimate of mercury, added to a solution of sal-ammoniacum in water, possesses the next place to the butter of antimony among the dispersive fluids, which Dr. Blair examined. The essential oils were found to hold the next rank to metallic solutions, among fluids which possess the dispersive quality, particularly those obtained from bituminous minerals, as native petrolea, pit coal, and amber. The dispersive power of the essential oil of sassafras, and the essential oil of lemons, when genuine, were found to be not much inferior to any of these. But of all the fluids fitted for optical purposes, Dr. Blair found that the muriatic acid mixed with a metallic solution, or, in other words, a fluid in which the marine acid and metalline particles, hold a due proportion, most accurately suited his purpose. In a spectrum formed by this fluid the green were among the most refrangible rays, and when its dispersion was corrected by that of glass, there was produced an inverted secondary spectrum, that is, one in which the green was above, when it would have been below with a common medium. He therefore placed a concave lens of muriatic acid with a metallic solution between the two lenses, as in fig. 60, where AB is the concave fluid lens, CF a plano-convex lens, with its plane side next the object, and ED, a meniscus. With this object-glass the rays of different colours were bent from their rectilineal course with the same equality and regularity as in reflection.

Telescopes constructed with such object-glasses were examined by the late Dr. Robison and professor Playfair. The focal distance of the object-glass of one of these did not exceed 17 inches, and yet it bore an aperture of 3½ inches. They viewed some single and double stars and some common objects with this telescope; and found, that, in magnifying power, brightness, and distinctness, it was manifestly superior to one of Mr. Dollond of 42 inches focal length. They had most distinct vision of a star, when using an erecting eye-piece, which made this telescope magnify more than a 100 times; and they found the field of vision as uniformly distinct as with Dollond’s 42 inch telescope magnifying 46 times; and were led to admire the nice figuring and centering of the very deep eye-glasses which were necessary for this amplification. They saw double stars with a degree of perfection which astonished them. These telescopes, however, have never yet come into general use; and one reason perhaps, is, that they are much more apt to be deranged, than telescopes constructed of object-glasses which are solid. If any species of glass, or other solid transparent substance could be found with the same optical properties, instruments might perhaps be constructed of a larger size, and considerably superior to our best achromatic telescopes.23 It is said that Mr. Blair, the son of Dr. Blair, some years ago, was engaged in prosecuting his father’s views, but I have not heard any thing respecting the result of his investigations.

Barlow’s refracting telescope with a fluid concave lens.

Professor Barlow, not many years ago, suggested a new fluid telescope, which is deserving of attention; and, about the year 1829 constructed one of pretty large dimensions. The fluid he employs for this purpose is the sulphuret of Carbon, which he found to be a substance which possessed every requisite he could desire. Its index is nearly the same as that of the best flint glass, with a dispersive power more than double. It is perfectly colourless, beautifully transparent, and although very expansible, possesses the same, or very nearly the same optical properties under all circumstances to which it is likely to be exposed in astronomical observations—except perhaps, direct observations on the solar disc, which will probably be found inadmissible. Mr. Barlow first constructed an object-glass with this fluid of 3 inches aperture, with which he could see the small star in Polaris with a power of 46, and with the higher powers several stars which are considered to require a good telescope, for example 70, ? Ophinchi, 39 Bootis, the quadruple star e LyrÆ, ? Aquarii, a Herculis, &c. He next constructed a 6 inch object-glass. With this instrument the small star in Polaris is so distinct and brilliant, with a power of 143, that its transit might be taken with the utmost certainty. As the mode of constructing these telescopes is somewhat novel, it may be expedient to enter somewhat into detail.

In the usual construction of achromatic telescopes, the two or three lenses composing the object-glass are brought into immediate contact; and in the fluid telescope of Dr. Blair, the construction was the same, the fluid having been enclosed in the object-glass itself. But in Mr. Barlow’s telescope, the fluid correcting lens is placed at a distance from the plate lens equal to half its focal length; and it might be carried still farther back, and yet possess dispersive power to render the object-glass achromatic. By this means the fluid lens—which is the most difficult part of the construction—is reduced to one half or to less than one half of the size of the plate lens; consequently, to construct a telescope of 10 or 12 inches aperture involves no greater difficulty in the manipulation, than in making a telescope of the usual description of 5 or 6 inches aperture, except in the simple plate lens itself; and, hence, a telescope of this kind, of 10 or 12 feet length, will be equivalent in its focal power to one of 16 or 20 feet. By this means, the tube may be shortened several feet and yet possess a focal power more considerable than could be conveniently given to it on the usual principle of construction. This will be better understood from the annexed diagram. (fig. 61.)

In this figure ABCD represent the tube of the 6 inch telescope, CD, the plate object-glass, F the first focus of rays, de the fluid concave lens, distant from the former 24 inches. The focal length MF being 48, and consequently, as 48 : 6 :: 24 : 3 inches, the diameter of the fluid lens. The resulting compound focus is 62.5 inches. It is obvious, therefore, that the rays df, ef, arrive at the focus under the same convergency, and with the same light as if they proceeded from a lens of 6 inches diameter, placed at a distance beyond the object-glass CD (as GH,) determined by producing those rays till they meet the sides of the tube in GH, namely at 62.5 inches beyond the fluid lens. Hence, it is obvious, the rays will converge as they would do from an object-glass GH of the usual kind with a focus of 10 feet 5 inches. We have thus, therefore, shortened the tube 38.5 inches, or have at least the advantage of a focus 38.5 inches longer than our tube; and the same principle may be carried much farther, so as to reduce the usual length of refracting telescopes nearly one half without increasing the aberration in the first glass beyond the least that can possibly belong to a telescope of the usual kind of the whole length. It should likewise be observed that the adjustment for focus may be made either in the usual way, or by a slight movement of the fluid lens, as in the Gregorian Reflectors, by means of the small speculum.

Mr. Barlow afterwards constructed another and a larger telescope on the same principle, the clear aperture of which is 7.8 inches. Its tube is 11 feet, which, together with the eye-piece, makes the whole length 12 feet, but its effective focus is on the principle stated above, 18 feet. It carries a power of 700 on the closest double stars in South’s and Herschel’s catalogue, and the stars are, with that power, round and defined, although the field is not then so bright as could be desired. The telescope is mounted on a revolving stand, which works with considerable accuracy as an azimuth and altitude instrument. To give steadiness to the stand it has been made substantial and heavy; its weight by estimation being 400 pounds, and that of the telescope 130 pounds, yet its motions are so smooth, and the power so arranged, that it may be managed by one person with the greatest ease, the star being followed by a slight touch, scarcely exceeding that of the keys of a piano-forte. The focal length of the plate lens is 78 inches, and of the fluid lens 59.8 inches—which at the distance of 40 inches produce a focal length of 104 inches, a total length of 12 feet, and an equivalent focus of 18 feet. The curves of the parallel meniscus checks for containing the fluid are—30 inches, and 144 inches, the latter towards the eye. The curves for the plate lens are 56.4 and 144. There is an interior tube 5 inches diameter, and 3 feet 6 inches long, which carries the cell in which the fluid is enclosed, and an apparatus by which it may be moved backwards and forwards, so that the proper adjustment may be made for colour, in the first instance, and afterwards the focus is obtained by the usual rack-work motion. The following is the mode by which the fluid was enclosed. After the best position has been determined practically for the checks forming the fluid lens, these, with the ring between them ground and polished accurately to the same curves, are applied together, and taken into an artificial high temperature, exceeding the greatest at which the telescope is ever expected to be used. After remaining here with the fluid some time, the space between the glasses is completely filled, immediately closed, cooled down by evaporation, and removed into a lower temperature. By this means a sudden condensation takes place, an external pressure is brought on the checks, and a bubble formed inside, which is of course filled with the vapour of the fluid; the excess of the atmospheric pressure beyond that of the vapour being afterwards always acting externally to prevent contact. The extreme edges are then sealed with the serum of human blood, or by strong fish-glue, and some thin pliable metal surface. By this process, Mr. Barlow says, ‘I have every reason to believe the lens becomes as durable as any lens of solid glass. At all events I have the satisfaction of stating, that my first 3 inch telescope has now been completed more than fifteen months, and that no change whatever has taken place in its performance, nor the least perceptible alteration either in the quantity or the quality of the fluid.’

The following are some of the observations which have been made with this telescope, and the tests to which it has been subjected. The very small star which accompanies the pole-star is generally one of the first tests applied to telescopes. This small point of light appeared brilliant and distinct; it was best seen with a power of 120, but was visible with a power of 700. The small star in Aldebaran was very distinct with a power of 120. The small star a LyrÆ was distinctly visible with the same power. The small star called by Sir J. Herschel Debilissima, between 4 e and 5 LyrÆ, whose existence, he says, could not be suspected in either the 5 or 7 feet equatorial, and invisible also with the 7 and 10 feet reflectors of six and 9 inches aperture, but seen double with the 20 feet reflector, is seen very satisfactorily double with this telescope. ? Persei, marked as double in South and Herschel’s catalogue, at the distance of 28´´, with another small star at the distance of 3´ 67´´, is seen distinctly sixfold, four of the small stars being within a considerably less distance than the remote one of ? marked in the catalogue. And, rejecting the remote star, the principal, and the four other stars, form a miniature representation of Jupiter and his satellites, three of them being nearly in a line on one side, and the other on the opposite. Castor, is distinctly double with 120, and well opened and stars perfectly round with 360 and 700: ? Leonis and a Piscium are seen with the same powers equally round and distinct. In e Bootis, the small star is well separated from the larger, and its blue colour well marked with a power of 360. ? CoronÆ Borealis is seen double with a power of 360 and 700. 52 Orionis, ? Orionis, and others of the same class are also well defined with the same powers. In regard to the planets which happened to be visible—Venus appeared beautifully white and well defined with a power of 120, but showed some colour with 360. Saturn with the 120 power, is a very brilliant object, the double ring and belts being well and satisfactorily defined, and with the 360 power, it is still very fine. The moon also is remarkably beautiful, the edges and the shadows being well marked, while the quantity of light is such as to bring to view every minute distinction of figure and shade.

The principal objections that may be made to this construction of a telescope are such as these:—Can the fluid be permanently secured? Will it preserve its transparency and other optical properties? Will it not act upon the surface of the glass and partially destroy it? &c. To such enquiries Mr. Barlow replies, that experience is the only test we have; our spirit levels, spirit thermometers, &c., show that some fluids at least may be preserved for many years, without experiencing any change, and without producing any in the appearance of the glass tubes containing them. But should any of these happen, except the last, nothing can be more simple than to supply the means of replacing the fluid at any time, and by any person, without disturbing the adjustment of the telescope. He expresses his hope that, should these experiments be prosecuted, an achromatic telescope may ultimately be produced which shall exceed in aperture and power, any instruments of the kind hitherto attempted. If the prejudice against the use of fluids could be removed, he feels convinced that well-directed practice would soon lead to the construction of the most perfect instruments, on this principle, at a comparatively small expense. ‘I am convinced,’ he says, ‘judging from what has been paid for large object-glasses, that my telescope, telescope stand, and the building for observation, with every other requisite convenience, have been constructed for a less sum than would be demanded for the object-glass only, if one could be produced of the same diameter of plate and flint-glass; and this is a consideration which should have some weight, and encourage a perseverance in the principle of construction.’24

ROGERS’ ACHROMATIC TELESCOPE ON A NEW PLAN.

The object of this construction is to render a small disc of flint-glass available to perform the office of compensation to a much larger one of crown-glass, and thus to render possible the construction of telescopes of much larger aperture than are now common, without hindrance from the difficulty at present experienced in procuring large discs of flint-glass. It is well known to those who are acquainted with telescopes, that in the construction of an ordinary achromatic object-glass, in which a single crown lens is compensated by a single one of flint, the two lenses admit of being separated only by an interval too small to afford any material advantage, in diminishing the diameter of the flint lens, by placing it in a narrower part of the cone of rays—the actual amount of their difference in point of dispersive power being such as to render the correction of the chromatic aberration impossible, when their mutual distance exceeds a certain limit. This inconvenience Mr. Rogers proposes to obviate, by employing, as a correcting lens—not a single lens of flint, but a compound one consisting of a convex crown and concave flint, whose foci are such as to cause their combination to act as a plain glass on the mean refrangible rays. Then it is evident, that by means of the greater dispersive power of flint than of crown glass, this will act as a concave on the violet, and as a convex on the red rays, and that the more powerfully, according as the lenses separately have greater powers or curvature. If then, such a compound lens be interposed between the object-glass of a telescope—supposed to be a single lens of plate or crown-glass—and its focus, it will cause no alteration in the focus for mean rays, while it will lengthen the focus for violet, and shorten it for red rays. Now this is precisely what is wanted to produce an achromatic union of all the rays in the focus; and as nothing in this construction limits the powers of the individual correcting lenses, they may therefore be applied any where that convenience may dictate; and thus, theoretically speaking, a disc of flint-glass, however small, may be made to correct the colour of one of crown however large.

This construction, likewise, possesses other and very remarkable advantages. For, first, when the correcting lens is approximately constructed on a calculation founded on its intended aperture, and on the refractive and dispersive indices of its materials, the final and complete dispersion of colour may be effected, not by altering the lenses by grinding them anew, but by shifting the combination nearer to, or farther from, the object-glass, as occasion may require, along the tube of a telescope, by a screw motion, till the condition of achromaticity is satisfied in the best manner possible. And secondly, the spherical aberration may in like manner be finally corrected, by slightly separating the lenses of the correcting glass, whose surfaces should for this purpose be figured to curvatures previously determined by calculation, to admit of this mode of correction—a condition which Mr. Rogers finds to be always possible. The following is the rule he lays down for the determination of the foci of the lenses of the correcting glass:—‘The focal length of either lens of the correcting lens is to that of the object-glass, in a ratio compounded of the ratio of the square of the aperture of the correcting lens to that of the object-glass, and of the ratio of the difference of the dispersive indices of the crown and flint glass, to the dispersive index of crown.’ For example, to correct the colour of a lens of crown or plate glass of 9 inches aperture, and 14 feet focal length (the dimensions of the telescope of Fraunhofer at Dorpat) by a disc of flint glass 3 inches in diameter, the focus of either lens of the correcting lens will require to be about 9 inches. To correct it by a 4 inch disc will require a focus of about 16 inches each.

Mr. Rogers remarks, that it is not indispensable to make the correcting glass act as a plane lens. It is sufficient if it be so adjusted as to have a shorter focus for red rays than for violet. If, preserving this condition, it be made to act as a concave lens, the advantage procured by Mr. Barlow’s construction of reducing the length of the telescope with the same focal power, is secured, and he considers, moreover, that by a proper adaptation of the distances, foci, &c., of the lenses, we might hope to combine with all these advantages that of the destruction of the secondary spectrum, and thus obtain a perfect telescope.

The above is an abstract of a paper read to the ‘Astronomical Society of London’ in April 1828, by A. Rogers, Esq.

The reader will easily perceive that the principle on which Mr. Rogers proposes to construct his telescope is very nearly similar to that of professor Barlow, described above, with this difference, that the correcting lens of the Professor’s telescope is composed of a transparent fluid, while that of Mr. Rogers is a solid lens consisting of a convex crown and concave flint. The general object intended to be accomplished by both is the same, namely, to make a correcting lens of a comparatively small diameter serve the purpose of a large disc of flint glass, which has hitherto been very expensive, and very difficult to be procured; and likewise to reduce the length of the telescope while the advantage of a long focal power is secured.—A telescope, on this principle, was constructed 7 or 8 years ago by Mr. Wilson, lecturer on Philosophy and Chemistry, Glasgow, before he was aware that Mr. Rogers had proposed a similar plan. I have had an opportunity of particularly inspecting Mr. Wilson’s telescope, and trying its effects on terrestrial objects with high powers, and was on the whole highly pleased with its performance. It appeared to be almost perfectly achromatic, and produced a distinct and well-defined image of minute distant objects, such as small letters on sign-posts, at 2, 3 and 4 miles distant. But I had no opportunity of trying its effects on double stars or any other celestial objects. The instrument is above 6 feet long; the object lens is a plano-convex of crown glass 4 feet focal distance, and 4 inches diameter, the plain side next the object.

At 26 inches distant from the object lens is the compound lens of 2 inches in diameter; and the two lenses of which it is composed are both ground to a radius of 3¾ inches. That made of crown glass is plano-convex, the other, made of flint glass, is plano-concave, and are placed close together, the convex side being next the object, and the concave side next the eye. The greater refractive power of the flint glass renders the compound one slightly concave in its effect (although the radius of curvature is similar in both), and lengthens the focus to 6 feet from the object-glass; and this is consequently the length of the instrument. The compound corrector so placed intercepts all those rays which go to form the image in the field of view, producing there an achromatic image. The concave power of the corrector renders the image larger than if directly produced by a convex lens of the same focus. The concavity of the corrector is valuable also in this respect, that a very slight alteration in its distance from the object-glass, changes the focal distance much more than if it were plain, and enables us to adjust the instrument to perfect achromatism with great precision.

CHAPTER V.

ON REFLECTING TELESCOPES.

SECT. 1.—HISTORY OF THE INVENTION, AND A GENERAL DESCRIPTION OF THE CONSTRUCTION OF THESE INSTRUMENTS.

Reflecting telescopes are those which represent the images of distant objects by reflection, chiefly from concave mirrors.

Before the achromatic telescope was invented, there were two glaring imperfections in refracting telescopes, which the astronomers of the 17th century were anxious to correct. The first was its very great length when a high power was to be applied, which rendered it very unwieldy and difficult to use. The second imperfection was the incorrectness of the image as formed by a single lens. Mathematicians had demonstrated that a pencil of rays could not be collected in a single point by a spherical lens, and also that the image transmitted by such a lens would be in some degree incurvated. After several attempts had been made to correct this imperfection by grinding lenses to the figure of one of the conic sections, Sir I. Newton happened to commence an examination of the colours formed by a prism; and having, by the means of this simple instrument, discovered the different refrangibility of the rays of light—to which we have several times adverted in the preceding descriptions—he then perceived that the errors of telescopes, arising from that cause alone, were some hundred times greater than such as were occasioned by the spherical figure of lenses; which induced this illustrious philosopher to turn his attention to the improvement of telescopes by reflection.

It is generally supposed that Mr. James Gregory—a son of the Rev. John Gregory, minister of Drumoak in the county of Aberdeen—was the first who suggested the construction of a reflecting telescope. He was a young man of uncommon genius, and an eminent mathematician; and in the year 1663, at the age of only 24, he published in London, his treatise entitled ‘Optica Promota,’ in which he explained the theory of that species of reflecting telescope which still bears his name, and which he stated as being his own invention. But as Gregory, according to his own account, was endowed with no mechanical dexterity, and could find no workman capable of realizing his invention—after some fruitless attempts to form proper specula, he was obliged to give up the pursuit; so that this telescope remained for a considerable time neglected. It was several years after Gregory suggested the construction of reflecting telescopes, till Newton directed his attention fully to the subject. In a letter addressed to the secretary of the Royal Society, dated in February, 1672, he says, ‘Finding reflections to be regular, so that the angle of reflection of all sorts of rays was equal to the angle of incidence, I understood that, by their mediation, optic instruments might be brought to any degree of perfection imaginable, providing a reflecting substance could be found which would polish as finely as glass, and reflect as much light as glass transmits, and the art of communicating to it a parabolic figure be also obtained. Amidst these thoughts I was forced from Cambridge by the intervening plague, and it was more than two years before I proceeded further.’

It was towards the end of 1668, or in the beginning of the following year, when Newton, being obliged to have recourse to reflectors, and not relying on any artificer for making the specula, set about the work himself, and early in the year 1672, completed two small reflecting telescopes. In these he ground the great speculum into a spherical concave, although he approved of the parabolic form, but found himself unable to accomplish it. These telescopes were of a construction somewhat different from what Gregory had suggested, and though only 6 inches long, were considered as equal to a 6 feet common refracting telescope. It is not a little singular, however, that we hear no more about the construction of reflectors till more than half a century afterwards. It was not till the year 1723, that any reflectors were known to have been made, adapted to celestial observations. In that year, Mr. Hadley, the inventor of the reflecting quadrant, which goes by his name, published in No. 376 of the Philosophical Transactions, an account of a large reflector on Newton’s plan, which he had just then constructed, the performance of which left no room to doubt that this invention would remain any longer in obscurity. The large speculum of this instrument was 62? inches focal distance and 5 inches diameter, was furnished with magnifying powers of from 190 to 230 times, and equalled in performance the famous aerial telescope of Huygens of 123 feet in length.25 Since this period, the reflecting telescope has been in general use among astronomers in most countries of Europe, and has received numerous improvements, under the direction of Short, Mudge, Edwards and Herschel—the last of whom constructed reflectors of 7, 10, 20, and even 40 feet in focal length, which far surpassed, in brightness and magnifying power, all the instruments of this description, which had previously been attempted.

I shall now proceed to give a brief sketch of the nature of a reflecting telescope, and the different forms in which they have been proposed to be constructed.

Fig. 62 represents the reflecting telescope as originally proposed by Gregory. ABEF represents a tube open at AF towards the object; at the other end is placed a concave speculum BE, with a hole CD in its centre, the focus of which is at e. A little beyond this focus, towards the object end of the telescope AF, is placed another small concave mirror G, having its polished face turned towards the great speculum, and is supported by an arm GH fastened to a slider connected with the tube. At the end of the great tube BE is screwed in a small tube CDKI, containing a small plano-convex lens IK. Such are the essential parts of this instrument and their relative positions. It will be recollected in our description of the properties of concave mirrors (see page 92), that, when rays proceed from a distant object, and fall upon a concave-speculum, they paint an image or representation of the object in its focus before the speculum. Now suppose two parallel rays ab falling on the speculum BE, in cd; they are reflected to its focus e where an inverted image of the object is formed. This image is formed at a little more than the focal distance of the small speculum from its surface, and serves as it were for an object on which the small mirror may act. By the action of this mirror this first image is reflected to a point about f, where a second image is formed very large and erect. This image is magnified in the proportion of fG to eG, the rays from which are transmitted to the eye glass IK, through which the eye perceives the object clear and distinct, after the proper adjustments have been made.

Suppose the focal distance of the great mirror was 9 inches, and the focal distance of the small mirror 1½ inch—were we to remove the eye piece of this telescope, and look through the hole of the great mirror, we should see the image of the object depicted upon the face of the small speculum, and magnified, in the proportion of 9 to 1½, or, 6 times, on the same principle as a common convex object glass 9 inches focal length, with an eye glass whose focus is 1½ inch magnifies 6 times. This may be regarded as the first part of the magnifying power. If now, we suppose the small speculum placed a little more than 1½ inch from the image formed by the great speculum, a second image is formed about f, as much exceeding the first in its dimensions as it exceeds it in distance from the small speculum, on the principle on which the object glass of a compound microscope forms a large image near the eye glass. Suppose this distance to be 9 times greater, then the whole magnifying power will be compounded of 6 multiplied by 9, or 54 times. As a telescope it magnifies 6 times, and in the microscope part 9 times.—Such is a general idea of the Gregorian telescope, the minute particulars and structure of which can only be clearly perceived by a direct inspection of the instrument.

The Newtonian Reflector.—This instrument is somewhat different both in its form and in its mode of operation from that of Gregory. It is represented in fig. 63, where BAEF is the tube, and BE, the object concave mirror, which reflects the parallel rays ab to a plane speculum G, placed 45°, or half a right angle to the axis of the concave speculum. This small plane reflector must be of an oval form, the length of the oval should be to the breadth as 7 to 5, on account of the obliquity of its position. It is supported on an arm fixed to the side of the tube; an eye-glass is placed in a small tube, moveable in the larger tube, so as to be perpendicular to the axis of the large reflector, the perpendicular line passing through the centre of the small mirror. The small mirror is situated between the large mirror and its focus, that its distance from this focal point may be equal to the distance from the centre of the mirror to the focus of the eye-glass. When the rays ab from a distant object fall upon the large speculum at cd, they are reflected towards a focus at h; but being intercepted by the plane mirror G, they are reflected perpendicularly to the eye-glass at I, in the side of the tube, and the image formed near that position at e is viewed through a small plano-convex lens. The magnifying power of this telescope is in the proportion of the focal distance of the speculum to that of the eye-glass. Thus, if the focal distance of the speculum be 36 inches, and that of the eye-glass ¹/₃ of an inch, the magnifying power will be 108 times. It was this form of the reflecting telescope, that Newton invented, which Sir. W. Herschel adopted, and with which he made most of his observations and discoveries.

The Cassegrainian Reflector.—This mode of the reflecting telescope, suggested by M. Cassegrain, a Frenchman, is represented in fig. 64. It is constructed in the same way as the Gregorian, with the exception of a small convex speculum G being substituted in the room of the small concave in Gregory’s construction. As the focus of a convex mirror is negative, it is placed at a distance from the large speculum equal to the difference of their foci, that is, if the focal length of the large speculum be 18 inches, and that of the small convex 2 inches, they are placed at 16 inches distant from each other, on a principle similar to that of the Galilean telescope, in which the concave eye-glass is placed within the focus of the object-glass by a space equal to the focal length of the eye-glass. In this telescope, likewise, instead of two there is only one image formed, namely that in the focus of the eye-glass; and, on this account some are of opinion that the distinctness is considerably greater than in the Gregorian. Mr. Ramsden was of opinion that this construction is preferable to either of the former reflectors, because the aberrations of the two metals have a tendency to correct each other, whereas in the Gregorian both the metals being concave, any error in the specula will be doubled. It is his opinion that the aberrations in the Cassegrainian construction to that of the Gregorian is as 3 to 5. The length of this telescope is shorter than that of a Gregorian of equal focal length, by twice the focal length of the small mirror, and it shows every thing in an inverted position, and consequently is not adapted for viewing terrestrial objects.

Dr. Hook’s Reflector.—Before the reflecting telescope was much known, Dr. Hook contrived one, the form of which is represented, fig. 65, which differs in little or nothing from the Gregorian, except that the eye-glass I is placed in the hole of the great speculum BE.

Martin’s Reflector.—Mr. Bengamin Martin, a distinguished writer on optical and philosophical science, about a century ago, described a new form of the reflecting telescope, approximating to the Newtonian structure, which he contrived for his own use. It is represented in fig. 66. ABEF is the tube, in which there is an opening or aperture OP, in the upper part. Against this hole within the tube is placed a large plane speculum GH, at half a right angle with the axis or sides of the tubes, with a hole CD perforated through its middle. The parallel rays a b falling on the inclined plane GH are reflected perpendicularly and parallel on the great speculum BE in the bottom of the tube. From thence they are reflected converging to a focus e through the hole of the plane mirror CD, which being also the focus of the eye-glass IK, the eye will perceive the object magnified and distinct.

In the figures referred to in the above descriptions, only one eye-glass is represented to avoid complexity; but in most reflecting telescopes, the eye-piece consists of a combination of two plano-convex glasses, as in fig. 67, which produces a more correct and a larger field of view than a single lens. This combination is generally known by the name of the Huygenian eye-piece which shall be described in the section on the eye-pieces of telescopes.

The following rule has been given for finding the magnifying power of the Gregorian telescope:—Multiply the focal distance of the great mirror by the distance of the small mirror from the image next the eye; and multiply the focal distance of the small mirror by the focal distance of the eye-glass; then divide the product of the former multiplication by the product of the latter, and the quotient will express the magnifying power. The following are the dimensions of one of the reflecting telescopes constructed by Mr. Short—who was long distinguished as the most eminent maker of such instruments, on a large scale, and whose large reflectors are still to be found in various observatories throughout Europe.

The focal distance of the great mirror 9.6 inches; or P m, fig. 67, its breadth FD 2.3; the focal distance of the small mirror L n 1.5—or 1½ inch—its breadth g h 0.6—or ⁶/₁₀ of an inch; the breadth of the hole in the great mirror UV, 0.5—or half an inch—the distance between the small mirror and the next eye-glass LR, 14.2; the distance between the two eye-glasses SR, 2.4; the focal distance of the eye-glass next the metal, 3.8.; and the focal distance of the eye-glass next the eye, S a 1.1, or one inch and one tenth. The magnifying power of this telescope was about 60 times. Taking this telescope as a standard, the following table of the dimensions and magnifying powers of Gregorian reflecting telescopes, as constructed by Mr. Short, has been computed.

figure 67.

INDEX:
A: Focal distance of the great mirror.
B: Breadth of the great mirror.
C: Focus of the small speculum.
D: Breadth of the hole in the great speculum.
E: Distance between the small speculum and the first eye-glass.
F: Focal distance of the glass next the metals.
G: Focal distance of the glass next the eye.
H: Distance between the plain sides of the two glasses.
I: Magnifying power.
J: Distance between the second glass and the small eye-hole.

Mr. Short—who was born in Edinburgh in 1710, and died near London, 1768—was considered as the most accurate constructor of reflecting telescopes, during the period which intervened from 1732, to 1768. In 1743, he constructed a reflector for Lord Thomas Spencer, of 12 feet focal length, for which he received 600 guineas. He made several other telescopes of the same focal distance, with greater improvements and higher magnifiers; and in 1752, finished one for the king of Spain, for which, with its whole apparatus, he received £1200. This was considered the noblest instrument of its kind that had then been constructed, and perhaps it was never surpassed, till Herschel constructed his twenty and forty feet reflectors. High as the prices of large telescopes now are, Mr. Short charged for his instruments at a much higher rate than opticians now do, although the price of labour, and every other article required in the construction of a telescope, is now much dearer. But he had then scarcely any competitor, and he spared neither trouble nor expense to make his telescopes perfect, and put such a price upon them as properly repaid him. The following table contains a statement of the apertures, powers, and prices of Gregorian telescopes, as constructed by Mr. James Short.26

INDEX:
A: Number.
B: Focal length in inches.
C: Diameter of aperture in inches.
D: Prices in guineas.

From this table, it appears that Mr. Short charged 75 guineas for a 3 feet reflector, whereas such an instrument is now marked in the London opticians’ catalogues at £23, when mounted on a common brass stand, and £39. 18s., when accompanied with rack-work motions and other apparatus. It is now generally understood that in the above table, Short always greatly overrated the higher powers of his telescopes. By experiment they were generally found to magnify much less than here expressed.

General remarks on Gregorian Reflectors.—1. In regard to the hole UV, of the great speculum—its diameter should be equal, or nearly so, to that of the small speculum L, fig. 67. For if it be less, no more parallel rays will be reflected than if it were equal to g h, and it may do harm in contracting the visible area within too narrow limits. Nor must it be larger than the mirror L, because some parallel rays will then be lost, and those of most consequence as being nearest the centre. 2. The small hole at e to which the eye is applied, must be nicely adjusted to the size of the cone of rays proceeding from the nearest lens S. If it be larger, it will permit the foreign light of the sky or other objects to enter the eye, so as to prevent distinct vision; for the eye should receive no light, but what comes from the surface of the small mirror L. If the hole be smaller than the cylinder of rays at e then some of the necessary light will be excluded, and the object rendered more obscure. The diameter of this hole may be found by dividing the aperture of the telescope in inches by its magnifying power. Thus, if we divide the diameter of one of Short’s telescopes, the diameter of whose large speculum is 2.30, by 60, the magnifying power, the quotient will be .0383, which is nearly the ¹/₂₅ of an inch. Sometimes this hole is made so small as the ¹/₅₀ of an inch. When this hole is, by any derangement, shifted from its proper position, it sometimes requires great nicety to adjust it, and, before it is accurately adjusted, the telescope is unfit for accurate observation. 3. It is usual to fix a plate with a hole in it, at a b, the focus of the eye glass S, of such a diameter as will circumscribe the image, so as to exhibit only that part of it which appears distinct, and to exclude the superfluous rays. 4. There is an adjusting screw on the outside of the great tube, connected with the small speculum, by which that speculum may be pushed backwards or forwards to adjust the instrument to distinct vision. The hand is applied for this purpose at T.

Newtonian Telescopes.—These telescopes are now more frequently used for celestial observations than during the last century, when Gregorian reflectors were generally preferred. Sir W. Herschel was chiefly instrumental in introducing this form of the reflecting telescope to the more particular attention of astronomers, by the splendour and extent of the discoveries which it enabled him to make. In this telescope there is no hole required in the middle of the great speculum, as in the Gregorian construction, which circumstance secures the use of all the rays which flow from the central parts of the mirror.

The following table contains a statement of the apertures and magnifying powers of Newtonian Telescopes, and the focal distances of their eye-glasses. The first column contains the focal length of the great speculum in feet; the second, its linear aperture in inches; the third, the focal distance of the single glass in decimals, or in 1000ths of an inch, and the fourth column, contains the magnifying power. This portion of the table was constructed by using the dimensions of Mr. Hadley’s Newtonian Telescope, formerly referred to, as a standard—the focal distance of the great mirror being 62½ inches, its medium aperture 5 inches, and power 208. The fifth, sixth, and seventh columns contains the apertures of the concave speculum, the focal lengths of the eye-glasses and the magnifying powers, as calculated by Sir D. Brewster, from a telescope of Mr. Hauksbee, taken as a standard; whose focal length was 3 feet 3 inches, its aperture about 4 inches, and magnifying power 226 times.

INDEX:
A: Focal distance of concave metal.
B: Aperture of concave metal.
C: Focal distance of single eye-glass.
D: Magnifying power.
E: Aperture of the concave speculum.
F: Focal length of the eye-glass.
G: Magnifying power.

One great advantage of reflecting telescopes above common refractors, is, that they will admit of eye glasses of a much shorter focal distance, and consequently, will magnify so much the more, for the rays are not coloured by reflection from a concave mirror, if it be ground to a true figure, as they are by passing through a convex glass though figured and polished with the utmost exactness. It will be perceived from the above table, that the focal length of the eye glasses is very small, the lowest there stated being only about ¹/₁₀ of an inch, and the highest little more than ¼ of an inch focal distance. Sir W. Herschel obtained the high powers which he sometimes put upon his telescopes, by using small double convex lenses for eye glasses, some of which did not exceed the one fiftieth of an inch in focal length. When the focal length of the concave speculum, and that of the eye glass are given, the magnifying power is found by dividing the former by the latter, after having reduced the focal length of the concave speculum to inches. Thus the 6 feet speculum, multiplied by 12, produces 72 inches, which, divided by Brewster’s number for the focus of the eye glass = 200, or ¹/₅ of an inch, produces a quotient of 360 as the magnifying power. It has been calculated that, if the metals of a Newtonian telescope be worked as exquisitely as those in Sir W. Herschel’s 7 feet reflector, the highest power that such a telescope should bear with perfect distinctness, will be found by multiplying the diameter of the great speculum in inches, by 74, and the focal distance of the single eye glass may be found by dividing the focal distance of the great mirror by the magnifying power. Thus 6.25—the aperture in inches of Herschel’s 7 feet Newtonian—multiplied by 74 is 462½, the magnifying power; and 7 multiplied by 12, and divided by 462.5 is 0.182 of an inch, the focal distance of the single eye glass required. But it is seldom that more than one half of this power can be applied with effect to any of the planetary bodies. For general purposes the power produced by multiplying the diameter of the speculum by 30, or 40, will be found most satisfactory.

The following are the general prices of reflecting telescopes as made by the London opticians.

The above are the prices stated in Messrs. W. and S. Joneses catalogue.

The following list of prices of the various kinds of reflecting telescopes is from Messrs. Tulley’s (of Islington) catalogue.

Comparative brightness of achromatic and reflecting telescopes. The late astronomer royal, Dr. Maskelyne, from a comparison of a variety of telescopes, was led to the following conclusion,—‘that the aperture of a common reflecting telescope, in order to show objects as bright as the achromatic must be to that of an achromatic telescope as 8 to 5,’—in other words, an achromatic whose object glass is 5 inches diameter, will show objects with as great a degree of brightness as a reflector whose large speculum is 8 inches in diameter. This result, if correct, must be owing to the small number of rays reflected from a speculum compared with the number transmitted through an achromatic object glass.

SECT. 2.—THE HERSCHELIAN TELESCOPE.

Soon after Sir William Herschel commenced his astronomical career, he introduced a new era in the history of reflecting telescopes. After he had cast and polished an immense variety of specula for telescopes of different sizes-he, at length, in the year 1782, finished a 20 feet reflector with a large aperture. Being sensible of the vast quantity of light which is lost by a second reflection from the small speculum, he determined to throw it aside altogether, and mounted this 20 feet reflector on a stand that admitted of being used without a small speculum in making front observations—that is, in sitting with his back to the object, and looking directly towards the surface of the speculum. Many of his discoveries and measurements of double stars were made with this instrument, till, at length, in the year 1785 he put the finishing hand to that gigantic speculum, which soon became the object of universal astonishment, and which was intended for his forty feet reflecting telescope; he had succeeded so well in constructing reflecting telescopes of comparatively small aperture, that they would bear higher magnifying powers than had ever previously been applied; but he found that a deficiency of light could only be remedied by an increased diameter of the large speculum, which therefore was his main object, when he undertook to accomplish a work which to a man less enterprising, would have appeared impracticable. The difficulties he had to overcome were numerous; particularly in the operative department of preparing, melting, annealing, grinding, and polishing a mass of metal that was too unwieldly to be moved without the aid of mechanical powers. At length, however, all difficulties having been overcome, this magnificent instrument was completed with all its complicated apparatus, and erected for observation, on the 28th of August, 1789, and on the same day the sixth satellite of Saturn was detected, as a prelude of still farther discoveries which were afterwards made by this instrument, in the celestial regions.

It would be too tedious to attempt a description of all the machinery and apparatus connected with this noble instrument. The reader who wishes to peruse a minute description of the stairs, ladders, platform, rollers, and of every circumstance relating to joiner’s work, carpenter’s work, smith’s work, and other particulars connected with the formation and erection of this telescope, will find the details recorded in the 85th volume of the Philosophical Transactions of the Royal Society of London, for 1795, in which there are sixty-three pages of letter press, and eighteen plates illustrative of the subject. I shall content myself with giving a short outline of the essential parts belonging to this instrument.

The tube of this telescope is made of rolled or sheet iron, joined together without rivets; the thickness of the sheets is somewhat less than ¹/₃₆ part of an inch, or 14 pounds weight for a square foot; great care was taken that the cylindrical form should be secured, and the whole was coated over three or four times with paint, inside and outside, to secure it against the damp. This tube was removed from the place in which it was formed by twenty-four men, divided into six sets; so that two men on each side, with a pole of 5 feet long in their hands, to which was affixed a piece of course cloth, 7 feet long going under the tube, and joined to a pole 5 feet long, in the hands of two other men, assisted in carrying the tube. The length of this tube is 39 feet 4 inches, the diameter 4 feet 10 inches; and, on a moderate computation, it was ascertained, that a wooden tube of proper dimensions would have exceeded an iron one in weight by at least 3000 pounds. Reckoning the circumference of the tube 15 feet, its length 39? feet, and 14 lib. for the weight of a square foot, it must have contained 590 square feet, and weighed 8,260 pounds. Various hoops were fixed within the tube, and longitudinal bars of iron connecting some of them are attached to the two ends of the tube, by way of bracing the sheets, and preserving the shape perfect, when the pulleys are applied to give the necessary elevation at the upper end, and that the speculum may be kept secure at the lower end. The lower end of the tube is firmly supported on rollers that are capable of being moved forwards or backwards by a double rack, connected with a set of wheels and pinions. By an adjustment at the lower extremity of the tube, the speculum is turned to a small inclination, so that the line of collimation may not be coincident with the longitudinal axis of the tube, but may cross the tube diagonally, and meet the eye in the air at about two inches from the edge of the tube, which is the peculiarity of the construction, that supersedes the necessity of applying a second reflector. Hence no part of the head of the observer intercepts the incident rays, and the observation is taken with the face looking at the speculum, the back being turned to the object to be observed.

The large speculum is enclosed in a strong iron ring, braced across with bars of iron, and an enclosure of iron and ten sheets makes a case for it. It is lifted by three handles of iron attached to the sides of the ring, and is put into and taken out of its proper place in the tube by the help of a moveable crane, running on a carriage, which operation requires great care. The speculum is made of a metallic composition, and is 49½ inches in diameter; but the concave polished surface is only 48 inches, or 4 feet in diameter. Its thickness is 31 inches; and when it came from the cast its weight was 2118 pounds. The metals for its formation were procured at a warehouse in Thames Street, London, where they kept ingots of two kinds ready made, one of white, and the other of bell-metal; and it was composed of two ingots of bell-metal for one of white. It was not to be expected that a speculum of such large dimensions, could have a perfect figure imparted to its surface, nor that the curve, whatever it might be, would remain identically the same in changes of temperature; therefore we are not surprised when we are told, that the magnifying powers used with this telescope seldom exceeded 200; the quantity of light collected by so large a surface being the principal aim of the maker. The raising of the balcony, on which the observer stands, and the sliding of the lower end of the tube, in which the speculum rests, are effected by separate tackles, and require only occasional motions; but the elevation of the telescope requires the main tackle to be employed, and the motion usually given in altitude at once was two degrees; the breadth of the zone in which the observations were made, as the motion of the sphere in right ascension brought the objects into view. A star, however, could be followed for about a quarter of an hour. Three persons were employed in using this telescope, one to work the tackle, another to observe, and a third to mark down the observations. The elevation was pointed out by a small quadrant fixed to the main tube, near the lower end, but the polar distance was indicated by a piece of machinery, worked by a string, which continually indicated the degree and minute on a dial in the small house adjoining, while the time was shown by a clock in the same place, Miss Herschel performing the office of Registrar.

At the upper end the tube is open, and directed to the part of the heavens intended for observation, and the observer, standing on the foot board, looks down the tube, and perceives the object by rays reflected from the speculum, through the eye glass at the opening of the tube. When the telescope is directed to any objects near the zenith, the observer is necessarily at an elevation at least 40 feet from the ground. Near the place of the eye glass is the end of a tin pipe, into which a mouth-piece may be placed, so that, during an observation, a person may direct his voice into this pipe, while his eye is at the glass. This pipe, which is 1½ inch in diameter runs down to the bottom of the tube, where it goes into a turning joint, thence into a drawing tube, and out of this into another turning joint, from whence it proceeds, by a set of sliding tubes towards the front of the foundation timber. Its use is to convey the voice of the observer to his assistants, for at the last place, it divides itself into two branches, one going into the observatory, the other into the workman’s room, ascending in both places through the floor, and terminates in the usual shape of speaking trumpets. Though the voice passes in this manner through a tube, with many inflections, and through not less than 115 feet, it requires very little exertion to be well understood.

To direct so unwieldy a body to any part of the heavens at pleasure, many mechanical contrivances were evidently necessary. The whole apparatus rests upon rollers, and care was previously taken of the foundation in the ground. This consists of concentrical brick walls, the outermost 42 feet, the innermost 21 feet in diameter, 2 feet 6 inches deep under ground, 2 feet 3 inches broad at the bottom, and 1 foot 2 inches at the top, capped with paving stones 3 inches thick, and 12¾ inches broad.

In the centre is a large post of oak, framed together with braces under ground, and walled fast to brick-work to make it steady. Round this centre the whole frame is moved horizontally by means of 20 rollers, 12 upon the outer, and 8 upon the inner wall. The vertical motion is given to the instrument by means of ropes and pullies, passing over the main beam supported by the ladders. These ladders are 49 feet long, and there is a moveable gallery with 24 rollers to ease its motion. There is a stair-case intended for persons who wish to ascend into the gallery, without being obliged to go up the ladder. The ease with which the horizontal and vertical motions may be communicated to the tube may be conceived, from a remark of Sir W. Herschel, that, in the year 1789, he several times observed Saturn, two or three hours before and after its meridian passage with one single person to continue, at his directions, the necessary horizontal and vertical motions.

By this telescope the sixth and seventh satellites of Saturn were discovered, only one of which is within the reach of the 20 feet reflector, or even of a 25 feet instrument. The discovery of the satellites of the planet Uranus, however, was made by the 20 feet reflector, but only after it had been converted from the Newtonian to the Herschelian construction—which affords a proof of the superiority of the latter construction over the former when the same speculum is used. Never had the heavens before been observed with so extraordinary an instrument as the forty feet reflector. The nebulosities which are found among the fixed stars, in various regions of the heavens, appeared almost all to resolve themselves into an innumerable multitude of stars; others, hitherto imperceptible, seemed to have acquired a distinct light. On the entrance of Sirius into the field of the telescope, the eye was so violently affected, that stars of less magnitude could not immediately after be perceived; and it was necessary to wait for 20 minutes before these stars could be observed. The ring of Saturn had always before ceased to be visible when its plane was directed towards the earth; but the feeble light which it reflects in that position was enough for Herschel’s instrument, and the ring, even then, still remained visible to him.

It has been generally considered that this telescope was capable of carrying a power of 6000 times; and perhaps for the purpose of an experiment, and for trying its effect on certain objects, such a power may have been applied,—in which case the eye-glass must have been only ²/₂₅ of an inch focal distance, or somewhat less than one twelfth of an inch. But such a power could not be generally applied, with any good effect, to the planetary bodies; and I question much whether any power above 1000 times was ever generally used. For, it is the quantity of light which the telescope collects, more than the magnifying power, that enables us to penetrate, with effect, into the distant spaces of the firmament: and hence, as above stated, the power seldom exceeded 200, which on account of the large diameter of the speculum, would enable the instrument to penetrate into the distant celestial spaces perhaps further than if a power of as many thousands of times had been applied.

Sir John Herschel, who inherits all the science, skill, and industry of his father, some time ago ground and polished a new speculum for the 20 feet tube, formerly noticed, which is connected with a stand, pulleys and other appendages, similar to those above described, though of smaller dimensions. This telescope shows the double stars exceedingly well defined, and was one of the principal instruments used in forming his catalogue of these objects which was presented to the Royal Society, in conjunction with that of Sir James South, about the year 1828. I suppose, it is likewise the same telescope with which Sir John lately made his Sidereal observations at the Cape of Good Hope.

SECT. 3.—RAMAGE’S LARGE REFLECTING TELESCOPE.

The largest front view reflecting telescope in this country—next to Herschel’s 40 feet instrument—is that which was erected at the Royal Observatory at Greenwich, in the year 1820, by Mr. Ramage of Aberdeen. The diameter of the concave reflector is 15 inches, and its focal length 25 feet. It is erected on machinery which bears a certain resemblance to that of Herschel’s, which we have now described; but the mechanical arrangements are greatly simplified, so that the instrument is manageable by an observer without an assistant. The tube is composed of a twelve-sided prism of deal ⁵/₈ inch thick. At the mouth is a double cylinder of different diameters on the same axis; around this a cord is wound by a winch, and passes up from the small cylinder, over a pulley, and down through another pulley on to the large cylinder. When the winch, therefore, is turned to raise the telescope, the endless cord is unwound from the smaller cylinder, and wound on to the larger, the difference of the size of the two cylinders will be double the quantity raised, and a mechanical force to any extent may thus be obtained, by duly proportioning the diameters of the two cylinders: by this contrivance the necessity of an assistant is superseded. The view through this instrument first astonished those observers who had not been accustomed to examine a heavenly body with a telescope possessing so much light; and its performance was deemed quite extraordinary. But when the first impression had subsided, and different trials had been made in different states of the atmosphere, it was discovered that the central portion of the speculum was more perfectly figured than the ring bordering on the extreme edges. When the aperture was limited to ten or twelve inches, the performance as to the distinctness in its defining power, was greatly improved, and the light was so brilliant, that the Astronomer Royal was disposed to entertain an opinion, that it might equal that of a good achromatic refractor of the same dimensions. When, however, very small and obscure objects are to be observed, the whole light of the entire aperture may be used with advantage on favourable evenings.

The eye-pieces adapted to this telescope have powers which magnify the object linearly from 100 to 1500 times, which are competent to fulfil all the purposes of vision when cleared of aberration. When the telescope is placed in the plane of the meridian and elevated together with the gallery, into any required altitude, the meridional sweeps, formerly practised by Sir W. Herschel, and continued by Sir John with great success, in the examination of double stars and nebula, may be managed with great ease.

Mr. Ramage had a telescope of about the same size, erected in an open space in Aberdeen, which I had an opportunity of inspecting when I paid a visit to that gentleman in 1833; but cloudy weather prevented my obtaining a view of any celestial bodies through it. He showed me at that time two or three large speculums, from 12 to 18 inches in diameter, which he had finished some time before, and which appeared most beautifully polished. He told me, too, that he had ground and polished them simply with his hand, without the aid of any machinery or mechanical power—a circumstance which, he said, astonished the opticians of London, when it was stated, and which they considered as almost incredible. His experience in casting and polishing metals of various sizes, during a period of 15 or 16 years, qualified him to prepare specula of great lustre, and with an unusually high polish. It has been asserted that a fifty feet telescope by Ramage of 21 inches aperture was intended to be substituted for the 25 feet instrument erected at Greenwich, and the speculum it is understood, was prepared, and ready for use, provided the Navy Board was disposed to defray the expense of carrying the plan into execution. But, unfortunately, this ingenious artist was unexpectedly cut off in the midst of his career, about the year 1835.

SECT. 4.—THE AERIAL REFLECTOR—CONSTRUCTED BY THE AUTHOR.

A particular description of this telescope was given in the ‘Edinburgh New Philosophical Journal’ for April—July, 1826, conducted by Professor Jameson, the greater part of which was copied in the ‘London Encyclopedia,’ ] under the article Telescope. From this description I shall endeavour to condense a brief account of this instrument with a few additional remarks.

About the year 1822, an old speculum 27 inches in focal length, very imperfectly polished happened accidentally to come into my possession; and feeling no inclination to fit it up in the Gregorian form, I formed the resolution of throwing aside the small speculum, and attempting the front view notwithstanding the uniform assertion of opticians, that such an attempt in instruments of a small size is impracticable. I had some ground for expecting success in this attempt, from several experiments I had previously made, particularly from some modifications I had made in the construction of astronomical eye-pieces, which have a tendency to correct the aberration of the rays of light, when they proceed somewhat obliquely from a lens or speculum. In the first instance, I placed the speculum at the one end of a tube of the form of a segment of a cone—the end next the eye being somewhat wider than that at which the speculum was fixed, and its length about an inch shorter than the focal distance of the mirror. A small tube for receiving the different eye-pieces was fixed in the inside of the large tube at the end next the eye, and connected with an apparatus by which it could occasionally be moved either in a vertical or horizontal direction. With the instrument fitted up in this manner, I obtained some interesting views of the moon, and of terrestrial objects. But finding that one side of the tube intercepted a considerable portion of light from the object, I determined to throw aside the tube altogether, and to fit up the instrument on a different plan.

A short mahogany tube, about 3 inches long, was prepared, to serve as a socket for holding the speculum. To the side of this tube an arm was attached, about the length of the focal distance of the mirror, at the extremity of which a brass tube for receiving the eye-pieces, was fixed, connected with screws and sockets, by which it might be raised or depressed, and turned to the right hand or to the left, and with adjusting apparatus by which it might be brought nearer to or farther from the speculum. Fig. 69 exhibits a general representation of the instrument in profile. AB is the short tube which holds the speculum; CD the arm which carries the eye-tubes, which consists of two distinct pieces of mahogany; the part D being capable of sliding along the under side of C, through the brass sockets EF. To the under part of the socket F is attached a brass nut with a female screw, in which the male screw ab acts by applying the hand to the knob c, which serves for adjusting the instrument to distinct vision. G is the brass tube which receives the eye-pieces. It is supported by a strong brass wire de, which passes through a nut connected with another strong wire, which passes through the arm D. By means of the nut f this tube may be elevated or depressed, and firmly fixed in its proper position; and by the nut d it may be brought nearer to or further from, the arm D.

By the same apparatus, it is also rendered capable of being moved either in a vertical or horizontal direction: but when it is once adjusted to its proper position, it must be firmly fixed, and requires no further attention. The eye-piece represented in this figure is the one used for terrestrial objects, which consists of the tubes belonging to a pocket achromatic telescope. When an astronomical eye-piece is used, the length of the instrument extends only to the point I. In looking through this telescope, the right eye is applied at the point H, and the observer’s head is understood to be uncovered, or, at least, tightly covered with a thin cap. For those who use only the left eye, the arm would require to be placed on the opposite side of the tube, or the arm, along with the tube, be made to turn round 180 degrees.

Fig. 70 represents a front, or rather an oblique view of the instrument, in which the position of the speculum may be seen. All the specula which I fitted up in this form, having been originally intended for Gregorian reflectors, have holes in their centres. The eye-piece is therefore directed to a point nearly equi-distant from the hole to the left hand edge of the speculum, that is, to the point a. In one of these instruments fitted up with a four feet speculum, the line of vision is directed to the point b on the opposite side of the speculum, but, in this case, the eye-tube is removed farther from the arm, than in the former case. The hole in the centre of the speculum is obviously a defect in this construction of a reflecting telescope, as it prevents us from obtaining the full advantage of the rays which fall near the centre of the mirror; yet the performance of the instruments, even with this disadvantage, is superior to what we should previously have been led to expect.

The principal nicety in the construction of this instrument, consists in the adjustment and proper direction of the eye-tube. There is only one position in which vision will be perfectly distinct. It must be neither too high nor too low,—it must be fixed at a certain distance from the arm,—and must be directed to a certain point of the speculum. This position must be ultimately determined by experiment, when viewing terrestrial objects. A person unacquainted with this construction of the telescope, would, perhaps, find it difficult, in the first instance, to make this adjustment; but were it at any time deranged, through accident or otherwise, I can easily make the adjustment anew, in the course of a minute or two.

In pointing this telescope to the object intended to be viewed, the eye is applied at K, fig, 69, and looking along the arm, towards the eye-piece, till it nearly coincide with the object, it will, in most cases, be readily found. In this way I can easily point this instrument to Jupiter or Saturn, or to any of the other planets, visible to the naked eye, even when a power of 160 or 170 times is applied. When high magnifying powers, however, are used, it may be expedient to fix, on the upper part of the short tube in which the speculum rests, a Finder, such as that which is used in Newtonian telescopes. When the moon is the object intended to be viewed, she may be instantly found by moving the instrument till her reflected image be seen from the eye-end of the telescope on the face of the mirror.

I have fitted up several instruments of the above description with specula of 16, 27, 35, and 49 inches focal distance. One of these having a speculum of 27 inches focal length, and an astronomical eye-piece, producing a magnifying power of about 90 times, serves as a good astronomical telescope. By this instrument the belts and satellites of Jupiter, the ring of Saturn, and the mountains and cavities of the moon, may be contemplated with great ease and distinctness. With a magnifying power of 35 or 40 times, terrestrial objects appear remarkably bright and well-defined. When compared with a Gregorian, the quantity of light upon the object appears nearly doubled, and the image is equally distinct—although the speculum has several blemishes, and its surface is but imperfectly polished. It represents objects in their natural colours, without that dingy and yellowish tinge which appears when looking through a Gregorian. Another of these instruments is about four feet long. The speculum which belongs to it is a very old one: when it came into my possession, it was so completely tarnished, as scarcely to reflect a ray of light. After it was cleaned, it appeared to be scarcely half polished, and its surface is covered with yellowish stains which cannot be erased. Were it fitted up upon the Gregorian plan, it would, I presume, be of very little use, unless when a very small magnifying power was applied. Yet, in its present form, it bears, with distinctness, a magnifying power of 130 times, and is equal in its performance to a 3½ feet achromatic. It exhibits distinct and interesting views of the diversities of shade, and of the mountains, vales, cavities, and other inequalities of the moon’s surface. With a power of about 50 times, and a terrestrial eye-piece, it forms an excellent telescope for land objects, and exhibits them in a brilliant and novel aspect. The smallest instrument I have attempted to construct on this plan, is only 5½ inches focal distance, and 1¾ inch diameter. With a magnifying power of about 15 times, it shows terrestrial objects with distinctness and brilliancy. But I should deem it inexpedient to fit up any instrument of this description with specula of a shorter focal distance than 20 or 24 inches. The longer the focal distance the more distinctness may be expected, although the aperture of the speculum should be comparatively small.

The following are some of the properties and advantages peculiar to this construction of the reflecting telescope.

1. It is extremely simple, and may be fitted up at a comparatively small expense. Instead of large and expensive brass tubes, such as are used in the Gregorian and Newtonian construction, little more is required than a short mahogany tube, two or three inches long, to serve as a socket for the speculum, with an arm connected with it about the focal length of the speculum. The expense of small specula, either plain or concave, is saved, together with the numerous screws, springs, &c., for centering the two specula, and placing the small mirror parallel to the large one. The only adjustment requisite in this construction, is that of the eye-tube to the speculum; and, by means of the simple apparatus above described, it can be effected in the course of a few minutes. Almost the whole expense of the instrument consists in the price of the speculum and the eye-pieces. The expense of fitting up the four feet speculum, alluded to above—exclusive of speculum and eye-piece—but including mahogany tube and arm, brass sockets, screws, eye-tube, brass joint, and a cast-iron stand painted and varnished, did not amount to £1 : 8s. A Gregorian of the same size would have required a brass tube at least 4½ feet in length, which would cost 5 or 6 guineas, besides the apparatus connected with the small speculum, and the additional expense connected with the fitting up of the joint and stand requisite for supporting and steadying so unwieldy an instrument. While the one instrument would require two persons to carry it from one room to another, and would occupy a considerable space in an ordinary apartment, the other can be moved, with the utmost ease, with one hand, to any moderate distance, and the space it occupies is extremely small.

2. It is more convenient for viewing celestial objects at a high altitude, than other telescopes. When we look through a Gregorian reflector or an achromatic telescope of 4 or 5 feet in length, to an object elevated 50 or 60 degrees above the horizon, the body requires to be placed in an uneasy and distorted position, and the eye is somewhat strained, while the observation is continued. But when viewing similar objects by the Aerial Reflector, we can either stand perfectly erect, or sit on a chair, with the same ease as we sit at a desk when reading a book or writing a letter. In this way, the surface of the moon or any of the planets, may be contemplated for an hour or two, without the least weariness or fatigue. A delineation of the lunar surface may be taken with this instrument with more ease and accuracy than with any other instrument, as the observer can sketch the outline of the object by one eye on a tablet placed a little below the eye-piece, while the other eye is looking at the object. For the purpose of accommodating the instrument to a sitting or standing posture a small table was constructed, capable of being elevated or depressed at pleasure, on which the stand of the telescope is placed. When the telescope is 4 or 5 feet long, and the object at a very high elevation, the instrument may be placed on the floor of the apartment, and the observer will stand in an erect position.

3. This instrument is considerably shorter than a Gregorian telescope whose mirror is of the same focal length. When an astronomical eye-piece is used, the whole length of the instrument is nothing more than the focal length of the speculum. But a Gregorian whose large speculum is 4 feet focus, will be nearly 5 feet in length, including the eye-piece.

4. The Aerial Reflector far excels the Gregorian in brightness. The deficiency of light in the Gregorians is owing to the second reflection from the small mirror; for it has been proved by experiment that nearly the one half of the rays of light which fall upon a reflecting surface is lost by a second reflection. The image of the object may also be presumed to be more correct, as it is not liable to any distortion by being reflected from another speculum.

5. There is less tremor in these telescopes than in Gregorian Reflectors. One cause, among others, of the tremors complained of in Gregorians is, I presume, the formation of a second image at a great distance from the first, besides that which arises from the elastic tremor of the small speculum, when carried by an arm supported only at one end. But as the image formed by the speculum in the aerial telescope is viewed directly, without being exposed to any subsequent reflection, it is not so liable to the tremors which are so frequently experienced in other reflectors. Notwithstanding the length of the arm of the 4 feet telescope above mentioned, a celestial object appears remarkably steady, when passing across the field of view, especially when it is at a moderate degree of altitude; and it is easily kept in the field by a gentle motion applied to the arm of the instrument.

In prosecuting my experiments in relation to these instruments, I wished to ascertain what effect might be produced by using a part of a speculum instead of the whole. For this purpose, I cut a speculum, three feet in focal length, through the centre, so as to divide it into two equal parts, and fitted up each part as a distinct telescope; so that I obtained two telescopes from one speculum. In this case I found that each half of the speculum performed nearly as well as the whole speculum had done before, at least there appeared to be no very sensible diminution in the brightness of the object, when viewed with a moderate power, and the image was equally accurate and distinct; so that if economy were a particular object aimed at in the construction of these instruments, two good telescopes might be obtained from one speculum; or if a speculum happened to be broken accidentally into large fragments, one or more of the fragments might be fitted up on this principle to serve as a tolerably good telescope.

From the experiments I have made in reference to these instruments, it is demonstrable, that a tube is not necessary in the construction of a reflecting telescope—at least on the principle now stated—whether it be used by day or by night for terrestrial or celestial objects; for I have frequently used these telescopes in the open air in the day time, without any inconvenience from extraneous light. Therefore, were a reflecting telescope of 50 or 60 feet in length to be constructed, it might be fitted up at a comparatively small expence, after the expense of the metallic substances, and of casting, grinding, and polishing the speculum is defrayed. The largest instrument of this description which has hitherto been constructed is the 40 feet reflector of Sir W. Herschel. This complicated and most unwieldy instrument had a tube of rolled or sheet iron 39 feet 4 inches in length, about 15 feet in circumference, and weighed about 8000 pounds. Now, I conceive that such enormous tubes, in instruments of such dimensions, are altogether unnecessary. Nothing more is requisite than a short tube for holding the speculum. Connected with one side of this tube (or with both sides were it found necessary), two strong bars of wood, projecting a few feet beyond the speculum end, and extending in front as far as the focal length of the mirror, and connected by cross bars of wood, iron or brass—would be quite sufficient for a support to the eye-piece, and for directing the motion of the instrument. A telescope of 40 or 50 feet in length, constructed on this plan, would not require one fifth of the expense, nor one fourth of the apparatus and mechanical power for moving it to any required position, which were found necessary in the construction of Sir W. Herschel’s large reflecting telescope. The idea here suggested will perhaps be more readily appreciated by an inspection of fig. 71, where A is the short tube, BC and DE the two large bars or arms, connected with cross bars, for the purpose of securing strength and steadiness. At I and K, behind the speculum, weights might be applied, if necessary, for counterbalancing the lever power of the long arm. F represents the position of the eye-piece, and GH the joint and part of the pedestal on which the instrument is placed. With regard to telescopes of smaller dimensions, as from 5 to 15 feet in focal length—with the exception of the expense of the specula and eye-pieces—they might be fitted up for a sum not greater than from 3 to 10 or 15 guineas.

figure 71.

Were any person to attempt the construction of those telescopes, it is possible he might not succeed in his first attempts without more minute directions than I have yet given. The following directions may perhaps tend to guide the experimenter in adjusting the eye-tube to the speculum, which is a point that requires to be particularly attended to, and on which depends the accurate performance of the instrument. After having fixed the eye-piece nearly in the position it should occupy, and directed the instrument to a particular object, look along the arm of the telescope, from K (fig. 69.) to the extremity of the eye-piece at H, and observe, whether it nearly coincides with the object. If the object appear lower than this line of vision, the eye-piece must be lowered, and if higher, it must be raised, by means of the nuts and screws at gd and fe, till the object and the line of vision now stated nearly coincide. The eye-piece should be directed as nearly perpendicular to the front of the speculum as possible, but so that the reflected image of one’s head from the mirror shall not interfere to obstruct the rays from the object. An object may be seen with an approximate degree of distinctness, but not accurately, unless this adjustment be pretty accurately made. The astronomical eye-pieces used for these telescopes are fitted with a brass cap which slides on the end next the eye, and is capable of being brought nearer to or farther from the first eye-glass. In the centre of this cap, next the eye, is a small hole, about the ¹/₄₀th or ¹/₅₀th of an inch diameter, or about as wide as to admit the point of a pin or a moderate-sized needle. The distance of this hole from the lens next the eye must be adjusted by trial, till the whole field of view appear distinct. A common astronomical eye-piece, without this addition, does not answer well. I find by experience, that terrestrial eye-pieces, such as those used in good achromatic telescopes, are, on the whole, best adapted to this construction of a reflecting telescope.

I have sometimes used these instruments for the purpose of viewing perspective prints, which they exhibit in a beautiful and interesting manner. If a coloured perspective be placed at one end of a large room or gallery, and strongly illuminated either by the sun or by two candles, and one of the reflectors furnished with a small magnifying power, placed at the opposite end of the room—the representation of a street or a landscape will be seen in its true perspective, and will appear even more pleasant and interesting than when viewed through the common optical diagonal machine. If an inverting eye-piece be used—which is most eligible in this experiment—the print, of course, must be placed in an inverted position.

That reflecting telescopes of the descriptions now stated are original in their construction, appears from the uniform language of optical writers, some of whom have pronounced such attempts to be altogether impracticable. Sir David Brewster, one of the latest and most respectable writers on this subject, in the ‘Edinburgh Encyclopedia’ art optics, and in the last edition of his appendix to ‘Ferguson’s Lectures,’ has the following remarks:—‘If we could dispense with the use of the small specula in telescopes of moderate length, by inclining the great speculum, and using an oblique, and consequently a distorted reflection, as proposed first by La Maire, we should consider the Newtonian telescope as perfect; and on a large scale, or when the instrument exceeds 20 feet, it has undoubtedly this character, as nothing can be more simple than to magnify, by a single eye-glass, the image formed by a single speculum. As the front view is quite impracticable, and indeed has never been attempted in instruments of a small size, it becomes of great practicable consequence to remove as much as possible, the evils which arise from the use of a small speculum,’ &c.

The instruments now described have effectuated, in some degree, the desirable object alluded to by this distinguished philosopher, and the mode of construction is neither that of Sir W. Herschel’s front view, nor does it coincide with that proposed by La Maire, which appears to have been a mere hint that was never realized in the construction of reflecting telescopes of a small size. The simplicity of the construction of these instruments, and the excellence of their performance, have been much admired by several scientific gentlemen and others to whom they have been exhibited. Prior to the description of them in the Edin. Philos. Journal, they were exhibited in the Calton Hill Observatory, Edinburgh, in the presence of Professor Wallace, and another gentleman, who compared their performance with that of an excellent Gregorian. As this instrument is distinguished from every other telescope, in being used without a tube, it has been denominated ‘The aerial reflector.’

SECT. 4.—EARL OF ROSSE’S REFLECTING TELESCOPES.

This nobleman, unlike many of his compeers, has, for a considerable number of years past, devoted his attention to the pursuits of science, and particularly to the improvement of reflecting telescopes. He is evidently possessed of high mathematical attainments, combined with an uncommon degree of mechanical ingenuity. About 14 or 15 years ago, he engaged in various experiments with the view of counteracting the effects of the spherical aberration of the specula of reflecting telescopes—which imperfection, if it could be completely remedied, would render the reflecting telescope almost a perfect instrument, as it is not affected by the different refrangibility of the rays of light. His method, we believe, consisted in forming a large speculum of two or three separate pieces of metal, which were afterwards accurately combined into one—a central part which was surrounded by one or two rings ground on the same tool. When the images formed by the separate pieces, were made exactly to coincide, the image of the object towards which the whole speculum was directed, was then found to be as distinct as either image had been when separate. But at the period referred to, a sufficient number of experiments had not been made to determine that his lordship had completely accomplished the object he intended.

Great interest, however, has of late been excited by the improvements which his lordship has made in the formation of specula. Sir W. Herschel never made public the means by which he succeeded in giving such gigantic developement to the reflecting telescope: and therefore the construction of a large reflector has been considered as a perilous adventure. But, according to a report of Dr. Robinson of Armagh, to the Irish academy, the Earl of Rosse has overcome the difficulties which have hitherto been met with, and carried to an extent which even Herschel himself did not venture to contemplate, the illuminating power of this telescope, along with a sharpness of definition little inferior to that of the achromatic; and it is scarcely possible, he observes, to preserve the necessary sobriety of language in speaking of the moon’s appearance with this instrument, which Dr. Robinson believes to be the most powerful ever constructed. The difficulty of constructing large specula, and of imparting to them the requisite degree of polish, has hitherto been considered so great, that from 8 to 12 inches diameter has been in general their utmost size. Indeed, except with the greatest reluctance, London opticians would not accept of orders for specula of more than 9 inches in diameter. It appears, however, that the Earl of Rosse has succeeded, by a peculiar method of moulding, in casting object-mirrors of true speculum metal of three feet in diameter, and of a weight exceeding 17 cwt. He is about to construct a telescope, the speculum of which is six feet in diameter, fifty feet focal distance, and of the weight of four tons; and from what he has already accomplished, it is not doubted that he possesses the power to carry his design into effect. These great masses of metal, which, in the hands of all other makers of specula would have been as untractable as so much unannealed flint-glass, the Earl of Rosse has further succeeded in bringing to the highest degree of polish, and the utmost perfection of curvature by means of machinery. The process is conducted under water, by which means those variations of temperature, so fatal to the finest specula hitherto attempted, are effectually guarded against. To convince Dr. Robinson of the efficacy of this machinery, the earl took the three feet speculum out of its telescope, destroyed its polished surface, and placed it under the mechanical polisher. In six hours it was taken out with a perfect new surface as bright as the original. Under the old system of hand-polishing, it might have required months, and even years, to effect this restoration. Even before achieving these extraordinary triumphs on the solid substance, his lordship had constructed a six feet reflector by covering a curved surface of brass with squares of the true speculum metal, which gave an immense quantity of light, though subject to some irregularities, arising from the number of joinings necessary in such a mosaic work. Of the performance of his lordship’s great telescope, mounted with this reflector, those who have seen it speak in terms of high admiration; but in reference to the smaller and more perfect instrument, furnished with the solid three feet speculum, the language of the Armagh astronomer assumes a tone of enthusiasm and even of sublimity. By means of this exquisite instrument, Dr. Robinson and Sir J. South, in the intervals of a rather unfavourable night, saw several new stars, and corrected numerous errors of other observers. For example, the planet Uranus, supposed to possess a ring similar to that of Saturn, was found not to have any such appendage; and those nebulÆ, hitherto regarded, from their apparently circular outline, as ‘coalescing systems,’ appeared, when tested by the three feet speculum, to be very far indeed from presenting a globular appearance; numerous off-shoots and appendages, invisible by other telescopes, appearing in all directions radiating from their edges. Such discoveries, which reflect great honour on the Earl of Rosse, will doubtless have great effect on the interests of astronomical science.27

SECT. 5.—REFLECTING TELESCOPES WITH GLASS SPECULA.

After making a variety of experiments with aerial telescopes constructed of metallic specula of different focal lengths, I constructed a telescope on the same plan, with a concave glass mirror. Having obtained a fragment of a very large convex mirror which happened accidentally to have been broken, I caused the convex side to be foliated, or silverised, and found its focal length to be about 27 inches. This mirror, which was about 5 inches diameter, I placed in one of the aerial reflectors, instead of the metallic speculum, and tried its effects with different terrestrial eye-pieces. With a power of about 35 or 40 times, it gave a beautiful and splendid view of distant terrestrial objects—the quantity of light reflected from them, being considerably greater than when a metallic speculum was used, and they appeared on the whole well-defined. The only imperfection—as I had foreseen—consisted in a double image being formed of objects which were remarkably bright and white, such as a light-house whitened on the outside, and strongly illuminated by the sun. One of the images was bright and the other faint. This was obviously owing to the two reflections from the two surfaces of the mirror—one from the convex silverised side, and the other from the concave side next the eye, which produced the faint image—which circumstance has been generally considered as a sufficient reason for rejecting the use of glass specula in telescopes. But although very bright objects exhibited a double image, almost all the other objects in the terrestrial landscape appeared quite distinct and without any secondary image, so that a common observer could scarcely have noticed any imperfection. When the instrument, however, was directed to celestial objects, the secondary image was somewhat vivid, so that every object appeared double. Jupiter appeared with two bodies, at a little distance from each other, and his four satellites appeared increased to eight. The moon likewise appeared as a double orb, but the principal image was distinct and well-defined. Such a telescope, therefore, was not well-adapted for celestial observations, but might answer well enough for viewing terrestrial objects.

Considering that the injurious effects of the secondary image arose from the images reflected from the two surfaces being formed near the same point, and at nearly the same focal distance, I formed a plan for destroying the secondary image, or at least counteracting its effects, by forming the concavity of the mirror next the eye of a portion of a sphere different from that of the convex side which was silverised, and from which the principal image is formed. But, for a long time, I could find no opticians possessed of tools of a sufficient length of radii for accomplishing my design. At length a London working optician undertook to finish a glass speculum, according to my directions, which were, that the convex surface of the mirror should be ground on a tool which would produce a focal distance by reflection of about 4 feet; and that the concave surface should have its focal distance at about 3 feet 3 inches, so that the secondary image might be formed at about 9 inches, within the focal distance of the silverised side, and not interfere to disturb the principal image. But, either from ignorance or inattention, the artist mistook the radius for the half radius of concavity, and the speculum turned out to be only 23 inches focal distance by reflection. This mirror was fitted up as a telescope, on the aerial plan, and I found, as I expected, the secondary image completely destroyed. It produced a very beautiful and brilliant view of land objects, and even the brightest objects exhibited no double image. The mirror was nearly 5 inches in diameter, but the image was most accurately defined when the aperture was contracted to about 3 inches. It was fitted with a terrestrial eye-piece which produced a magnifying power of about 25 times. When directed to the moon, it gave a very distinct and luminous view of that orb, without the least appearance of a secondary image. But as the focal distance of the speculum was scarcely half the length I had prescribed, I did not apply to it any high astronomical powers; as I find, that these can only be applied with effect, in this construction, to a speculum of a considerable focal length. Happening to have at hand a convex lens 10 feet focal length, and 4 inches in diameter—the one side of which had been ground to a certain degree of concavity—I caused the convex side to be foliated, which produced a focus by reflection, at 13½ inches distant. To this mirror I applied terrestrial powers of 15 and 24, with considerable distinctness. The power of 15 produced a very brilliant and distinct view of land objects. Had the mirror been at least 3 times the focal length, it would have formed an excellent telescope, with the same aperture.

SECT. 6.—A REFLECTING TELESCOPE, WITH A SINGLE MIRROR AND NO EYE-PIECE.

On the same principle as that by which a refracting telescope may be constructed by means of a single lens—as represented fig. 51, (page 234) we may form a telescope by reflection with a single mirror, and without an eye-piece. Let AB, fig. 72, represent a large concave speculum, and C its focus—if an eye be placed at D, about 8 or 10 inches within the focal point C, all the objects in the direction of C, or behind the spectator, will be seen magnified by reflection on the face of the mirror, and strongly illuminated. The magnifying power, in this case, will be nearly in the proportion of the focal length of the mirror to the focal length of the eye for near objects. If for example, the focal distance of the mirror be 8 feet, and the distance from the eye at which we see near objects most distinctly, be 8 inches—the magnifying power will be in the ratio of 8 to 96, or 12 times. I have a glass mirror of this description, whose focal length is 4 feet 8 inches, and diameter 6 inches, which magnifies distant objects about 7 times, takes in a large field of view, and exhibits objects with great brilliancy. It presents a very distinct picture of the moon, showing the different streaks of light and shade upon her surface; and, in some cases, shows the larger spots which traverse the solar disc. This mode of viewing objects is extremely easy and pleasant, especially when the mirror is of a large diameter; and the observer is at first struck and gratified with the novel aspect in which the objects appear.

Were a concave mirror of this description—whether of glass or of speculum metal—to be formed to a very long focus, the magnifying power would be considerable. One of 50 feet focal length, and of a corresponding diameter, might produce a magnifying power, to certain eyes, of about 75 times; and, from the quantity of light with which the object would be seen, its effect would be much greater than the same power applied to a common telescope. Sir W. Herschel states, that, on one occasion, by looking with his naked eye on the speculum of his 40 feet Reflector, without the interposition of any lens or mirror, he perceived distinctly one of the satellites of Saturn, which requires the application of a considerable power to be seen by an ordinary telescope. Such an instrument is one of the most simple forms of a telescope, and would exhibit a brilliant and interesting view of the moon, or of terrestrial objects.

PRICES OF REFLECTING TELESCOPES.

1. Prices as stated by Messrs. W. and S. Jones, Holborn, London.

2. Prices as stated by Messrs. Tulley, Islington.

3. Prices stated by Mr. G. Dollond, St. Paul’s Church Yard.

4. Prices of single speculums and reflecting telescopes, as made by Mr. Grub, Charlemont Bridge works, Dublin.

ON THE EYE-PIECES OF TELESCOPES.

Although the performance of telescopes chiefly depends on the goodness of the object-glass, or the object-speculum of the instrument, yet it is of considerable importance, in order to distinct vision, and to obtain a large and uniformly distinct field of view, that the eye-piece be properly constructed. The different kinds of eye-pieces may be arranged into two general divisions—Astronomical and terrestrial.

1. Astronomical eye-pieces.—The most simple astronomical eye-piece is that which consists of a single convex lens; and when the focal distance of this lens, and that of the object-glass of the instrument is accurately ascertained, the magnifying power may be nicely determined, by dividing the focal length of the object-lens by that of the eye-glass. But, as the pencil of white light transmitted by the object-glass, will be divided by the eye-glass into its component colours, the object will appear bordered with coloured fringes, and the distinctness of vision consequently injured. Besides, the spherical aberration, when a single lens is used, is much greater than when two or more glasses are employed. Hence astronomical eye-pieces are now formed by a combination of at least two lenses.

The combination of lenses now generally used for astronomical purposes, is that which is usually denominated the Huygenian eye-piece, having been first proposed by the celebrated Huygens, as a great improvement on the single lens eye-piece. The following figure (73) represents a section of this eye-piece. Let AB be a compounded pencil of white light proceeding from the object-glass; BF a plano-convex field-glass, with its plane side next the eye-glass E. The red rays of the pencil AB, after refraction would cross the axis in R, and the violet rays in V, but meeting the eye-glass E, the red rays will be refracted to O, and the violet nearly in the same direction, when they will cross each other about the point O, in the axis, and unite. The distance of the two glasses FE, to produce this correction, when made of crown glass, must be equal to half the sum of their focal distances nearly. For example, suppose the focal distance of the largest, or field lens, to be 3 inches, and the focal distance of the lens next the eye, 1 inch, the two lenses should be placed exactly at the distance of 2 inches; the sum of their focal length being 4, the half of which is 2. In other words, the glass next the eye should be placed as much within the focus of the field-glass as is equal to its own focal distance. The focal length of a single lens, that has the same magnifying power as this compound eye-piece—is equal to twice the product of the focal lengths of the two lenses, divided by the sum of the same numbers. Or, it is equal to half the focal length of the field-glass. Thus, in reference to the preceding example, twice the product of the focal length of the two lenses—is equal to 6, and their sum is 4. The former number divided by the latter, produces a quotient of 1½, which is the focal length of a single lens, which would produce the same magnifying power as the eye-piece; and 1½ is just half the focal length of the field-glass. The proportion of the focal lengths of the two lenses to each other, according to Huygens, should be as 3 to 1; that is, if the field-glass be 4½ inches, the eye-glass should be 1½; and this is the proportion most generally adopted. But some opticians have recommended that the proportions should be as 3 to 2. Boscovich recommended two similar lenses; and in this case the distance between them was equal to half the sum of their focal distances, as in the Huygenian eye-piece.

The image is formed at IM, at the focal distance of the lens next the eye, and at the same distance from the field-glass. When distinct vision is the principal object of an achromatic telescope, the two lenses are usually both plano-convex, and fixed with their curved faces towards the object glass, as in the figure. Sometimes, however, they consist of what is called crossed lenses, that is lenses ground on one side to a short focus, and on the other side to a pretty long focus, the sides with the deepest curves being turned towards the object glass. A diaphragm, or aperture of a proper diameter, is placed at the focus of the eye lens, where the image formed by the object-glass falls, for the purpose of cutting off the extreme rays of the field lens, and rendering every part of the field of view equally distinct. This is likewise the form of the eye-piece generally applied to Gregorian reflectors. In short, when accurately constructed, it is applicable to telescopes of every description. This eye-piece, having the image viewed, by the eye behind the inner lens, is generally called the negative eye-piece, and is that which the optical-instrument makers usually supply, of three or four different sizes, for so many magnifying powers, to be applied to different celestial objects, according to their nature or the state of the atmosphere in which they are used.

Ramsden’s eye-piece.—There is another modification of lenses, known by the name of the Positive, or Ramsden’s eye-piece, which is much used in Transit instruments, and telescopes which are furnished with micrometers, and which affords equally good vision as the other eye-piece. In this construction the lenses are plano-convex, and nearly of the same focus, but are placed at a distance from each other less than the focal distance of the glass next the eye, so that the image of the object viewed is beyond both the lenses, when measuring from the eye. The flat faces of the two lenses are turned into contrary directions in this eye-piece—one facing the object-glass, and the other the eye of the observer; and as the image formed at the focus of the object-glass, lies parallel to the flat face of the contiguous lens, every part of the field of view is distinct at the same adjustment, or, as opticians say, there is a flat field, which, without a diaphragm, prevents distortion of the object. This eye-piece is represented in fig. 74, where AB and CD are two plano-convex lenses, with their convex sides inwards. They have nearly the same focal length, and are placed at a distance from each other, equal to about two thirds of the focal length of either. The focal length of an equivalent single lens is equal to three fourths the focal length of either lens, supposing them to have equal focal distances. This eye-piece is generally applied, when wires of spider’s lines are used in the common focus; as the piece containing the lenses can be taken out without disturbing the lines, and is adjustable for distinct vision; and whatever may be the measure of any object given by the wire micrometer, at the solar focus, it is not altered by a change of the magnifying power, when a second eye-piece of this construction is substituted.

Aberration of lenses.—In connection with the above descriptions, the following statements respecting the spherical aberration of lenses may not be inappropriate. Mr. John Dollond, in a letter to Mr. Short, remarks, that ‘the aberration in a single lens is as the cube of the refracted angle; but if the refraction be caused by two lenses, the sum of the cubes of each half will be ¼ of the refracted angle, twice the cube of 1 being ¼ the cube of 2. So three times the cube of 1 is only one ninth of the cube of 3.’ &c. Hence the indistinctness of the borders of the field of view of a telescope is diminished by increasing the number of lenses in an eye piece. Sir J. Herschel has shown that if two plano-convex lenses are put together as in fig. 75, the aberration will be only 0.2481, or one fourth of that of a single lens in its best form. The focal length of the first of these lenses, must be to that of the second as 1 to 2.3. If their focal lengths are equal, the aberration will be 0.603, or nearly one half. The spherical aberration, however, may be entirely destroyed by combining a meniscus and double convex lens, as shown in fig. 76, the convex sides being turned to the eye when they are used as lenses, and to parallel rays, when they are used as burning glasses. Sir J. Herschel has computed the following curvatures for such lenses.

On the general principles above stated, a good astronomical eye-piece may be easily constructed with two proper lenses, either according to the plan of Huygens or that of Ramsden; and, from what has been now stated it is demonstrably certain, that, in all cases where two glasses are properly combined, such an eye-piece is superior to a single lens, both in point of distinctness, and of the enlargement of the field of view. I lately fitted up an eye-piece, on Ramsden’s principle, with two lenses, each about 3 inches focal length, and 1? inch diameter, placed at half an inch distant, with their convex surfaces facing each other as in fig. 74, which forms an excellent eye-piece for an achromatic telescope, 6 feet 8 inches focal distance, and 4 inches aperture, particularly for viewing clusters of stars, the Milky Way, and the large nebulÆ. The field of view is large, the magnifying power is only between 50 and 60 times, and the quantity of light being so great, every celestial object appears with great brilliancy, and it is in general much preferable, when applied to the stars than any of the higher powers. When applied to Presepe in Cancer, it exhibits that group at one view, as consisting of nearly a 100 stars which exhibit a beautiful and most striking appearance.

It may appear a curious circumstance that any eye-piece which is good with a short telescope, is also good with a long one, but that the reverse is not true; for it is found to be more difficult to make a good eye-piece for a short than for a long focal distance of the object-glass.

Celestial eye-pieces are sometimes constructed so as to produce variable powers. This is effected by giving a motion to the lens next the eye, so as to remove it nearer to or farther from the field lens; for at every different distance at which it is placed from the other lens, the magnifying power will either be increased or diminished. The greatest power is when the two lenses are nearly in contact, and the power diminishes in proportion to the distance at which the glass next the eye is removed from the other. The scale of distance, however, between the two lenses, cannot be greater than the focal distance of the field, or inner glass; for if it were, the lenses would no longer form an eye-piece, but would be changed into an inverting opera-glass. For effecting the purpose now stated, the eye-glass is fixed in a tube which slides upon an interior tube on which is marked a scale of distances, corresponding to certain magnifying powers; and, in this way an eye-piece may be made to magnify about double the number of times, when the lenses are in one position than when they are in another—as, for example, all the powers from 36 to 72 times may be thus applied, merely by regulating the distance between the two lenses. When the glasses are varied in this manner the eye-piece becomes sometimes a positive eye-piece, like Ramsden’s, and sometimes a negative one like that of Huygens.

Diagonal eye-pieces. The eye-pieces to which we have now adverted, when adapted to refracting telescopes, both reverse and invert the object, and therefore are not calculated for showing terrestrial objects in their natural position. But as the heavenly bodies are of a spherical form, this circumstance detracts nothing from their utility. When the celestial object, however, is at a high altitude, the observer is obliged to place his head in a very inconvenient position, and to direct his eye nearly upwards; in which position he cannot remain long at ease, or observe with a steady eye. To remedy this inconvenience, the diagonal eye-piece has been invented, which admits of the eye being applied at the side—or at the upper part of the eye-piece, instead of the end; and when such an eye-piece is used, it is of no importance in what direction the telescope is elevated, as the observer can then either sit or stand erect, and look down upon the object with the utmost ease. This object is effected by placing a flat piece of polished speculum-metal at an angle of 45 degrees in respect to the two lenses of the eye-piece, which alters the direction of the converging rays, and forms an image which becomes erect with respect to altitude, but is reversed with respect to azimuth;—that is, in other words, when we look down upon the objects in the field of view, they appear erect; but that part of an object which is in reality on our right hand appears on our left; and if it be in motion, its apparent is opposite to its real motion; if it be moving towards the west, it will seem to move towards the east.

There are three situations in which the diagonal reflector in this eye-piece may be placed. It may be placed either 1. before the eye-piece,—or 2. behind it,—or 3. between the two lenses of which the eye-piece consists. The most common position of the reflector is between the lenses; and this may be done both in the negative and the positive eye-pieces; but as the distance between the two lenses is necessarily considerable, to make room for the diagonal position of the reflector, the magnifying power cannot be great; otherwise, a diagonal eye-piece of this construction remains always in adjustment, and is useful in all cases where a high power is not required. The following is a description and representation of a diagonal eye-piece of this kind in my possession.

In fig. 77, AB represents the plano-convex lens next the object, which is about 2 inches in focal length, and ¾ inch in diameter; CD, a plain metallic speculum of an oval form, well polished, and placed at half a right angle to the axis of the tube; and EF another plano-convex lens, about 1½ inch focal distance. The centre of the speculum is about 1¼ inch from the lens AB, and about ½ or ¹/₃ inch from EF; so that this eye-piece is a positive one, on the principle proposed by Ramsden. The rays proceeding from the lens AB, and falling upon the speculum, are reflected in a perpendicular direction to the lens EF, where they enter the eye at G, which looks down upon the object through the side of the tube. The real size of this eye-piece is much about the same as that represented in the figure. When applied to an achromatic telescope of 44½ inches focal distance it produces a magnifying power of 36 times, and exhibits a very beautiful view of the whole of the full moon. It likewise presents a very pleasing prospect of terrestrial objects, which appear as if situated immediately below us.

Another plan of the diagonal eye-piece is represented in fig. 78, where the speculum is fixed within the sliding tube which receives the eye-piece, or immediately below it. The part of the tube at AB slides into the tube of the telescope, CD is the speculum placed at half a right angle to the axis of the tube, and EF, the tube containing the lenses, which stands at right angles to the position of the telescope, and slides into an exterior tube, and the eye is applied at G. This construction of the diagonal eye-piece may be used with any eye-piece whatever, whether the Huygenian or that of Ramsden. It will admit of any magnifying power, and if several different eye-pieces be fitted to the sliding tube, they may be changed at pleasure. This form of the diagonal eye-piece, I therefore consider as the best and the most convenient construction, although it is not commonly adopted by opticians.

When any of these eye-pieces are applied to a telescope, with the lens E on the upper part of it, we look down upon the object, if it be a terrestrial one, as if it were under our feet. If we turn the eye-piece round in its socket a quarter of a circle towards the left, an object directly before us in the south, will appear as if it were in the west and turned upside down. If, from this position, it is turned round a semicircle towards the right, and the eye applied, the same object will appear as if it were situated in the east, and inverted; and if it be turned round another quadrant, till it be directly opposite to its first position, and the eye applied from below, the object or landscape will appear as if suspended in the atmosphere above us. This eye-piece, therefore, is capable of exhibiting objects in a great variety of aspects, and the use of it is both pleasant and easy for the observer. But there is a considerable loss of light, occasioned by the reflection from the speculum, which is sensibly felt when very high powers are applied; and therefore when very small stars are to be observed, such as some of those connected with double or triple stars, the observer should not study his own ease so much as the quantity of light he can retain with a high power, which object is best attained with an ordinary eye-piece and a telescope of large aperture.

We have said that a diagonal eye-piece may be constructed with a reflector before the eye-piece. In this case, the speculum is sometimes made to slide before the eye at the requisite angle of reclination, in which application each eye-piece must necessarily have a groove to receive it, and the eye must be applied without a hole to direct it, but it may be put on and taken off without disturbing the adjustment for distinct vision, and is very simple in its application. But, on the whole, the form represented in fig. 78, is the most convenient, and should generally be preferred, as any common astronomical eye-piece can be applied to it. I have used a diagonal eye-piece of this kind, with good effect, when a power of 180 has been applied to the sun and other celestial objects.

Instead of a metallic speculum, a rectangular prism of glass is sometimes substituted; for the rays of light are then bent by reflection from the second polished surface, which ought to be dry, and undergo two refractions which achromatise them; and the same effect is thus produced as by polished metal. Ramsden sometimes gave one of the polished faces of a right angled prism a curve, which prism served instead of a lens in an eye-piece, and also performed the office of a reflector. A semi-globe, or what has been called a Bull’s eye, has also been used as a diagonal eye-piece, and when the curve is well-formed, and the glass good, it is achromatic, and is said to perform pretty well, but it is not superior to the forms already described.

SECT. 2.—TERRESTRIAL EYE-PIECES.

When describing the common refracting telescope, (p. 228.) I have noticed that three eye-glasses, placed at double their focal distances from each other, formerly constituted the terrestrial eye-piece, as represented in fig. 47. But this construction, especially for achromatic instruments, has now become obsolete, and is never used, except in small pocket spy-glasses formed with a single object lens. In its place a four glassed eye-piece has been substituted, which is now universally used in all good telescopes, and which, besides improving the vision and producing an erect position of the images of objects, presents a considerably larger field of view. During the progressive stages of improvement made in the construction of erect eye-pieces by Dollond and Ramsden, three, four, and five lenses were successively introduced; and hence, in some of the old telescopes constructed by these artists, we frequently find five lenses of different descriptions composing the eye-piece. But four lenses, arranged in the manner I am now about to describe, have ultimately obtained the preference. In a telescope having a celestial eye-piece of the Huygenian form, the image that is formed in the focus of the object glass, is that which is seen magnified, and in an inverted position; but when a four glassed eye-piece is used, which produces an erect view of the object, the image is repeated, and the second image, which is formed by the inner pair of lenses AB on an enlarged scale, is that which the pair of lenses CD at the eye-end render visible on a scale still more enlarged. The modern terrestrial eye-piece, represented in fig. 79, is, in fact, nothing else than a compound microscope, consisting of an object lens, an amplifying lens, and an eye-piece composed of a pair of lenses on the principle of the Huygenian eye-piece. Its properties will be best understood by considering the first image of an object, which is formed in the focus of the object glass, as a small luminous object to be rendered visible, in a magnified state, by a compound microscope. The object to be magnified may be considered as placed near the point A, and the magnified image at i, which is viewed by the lens D. Hence, if we look through such an eye-piece at a small object placed very near the lens A, we shall find that it acts as a compound microscope of a moderate magnifying power increasing, in some cases, the diameter of the object about 10 times, and 100 times in surface.

figure 79.

In order to distinguish the different lenses in this eye-piece, we may call the lens A, which is next to the first image, the object-lens, the next to it B, the amplifying-lens, the third, or C, the field-lens, and the one next the eye, D, the eye-lens. The first image formed a little before A, may be denominated the radiant, or the object from which the rays proceed. Now, it is well known as a principle in optics, that if the radiant be brought nearer to the lens than its principal focus, the emerging rays will diverge, and, on the contrary, if the radiant be put farther from the lens than its principal focal distance, the emerging rays will converge to a point at a distance beyond the lens, which will depend on the distance of the radiant from the first face of the lens. In this place an image of the radiant will be formed by the concurrence of the converging rays, but in a contrary position; and the length of the image will exceed the length of the radiant in the same proportion, as the distance of the image from the radiant exceeds that of the radiant from the lens. This secondary image of the radiant at i, is not well-defined, when only one lens, as A, is used, owing to the great spherical aberrations, and therefore the amplifying lens is placed at the distance of the shorter conjugate focus, with an intervening diaphragm of a small diameter at the place of the principal focus; the uses of which lens and diaphragm are, first to cut off the coloured rays that are occasioned by the dispersive property of the object lens,—and secondly, to bring the rays to a shorter conjugate focus for the place of the image, than would have taken place with a single lens having only one refraction. As the secondary image is in this way much better defined and free from colouration, the addition of this second lens is a great improvement to vision. For this reason I am clearly of opinion, that the object glass of a compound microscope, instead of consisting of a small single lens, should be formed of two lenses on the principle now stated, which would unquestionably add to the distinctness of vision.

With respect to the proportions of the focal lengths of the lenses in this four glass eye-piece, Mr. Coddington states, that if the focal lengths, reckoning from A to D, fig. 79, be as the numbers 3, 4, 4 and 3, and the distances between them on the same scale, 4, 6, and 5, 2, the radii, reckoning from the outer surface of A, should be thus:—

Sir D. Brewster states, that a good achromatic eye-piece may be made of 4 lenses, if their focal lengths, reckoning from that next the object, be as the numbers 14, 21, 27, 32; their distances 23, 44, 40; their apertures 5.6; 3.4; 13.5; 2.6; and the aperture of the diaphragm placed in the interior focus of the fourth eye-glass, 7. Another proportion may be stated:—Suppose the lens next the object A, to be 1? inch focal length, then B may be 2½ inches, C 2 inches, and D 1½; and their distances AB 2½; BC 3?; and CD 2?. In one of Ramsden’s small telescopes, whose object glass was 8½ inches in focal length, and its magnifying power 15.4, the focal lengths of the eye glasses were A 0.775 of an inch, B 1.025, C 1.01, D 0.79;—the distances AB 1.18, BC 1.83, and CD 1.105. In the excellent achromatic telescope of Dollond’s construction which belonged to the Duc de Chaulnes, the focal lengths of the eye glasses, beginning with that next the object, were 14¼ lines, 19, 22¾, 14; their distances 22.48 lines, 46.17, 21.45, and their thickness at the centre, 1.23 lines, 1.25, 1.47. The fourth lens was plano-convex, with the plane side to the eye, and the rest were double convex lenses. This telescope was in focal length 3 feet 5½ inches.

The magnifying power of this eye-piece, as usually made, differs only in a small degree from what would be produced by using the first or the fourth glass alone, in which case the magnifying power would be somewhat greater, but the vision less distinct, and were the lens next the eye used alone without the field glass, the field of view would be much contracted. Stops should be placed between the lenses A and B, near to B, and a larger one between C and D, to prevent any false light from passing through the lenses to the eye. The more stops that are introduced into a telescope—which should all be blackened—provided they do not hinder the pencils of light proceeding from the object, the better will the instrument perform.

For the information of amateur constructors of telescopes, I shall here state the dimensions of two or three four glassed eye-pieces in my possession, which perform with great distinctness, and present a pretty large field of view. In one of these, adapted to a 44½ inch achromatic, the lens A, next the object, is 1? inch, focal length, and about 1 inch diameter, with the plane side, next the object. The focal length of the lens B 2¹/₁₀ inches, diameter ⁷/₁₀ inch, with its plane side next A; distance of these lenses from each other 2⁴/₁₀ inches. Distance of the field lens C from the lens B 5½ inches. The small hole or diaphragm between A and B is at the focus of A, and is about ¹/₆ inch diameter, and about ³/₈ of an inch from the lens B. The field lens C is 2 inches focal length, and 1¼ inch diameter, with its plane side next the eye. The lens next the eye D is 1 inch focal distance, ½ inch diameter, and is distant from the field glass 1¾ inch, with its plane side next the eye. The magnifying power of this eye-piece is equivalent to that of a single lens whose focal length is half an inch, and with the 44½ inch object glass produces a power of about 90 times. The lens next the eye can be changed for another 1? inch focal length, which produces a power of 65; and the two glasses CD can be changed for another set, of a longer focal distance which produces a power of 45 times. The whole length of this eye-piece is 11½ inches.

In another eye-piece, adapted to a pocket achromatic, whose object glass is 9 inches focal length, the lens A is 1 inch focal length, and ½ inch diameter; the lens B 1¼ inch, and ½ inch diameter, their distance 1½ inch, the lens C 1¹/₁₀ inch focal length, and ⁵/₈ inch diameter; the eye-lens D ⁵/₈ inch focal length, and ³/₈ inch diameter; distance between C and D 1? inch. The distance between B and C 1¾ inch. The whole length of this eye-piece is 4½ inches, and its power is nearly equal to that of a single lens of ½ or ⁶/₁₀ of an inch focal length, the magnifying power of the telescope being about 16 times. Another eye-piece of much larger dimensions, has the lens A of 2½ inches focal length, and ¾ inch diameter: the lens B 2¾ inches focus and ⁵/₈ inch diameter; and their distance 2¾ inches; the lens C 2? inches focus and 1? inch diameter; the lens D 1¾ inch focus and ¾ inch diameter; distance from each other 2¾ inches. The distance between the lenses B and C is 4 inches. The magnifying power is equal to that of a single lens 1? inch focal distance. When applied to an achromatic object glass 6 feet 7 inches focal length, it produces a power of about 70 times. This eye-piece has a moveable tube 9 inches in length in which the two lenses next the eye are contained, by pulling out which, and consequently increasing the distance between the lenses B and C, the magnifying power may be increased to 100, 120 or 140, according to the distance to which this moveable tube is drawn out. It has also a second and third set of lenses, corresponding to C and D of a shorter focal distance, which produce higher magnifying powers on a principle to be afterwards explained.

Description of an eye-piece, &c. of an old Dutch Achromatic Telescope.

About twenty or thirty years ago, I purchased, in an optician’s shop in Edinburgh, a small achromatic telescope, made in Amsterdam, which was supposed, by the optician, to have been constructed prior to the invention of achromatic telescopes by Mr. Dollond. It is mounted wholly of brass, and in all its parts is a piece of beautiful and exquisite workmanship, and the utmost care seems to have been taken to have all the glasses and diaphragms accurately adjusted. The object glass is a double achromatic, 6½ inches focal distance and 1 inch diameter, but the clear aperture is only ⁷/₈ inch diameter. It is perfectly achromatic, and would bear a power of 50 times, if it had a sufficient quantity of light. The following inscription is engraved on the tube adjacent to the object glass:—“Jan van Deyl en Zoon Invenit et Fecit, Amsterdam, Ao. 1769.” Although Dollond exhibited the principle of an achromatic telescope, eight or ten years before the date here specified, yet it is not improbable that the artist whose name is here stated, may not have heard of Dollond’s invention; and that he was really, as he assumes, one of the inventors of the achromatic telescope. For, the invention of this telescope by Dollond was not very generally known, except among philosophers and the London opticians, till a number of years after the date above stated. Euler, in his “Letters to a German Princess”—in which telescopes are particularly described, makes no mention of, nor the least allusion to the invention of Dollond, though this was a subject which particularly engaged his attention. Now, these letters were written in 1762, but were not published till 1770. When alluding to the defects in telescopes arising from the different refrangibility of the rays of light, in Letter 43, and that they might possibly be rectified by means of different transparent substances, he says, ‘But neither theory nor practice have hitherto been carried to the degree of perfection necessary to the execution of a structure which should remedy these defects.’ Mr. B. Martin, in his ‘Gentleman and Lady’s Philosophy,’ published in 1781, alludes to the achromatic telescope, but speaks of it as it were but very little, if at all superior to the common refracting telescope. And therefore, I think it highly probable that Jan van Deyl, was really an inventor of an achromatic telescope, before he had any notice of what Dollond and others had done in this way some short time before.

But my principal object in adverting to this telescope, is to describe the structure of the eye-piece, which is a very fine one, and which is somewhat different from the achromatic eye-piece above described. It consists of four glasses, two combined next the eye, and two next the object. Each of these combinations forms an astronomical eye-piece nearly similar to the Huygenian. The lens A, next the object, fig. 80, is ⁵/₈ inch focal distance, and ⁴/₁₀ inch diameter; the lens B ³/₈ inch focus, and ¹/₅ inch diameter, and the distance between them somewhat less than ⁵/₈ inch; the diameter of the aperture e about ¹/₁₅ of an inch. This combination forms an excellent astronomical eye-piece, with a large flat field, and its magnifying power is equivalent to that of a single lens ⁵/₈ or ⁶/₈ focal length. The lens C is ½ inch focal length, and ⁴/₁₀ inch diameter; the lens D ¼ inch focus, and about ¹/₅ inch diameter; their distance about ½ inch, or a small fraction more. The hole at d is about ¹/₂₀ or ¹/₂₅ of an inch diameter, and the distance between the lenses B and C about 1½ inch. The whole length of the eye-piece is 3¼ inches—exactly the same size as represented in the engraving. Its magnifying power is equal to that of a single lens ¼ inch focal length; and consequently the telescope, though only 9½ inches long, magnifies 26 times, with great distinctness, though there is a little deficiency of light when viewing land objects, which are not well illuminated.

The glasses of this telescope are all plano-convex, with their convex-sides towards the object—except the lens D, which is double convex, but flattest on the side next the eye, and they are all very accurately finished. The two lenses C and D form an astronomical eye-piece nearly similar to that formed by the lenses A and B. The focus of the telescope is adjusted by a screw, the threads of which are formed upon the outside of a tube into which the eye-piece slides. The eye-piece and apparatus connected with it, is screwed into the inside of the main tube, when not in use, when the instrument forms a compact brass cylinder 6 inches long, which is enclosed in a fish-skin case, lined with silk velvet, which opens with hinges.

The lenses in the eye-pieces formerly described, though stated to be plano-convexes, are for the most part crossed glasses, that is ground on tools of a long focus on the one side, and to a short focus on the other. The construction of the eye-piece of the Dutch telescope above described, is one which might be adopted with a good effect in most of our achromatic telescopes; and I am persuaded, from the application I have made of it to various telescopes, that it is even superior, in distinctness and accuracy, and in the flatness of field which it produces to the eye-piece in common use. The two astronomical eye-pieces of which it consists, when applied to large achromatic telescopes, perform with great accuracy, and are excellently adapted for celestial observations.

SECT. 3.—DESCRIPTION OF THE PANCRATIC EYE-TUBE.

From what we have stated, when describing the common terrestrial eye-piece now applied to achromatic instruments, (p. 349, fig. 79.), it appears obvious, that any variety of magnifying powers, within certain limits, may be obtained by removing the set of lenses CD, fig. 79, nearer to or farther from the tube which contains the lenses A and B, on the same principle as the magnifying power of a compound microscope is increased by removing the eye-glasses to a greater distance from the object-lens. If then, the pair of eye-lenses CD be attached to an inner tube that will draw out and increase their distance from the inner pair of lenses, as the tube a b c d, the magnifying power may be indefinitely increased or diminished, by pushing in or drawing out the sliding tube, and a scale might be placed on this tube, which, if divided into equal intervals, will be a scale of magnifying powers, by which the power of the telescope will be seen at every division, when the lowest power is once determined.

Sir David Brewster, in his ‘Treatise on New Philosophical instruments,’ Book i. chap. vii. page 59, published in 1813, has adverted to this circumstance, in his description of an ‘Eye-piece wire micrometer,’ and complains of Mr. Ezekiel Walker, having in the ‘Philosophical Magazine’ for August, 1811, described such an instrument as an invention of his own. Dr. Kitchener some years afterwards, described what he called a Pancratic or omnipotent eye-piece, and got one made by Dollond, with a few modifications different from that suggested by Brewster and Walker, which were little else than cutting the single tube into several parts, and giving it the appearance of a new invention. In fact, none of these gentlemen had a right to claim it as his peculiar invention, as the principle was known and recognised long before. I had increased the magnifying powers of telescopes, on the same principle, several years before any of these gentlemen communicated their views on the subject, although I never formally constructed a scale of powers. Mr. B. Martin, who died in 1782, proposed many years before, such a moveable interior tube as that alluded to, for varying the magnifying power.

In order to give the reader a more specific idea of this contrivance, I shall present him with a figure and description of one of Dr. Kitchener’s Pancratic eye-pieces, copied from one lately in my possession. The following are the exact dimensions of this instrument, with the focal distances, &c. of the glasses, &c. of which it is composed.

From the figure and description, the reader will be at no loss to perceive how the magnifying power is ascertained by this eye-piece. If the lowest power for a 44 inch telescope be found to be 100, when the three sliding tubes are shut into the larger one, then by drawing out the tube next the eye 4 divisions, a power of 140 is produced; by drawing out the tube next the eye its whole length, and the second tube to the division marked 220, a power of 220 times is produced, and drawing out all the tubes to their utmost extent, as represented in the figure, a power of 400 is obtained. These powers are by far too high for such a telescope, as the powers between 300 and 400 can seldom or never be used. Were the scale to begin at 50, and terminate at 200, it would be much better adapted to a 3½ feet telescope. Each alteration of the magnifying power requires a new adjustment of the eye-piece for distinct vision. As the magnifying power is increased, the distance between the eye-glass and the object-glass must be diminished. Dr. Kitchener says, that ‘the pancratic eye tube gives a better defined image of a fixed star, and shows double stars decidedly more distinct and perfectly separated than any other eye tube, and that such tubes will probably enable us to determine the distances of these objects from each other, in a more perfect manner than has been possible heretofore.’ These tubes are made by Dollond, London, and are sold for two guineas each. But I do not think they excel, in distinctness, those which are occasionally made by Mr. Tulley and other opticians.

CHAPTER VI.

MISCELLANEOUS REMARKS IN RELATION TO TELESCOPES.

The following remarks, chiefly in regard to the manner of using telescopes, may perhaps be useful to young observers, who are not much accustomed to the mode of managing these instruments.

1. Adjustments requisite to be attended to in the use of telescopes. When near objects are viewed with a considerable magnifying power, the eye-tube requires to be removed farther from the object-glass than when very distant objects are contemplated. When the telescope is adjusted for an object, 6, 8, or 10 miles distant, a very considerable alteration in the adjustment is requisite in order to see distinctly an object at the distance of two or three hundred yards, especially if the instrument is furnished with a high magnifying power. In this last case, the eye-tube requires to be drawn out to a considerable distance beyond the focus for parallel rays. I have found that, in a telescope which magnifies 70 times, when adjusted for an object at the distance of two miles, the adjustment requires to be altered fully one inch in order to perceive distinctly an object at the distance of two or three hundred yards; that is, the tube must be drawn, in this case, an inch farther from the object-glass, and pushed in the same extent, when we wish to view an object at the distance of two or three miles. These adjustments are made, in pocket perspectives, by gently sliding the eye-tube in or out, by giving it a gentle circular or spiral motion till the object appear distinct. In using telescopes which are held in the hand, the best plan is to draw all the tubes out to their full length, and then, looking at the object, with the left hand supporting the main tube near the object-glass, and the right supporting the eye-tube—gently and gradually push in the eye-piece till distinct vision be obtained. In Gregorian reflecting telescopes this adjustment is made by means of a screw connected with the small speculum; and in large achromatics, by means of a rack and pinion connected with the eye-tube. When the magnifying power of a telescope is comparatively small, the eye-tube requires to be altered only a very little.

There is another adjustment requisite to be attended to, in order to adapt the telescope to the eyes of different persons. Those whose eyes are too convex, or who are short-sighted, require the eye-tube to be pushed in, and those whose eyes are somewhat flattened, as old people, require the tube to be drawn out. Indeed there are scarcely two persons whose eyes do not require different adjustments in a slight degree. In some cases I have found that the difference of adjustment for two individuals, in order to produce distinct vision in each, amounted to nearly half an inch. Hence the difficulty of exhibiting the sun, moon, and planets through telescopes, and even terrestrial objects, to a company of persons who are unacquainted with the mode of using or adjusting such instruments—not one half of whom generally see the object distinctly—for, upon the proper adjustment of a telescope to the eye, the accuracy of vision, in all cases, depends; and no one except the individual actually looking through the instrument, can be certain that it is accurately adjusted to his eye, and even the individual himself, from not being accustomed to the view of certain objects, may be uncertain whether or not the adjustment be correct. I have found by experience that when the magnifying powers are high, as 150 or 200, the difference of adjustment required for different eyes is very slight; but when low powers are used, as 20, 30, or 40, the difference of the requisite adjustments is sometimes very considerable, amounting to ¼ or ½ of an inch.

2. State of the Atmosphere most proper for observing terrestrial and celestial objects. The atmosphere which is thrown around the globe—while it is essentially requisite to the physical constitution of our world, and the comfort of its inhabitants—is found in many instances a serious obstruction to the accurate performance of telescopes. Sometimes it is obscured by mists and exhalations, sometimes it is thrown into violent undulations by the heat of the sun and the process of evaporation, and even, in certain cases, where there appears a pure unclouded azure, there is an agitation among its particles and the substances incorporated with them, which prevents the telescope from producing distinct vision either of terrestrial or celestial objects. For viewing distant terrestrial objects, especially with high powers, the best time is early in the morning, a little after sun-rise, and, from that period till about 9 o’clock A.M., in summer; and, in the evening about two or three hours before sun-set. From about 10 o’clock A.M. till 4 or 5 in the afternoon, in summer, if the sky be clear and the sun shining, there is generally a considerable undulation in the atmosphere, occasioned by the solar rays and the rapid evaporation, which prevents high powers from being used with distinctness on any telescope, however excellent. The objects at such times, when powers of 50, 70, or 100 are applied, appear to undulate like the waves of the sea, and, notwithstanding every effort to adjust the telescope, they appear confused and indistinct. Even with very moderate magnifying powers this imperfection is perceptible. In such circumstances, I have sometimes used a power of 200 times on distant land objects, with good effect, a little before sun-set, when, in the forenoon of the same day, I could not have applied a power of 50 with any degree of distinctness. On days when the air is clear, and the atmosphere covered with clouds, terrestrial objects may be viewed with considerably high powers. When there has been a long-continued drought, the atmosphere is then in a very unfit state for enjoying distinct vision with high magnifying powers, on account of the quantity of vapours with which the atmosphere is then surcharged, and the undulations they produce. But, after copious showers of rain, especially if accompanied with high winds, the air is purified, and distant objects appear with greater brilliancy and distinctness than at any other seasons. In using telescopes, the objects at which we look should, if possible, be nearly in a direction opposite to that of the sun. When they are viewed nearly in the direction of the sun, their shadows are turned towards us, and they consequently appear dim and obscure. By not attending to this circumstance, some persons, in trying telescopes, have pronounced a good instrument to be imperfect, which, had it been tried on objects properly illuminated, would have been found to be excellent. In our variable northerly climate the atmosphere is not so clear and serene for telescopic observation as in Italy, the South of France, and in many of the countries which lie within the tropics. The undulations of the air, owing to the causes alluded to above, constitute one of the principal reasons why a telescope magnifying above a hundred times can seldom be used with any good effect in viewing terrestrial objects—though I have sometimes used a power of nearly 200 with considerable distinctness, in the stillness of a summer or autumnal evening, when the rays of the declining sun strongly illuminated distant objects.

The atmosphere is likewise frequently a great obstruction to the distinct perception of celestial objects. It is scarcely possible for one who has not been accustomed to astronomical observations, to form a conception of the very great difference there is in the appearance of some of the heavenly bodies in different states of the atmosphere. There are certain conditions of the atmosphere essentially requisite for making accurate observations with powerful telescopes, and it is but seldom, especially in our climate, that all the favourable circumstances concur. The nights must be very clear and serene—the moon absent—no twilight—no haziness—no violent wind—no sudden change of temperature, as from thaw to frost—and no surcharge of the atmosphere with aqueous vapour. I have frequently found that, on the first and second nights after a thaw, when a strong frost had set in, and when the heavens appeared very brilliant, and the stars vivid and sparkling—the planets, when viewed with high powers, appeared remarkably undefined and indistinct; their margins appeared waving and jagged, and the belts of Jupiter, which at other times were remarkably distinct, were so obscured and ill-defined, that they could with difficulty be traced. This is probably owing to the quantity of aqueous vapour, and perhaps icy particles, then floating in the air, and to the undulations thereby produced. When a hard frost has continued a considerable time, this impediment to distinct observation is in a great measure removed. But I have never enjoyed more accurate and distinct views of the heavenly bodies than in fresh serene evenings, when there was no frost and no wind, and only a few fleecy clouds occasionally hovering around. On such evenings, and on such alone, the highest powers may be applied. I have used magnifying powers on such occasions with good effect, which could not have been applied, so as to ensure distinct vision, more frequently than two or three days in the course of a year.

Sir William Herschel has observed, in reference to this point, ‘In beautiful nights, when the outside of our telescopes is dropping with moisture, discharged from the atmosphere, there are now and then favourable hours in which it is hardly possible to put a limit to the magnifying powers. But such valuable opportunities are extremely scarce, and with large instruments it will always be lost labour to observe at other times. In order therefore, to calculate how long a time it must take to sweep the heavens, as far as they are within the reach of my forty-feet telescope, charged with a magnifying power of 1000, I have had recourse to my journals to find how many favourable hours we may annually hope for in this climate. And, under all favourable circumstances, it appears, that a year which will afford ninety, or at most, one hundred hours is to be called very productive.’ ‘In the equator, with my twenty feet telescope, I have swept over zones of two degrees with a power of 157, but an allowance of ten minutes in Polar distance must be made for lapping the sweeps over one another where they join. As the breadth of the zones may be increased towards the poles, the northern hemisphere may be swept in about 40 zones; to these we must add 19 southern zones; then 59 zones which, on account of the sweeps lapping over one another, about 5 minutes of time in right ascension, we must reckon of 25 hours each, will give 1475 hours. And allowing 100 hours per year, we find that with the 20 feet telescope, the heavens may be swept in about 14 years and three quarters. Now the time of sweeping with different magnifying powers will be as the squares of the powers; and putting p and t for the power and time in the 20 feet telescope, and P = 1000 for the power in the 40 feet instrument, we shall have p² : t :: P² : ^tP2/_p² = 59840. Then making the same allowance for 100 hours per year, it appears that it will require not less than 598 years, to look with the 40 feet reflector, charged with the above-mentioned power, only one single moment into each point of space; and even then, so much of the southern hemisphere will remain unexplored, as will take up 213 years more to examine.’28

From the above remarks of so eminent an observer, the reader will perceive how difficult it is to explore the heavens with minuteness and accuracy, and with how many disappointments, arising from the state of the atmosphere, the astronomer must lay his account, when employed in planetary or sidereal investigation. Besides the circumstances now stated, it ought to be noticed that a star or a planet is only in a situation for a high magnifying power, about half the time it is above the horizon. The density of the atmosphere, and the quantity of vapours with which it is charged near the horizon, prevent distinct vision of celestial objects with high powers, till they have risen to at least 15 or 20 degrees in altitude, and the highest magnifiers can scarcely be applied with good effect, unless the object is near the meridian, and at a considerable elevation above the horizon. If the moon be viewed a little after her rising, and afterwards when she comes to her highest elevation in autumn, the difference in her appearance and distinctness will be strikingly perceptible. It is impossible to guess whether a night be well adapted for celestial observations, till we actually make the experiment, and instruments are frequently condemned, when tried at improper seasons, when the atmosphere only is in fault. A certain observer remarks,—‘I have never seen the face of Saturn more distinctly than in a night when the air has been so hazy, that with my naked eye, I could hardly discern a star of less than the third magnitude.’ The degree of the transparency of the air is likewise varying almost in the course of every minute, so that even in the course of the same half hour, planets and stars will appear perfectly defined, and the reverse. The vapours moving and undulating the atmosphere, even when the sky appears clear to the naked eye, will in a few instants destroy the distinctness of vision, and in a few seconds more, the object will resume its clear and well-defined aspect.29

3. On the magnifying powers requisite for observing the phenomena of the different planets—comets—double stars, &c.

There are some objects connected with astronomy which cannot be perceived without having recourse to instruments and to powers of great magnitude. But it is a vulgar error to imagine that very large and very expensive telescopes are absolutely necessary for viewing the greater part of the more interesting scenery of the heavens. Most of the phenomena of the planets, comets and double stars and other objects, are visible with instruments of moderate dimensions, so that every one who has a relish for celestial investigations, may, at a comparatively small expense, procure a telescope, for occasional observations, which will show the principal objects and phenomena described in books on astronomy. Many persons have been misled by some occasional remarks which Sir W. Herschel made, in reference to certain very high powers which he sometimes put, by way of experiment, on some of his telescopes, as if these were the powers requisite for viewing the objects to which he refers. For example, it is stated that he once put a power of 6450 times on his 7 feet Newtonian telescope of 6³/₁₀ inches aperture; but this was only for the purpose of an experiment, and could be of no use whatever when applied to the moon, the planets and most objects in the heavens. Herschel, through the whole course of his writings, mentions his only having used it twice, namely on the stars a LyrÆ, and ? Leonis, which stars can be seen more distinctly and sharply defined with a power of 420. To produce a power of 6450 on such a telescope, would require a lens of only ¹/₇₇th of an inch in focal distance, and it is questioned by some whether Herschel had lenses of so small a size in his possession, or whether it is possible to form them with accuracy.

Powers requisite for observing the phenomena of the planets.—The planet Mercury requires a considerable magnifying power, in order to perceive its phases with distinctness. I have seldom viewed this planet with a less power than 100 and 150, with which powers its half moon, its gibbous, and its crescent phase, may be distinctly perceived. With a power of 40, 50, or even 60 times, these phases can with difficulty be seen, especially as it is generally at a low altitude, when such observations are made. The phases of Venus are much more easily distinguished, especially the crescent phase, which is seen to the greatest advantage about a month before and after the inferior conjunction. With a power not exceeding 25 or 30 times, this phase, at such periods, may be easily perceived. It requires, however, much higher powers to perceive distinctly the variations of the gibbous phase; and if this planet be not viewed at a considerably high altitude when in a half-moon or gibbous phase, the obscurity and undulations of the atmosphere near the horizon, prevent such phases from being accurately distinguished, even when high powers are applied. Although certain phenomena of the planets may be seen with such low powers as I have now stated, yet, in every instance, the highest magnifying powers, consistent with distinctness, should be preferred, as the eye is not then strained, and the object appears with a greater degree of magnitude and splendour. The planet Mars requires a considerable degree of magnifying power, even when at its nearest distance from the earth, in order to discern its spots and its gibbous phase. I have never obtained a satisfactory view of the spots which mark the surface, and their relative position, with a less power than 130, 160, or 200 times; and even with such powers, persons not much accustomed to look through telescopes, find a difficulty in distinguishing them.

The strongest and most prominent belts of Jupiter, may be seen with a power of about 45; which power may be put upon a 20-inch achromatic, or a 1 foot reflector. But a satisfactory view of all the belts, and the relative positions they occupy, cannot be obtained with much lower powers than 80, 100, or 140. The most common positions of these belts are—one dark and well-defined belt to the south of Jupiter’s equator; another of nearly the same description to the north of it, and one about his north and his south polar circles. These polar belts are much more faint, and consequently not so easily distinguished as the equatorial belts. The moons of this planet, in a very clear night, may sometimes be seen with a pocket 1 foot achromatic glass, magnifying about 15 or 16 times. Some people have pretended that they could see some of these satellites with their naked eye; but this is very doubtful, and it is probable that such persons mistook certain fixed stars which happened to be near Jupiter for his satellites. But, in order to have a clear and interesting view of these, powers of at least 80 or 100 times should be used. In order to perceive their immersions into the shadow of Jupiter, and the exact moment of their emersions from it, a telescope not less than a 44 inch achromatic, with a power of 150 should be employed. When these satellites are viewed through large telescopes with high magnifying powers, they appear with well defined disks, like small planets. The planet Jupiter has generally been considered as a good test by which to try telescopes for celestial purposes. When it is near the meridian and at a high altitude, if its general surface, its belts, and its margin appear distinct and well-defined, it forms a strong presumptive evidence that the instrument is a good one.

The planet Saturn forms one of the most interesting objects for telescopic observation. The ring of Saturn may be seen with a power of 45; but it can only be contemplated with advantage when powers of 100, 150, and 200 are applied to a 3 or a 5 feet achromatic. The belts of Saturn are not to be seen distinctly with an achromatic of less than 2¾ inches aperture, or a Gregorian reflector of less than 4 inches aperture, nor with a less magnifying power than 100 times. Sir W. Herschel has drawn this planet with five belts across its disk; but it is seldom that above one or two of them can be seen by moderate-sized telescopes and common observers. The division of the double ring, when the planet is in a favorable position for observation, and in a high altitude, may sometimes be perceived with a 44-inch achromatic, with an aperture of 2¾ inches, and with powers of 150 or 180, but higher powers and larger instruments are generally requisite to perceive this phenomenon distinctly; and even when a portion of it is seen at the extremities of the ansÆ, the division cannot, in every case, be traced along the whole of the half-circumference of the ring which is presented to our eye. Mr. Hadley’s engraving of Saturn, in the ‘Philosophical Transactions’ for 1723, though taken with a Newtonian reflector with a power of 228, represents the division of the ring as seen only on the ansÆ or extremities of the elliptic figure in which the ring appears. The best period for observing this division is when the ring appears at its utmost width. In this position it was seen in 1840, and it will appear nearly in the same position in 1855. When the ring appears like a very narrow ellipse, a short time previous to its disappearance, the division, or dark space between the rings, cannot be seen by ordinary instruments.

Sir W. Herschel very properly observes, ‘There is not perhaps another object in the heavens that presents us with such a variety of extraordinary phenomena as the planet Saturn; a magnificent globe, encompassed by a stupendous double ring; attended by seven satellites; ornamented with equatorial belts; compressed at the poles; turning upon its axis; mutually eclipsing its ring and satellites, and eclipsed by them; the most distant of the rings also turning upon its axis, and the same taking place with the farthest of the satellites; all the parts of the system of Saturn occasionally reflecting light on each other; the rings and moons illuminating the nights of the Saturnian, the globe and satellites enlightening the dark parts of the ring; and the planet and rings throwing back the sun’s beams upon the moons, when they are deprived of them at the time of their conjunctions.’ This illustrious astronomer states, that with a new 7 feet mirror of extraordinary distinctness he examined this planet, and found that the ring reflects more light than the body, and with a power of 570 the colour of the body becomes yellowish, while that of the ring remains more white. On March 11, 1780, he tried the powers of 222, 332, and 440 successively, and found the light of Saturn less intense than that of the ring; the colour of the body turning, with the high powers, to a kind of yellow white, while that of the ring still remained white.

Most of the satellites of Saturn are difficult to be perceived with ordinary telescopes, excepting the 4th, which may be seen with powers of from 60 to 100 times. It was discovered by Huygens in 1655, by means of a common refracting telescope 12 feet long, which might magnify about 70 times. The next in brightness to this is the 5th satellite, which Cassini discovered in 1671, by means of a 17 feet refractor, which might carry a power of above 80 times. The 3rd was discovered by the same astronomer in 1672, by a longer telescope; and the 1st and 2nd, in 1684, by means of two excellent object-glasses of 100 and 136 feet, which might have magnified from 200 to 230 times. They were afterwards seen by two other glasses of 70 and 90 feet, made by Campani, and sent from Rome to the Royal Observatory at Paris, by the King’s order, after the discovery of the 3rd and 5th satellites. It is asserted, however, that all those 5 satellites were afterwards seen with a telescope of 34 feet, with an aperture of 3³/₁₀ inches, which would magnify about 120 times. These satellites, on the whole, except the 4th and 5th, are not easily detected. Dr. Derham, who frequently viewed Saturn through Huygens’ glass of 126 feet focal length, declares, in the preface to his ‘Astro-Theology,’ that he could never perceive above 3 of the satellites. Sir W. Herschel observes, that the visibility of these minute and extremely faint objects, depends more on the penetrating than upon the magnifying power of our telescopes; and that with a 10 feet Newtonian, charged with a magnifying power of only 60, he saw all the 5 old satellites; but the 6th and 7th, which were discovered and were easily seen with his 40-feet telescope, and were also visible in his 20-feet instrument, were not discernible in the 7 or the 10-feet telescopes, though all that magnifying power can do may be done as well with the 7-feet as with any larger instrument. Speaking of the 7th satellite, he says, ‘Even in my 40-feet reflector it appears no bigger than a very small lucid point. I see it, however, very well in the 20-feet reflector; to which the exquisite figure of the speculum not a little contributes.’ A late observer asserts, that in 1825, with a 12-feet achromatic, of 7 inches aperture, made by Tulley, with a power of 150, the 7 satellites were easily visible, but not so easily with a power of 200; and that the planet appeared as bright as brilliantly burnished silver, and the division in the ring and a belt were very plainly distinguished, with a power of 200.

The planet Uranus, being generally invisible to the naked eye, is seldom an object of attention to common observers. A considerable magnifying power is requisite to make it appear in a planetary form with a well-defined disk. The best periods for detecting it are, when it is near its opposition to the sun, or when it happens to approximate to any of the other planets, or to a well-known fixed star. When none of these circumstances occur, its position requires to be pointed out by an Equatorial Telescope. On the morning of the 25th January, 1841, this planet happened to be in conjunction with Venus, at which time it was only 4 minutes north of that planet. Several days before this conjunction, I made observations on Uranus. On the evening of the 24th, about 8 hours before the conjunction, the two planets appeared in the same field of the telescope, the one exceedingly splendid, and the other more obscure, but distinct and well-defined. Uranus could not be perceived, either with the naked eye, or with an opera glass; but could be distinguished as a very small star by means of a pocket achromatic telescope magnifying about 14 times. It is questionable whether, under the most favourable circumstances, this planet can ever be distinguished by the naked eye. With magnifying powers of 30 and 70, it appeared as a moderately large star with a steady light, but without any sensible disk. With powers of 120, 180, and 250, it presented a round and pretty well-defined disk, but not so luminous and distinct as it would have done in a higher altitude.

The Double Stars require a great variety of powers, in order to distinguish the small stars that accompany the larger. Some of them are distinguished with moderate powers, while others require pretty large instruments, furnished with high magnifying eye-pieces. I shall therefore select only a few as a specimen. The star Castor, or a Geminorum, may be easily seen to be double with powers of from 70 to 100. I have sometimes seen these stars, which are nearly equal in size and colour, with a terrestrial power of 44 on a 44-inch achromatic. The appearance of this star with such powers is somewhat similar to that of ? CoronÆ in a 7 feet achromatic, of 5 inches aperture, with a power of 500. ? AndromedÆ may be seen with a moderate power. In a 30-inch achromatic of 2 inches aperture, and a power of 80, it appears like e Bootis, when seen in a 5-feet achromatic, with a power of 460. This star is said to be visible even in a 1-foot achromatic with a power of 35. e LyrÆ, which is a quintuple star, but appears to the naked eye as a single star,—may be seen to be double with a power of from 6 to 12 time. ? Leonis is visible in a 44-inch achromatic, with a power of 180 or 200. Rigel in a 3½-feet achromatic, may be seen with powers varying from 130 to 200. The small star, however, which accompanies Rigel, is sometimes difficult to be perceived, even with such powers. e Bootis is seldom distinctly defined with an achromatic of less aperture than 3¼ inches, or a reflector of less than 5 inches, with a power of at least 250.

These and similar stars are not to be expected to be seen equally well at all times, even when the magnifying and illuminating powers are properly proportioned; as much depends upon the state of the weather, and the pureness of the atmosphere. In order to perceive the closest of the double stars, Sir W. Herschel recommends, that the power of the telescope should be adjusted upon a star known to be single, of nearly the same altitude, magnitude, and colour with the double star which is to be observed, or upon one star above and another below it. Thus, the late Mr. Aubert, the astronomer, could not see the two stars of ? Leonis, when the focus was adjusted upon that star itself; but he soon observed the small star, after he had adjusted the focus upon Regulus. An exact adjustment of the focus of the instrument is indispensably requisite, in order to perceive such minute objects.

In viewing the NebulÆ, and the very small and immensely distant fixed stars, which require much light to render them visible, a large aperture of the object-glass or speculum, which admits of a great quantity of light, is of more importance than high magnifying powers. It is light chiefly, accompanied with a moderate magnifying power, that enables us to penetrate into the distant regions of space. Sir W. Herschel, when sweeping the profundities of the Milky way, and the Hand and Club of Orion, used a telescope of the Newtonian form, 20-feet focal length, and 18⁷/₁₀ inches diameter, with a power of only 157. On applying this telescope and power to a part of the Via Lactea, he found that it completely resolved the whole whitish appearance into stars, which his former telescopes had not light enough to effect; and which smaller instruments with much higher magnifying powers would not have effected. He tells us, that with this power, ‘the glorious multitude of stars,’ in the vicinity of Orion, ‘of all possible sizes, that presented themselves to view, was truly astonishing, and that he had fields which contained 70, 90 and 110 stars, so that a belt of 15 degrees long, and 2 degrees broad, which passed through the field of the telescope in an hour, could not contain less than fifty thousand stars that were large enough to be distinctly numbered.’ In viewing the Milky way, the NebulÆ, and small clusters of stars, such as PrÆsepe in Cancer, I generally use a power of 55 times, on an achromatic telescope 6 feet 6 inches in focal length, and 4 inches diameter. The eye-piece, which produces this power—which I formed for the purpose—consists of two convex lenses, the one next the eye 3 inches focal length, and 1²/₁₀ inch diameter, and that next the object 3½ inches focus, and 1⁴/₁₀ inch diameter, the deepest convex surfaces being next each other, and their distance ¼ inch. With this eye-piece a very large and brilliant field of view is obtained; and I find it preferable to any higher powers in viewing the nebulosities, and clusters of stars. In certain spaces of the heavens, it sometimes presents in one field, nearly a hundred stars. It likewise serves to exhibit a very clear and interesting view of the full moon.

In observing Comets, a very small power should generally be used, even on large instruments. These bodies possess so small a quantity of light, and they are so frequently enveloped in a veil of dense atmosphere, that magnifying power sometimes renders them more obscure; and therefore the illuminating power of a large telescope, with a small power, is in all cases to be preferred. A comet eye-piece should be constructed with a very large and uniformly distinct field, and should magnify only from 15 to 30 or 40 times, and the lenses of such an eye-tube should be nearly two inches in diameter. The late Rev. F. Wollaston recommended for observing comets, ‘a telescope with an achromatic object-glass of 16 inches focal length, and 2 inches aperture, with a Ramsden’s eye-glass magnifying about 25 times, mounted on a very firm equatorial stand, the field of view taking in 2 degrees of a great circle.’

In viewing the moon, various powers may be applied according to circumstances. The best periods of the moon for inspecting the inequalities on its surface, are either when it assumes a crescent or a half-moon phase, or two or three days after the period of half-moon. Several days after full-moon, and particularly about the third quarter, when this orb is waning, and when the shadows of its mountains and vales are thrown in a different direction from what they are when on the increase,—the most prominent and interesting views may be obtained. The most convenient season for obtaining such views is during the autumnal months, when the moon, about the third quarter, sometimes rises as early as 8 o’clock P.M., and may be viewed at a considerably high altitude by ten or eleven. When in the positions now alluded to, and at a high altitude, very high magnifying powers may sometimes be applied with good effect, especially if the atmosphere be clear and serene. I have sometimes applied a power, in such cases, of 350 times, on a 46-inch achromatic, with considerable distinctness; but it is only two or three times in a year, and when the atmosphere is remarkably favourable, that such a power can be used. The autumnal evenings are generally best fitted for such observations. The full moon is an object which is never seen to advantage with high powers, as no shadows or inequalities on its surface can then be perceived. It forms, however, a very beautiful object, when magnifying powers not higher than 40, 50, or 60 times are used. A power of 45 times, if properly constructed, will show the whole of the moon with a margin around it, when the darker and brighter parts of its surface will present a variegated aspect, and appear somewhat like a map to the eye of the observer.

4. Mode of exhibiting the Solar spots.

The solar spots may be contemplated with advantage by magnifying powers varying from 60 to 180 times; about 90 times is a good medium power, though they may sometimes be distinguished with very low powers, such as those usually adapted to a one-foot telescope, or even by means of a common opera-glass. The common astronomical eye-pieces given along with achromatic telescopes, and the sun-glasses connected with them, are generally ill-adapted for taking a pleasant and comprehensive view of the solar spots. In the higher magnifying powers, the first eye-glass is generally at too great a distance from the eye, and the sun-glass which is screwed over it, removes it to a still greater distance from the point to which the eye is applied, so that not above one third of the field of view can be taken in. This circumstance renders it difficult to point the instrument to any particular small spot on the solar disk which we wish minutely to inspect; and besides, it prevents us from taking a comprehensive view of the relative positions of all the spots that may at any time be traversing the disk. To obviate this inconvenience, the sun-glass would require to be placed so near to the glass next the eye as almost to touch it. But this is sometimes difficult to be attained, and, in high powers, even the thickness of the sun-glass itself is sufficient to prevent the eye from taking in the whole field of view. For preventing the inconveniences to which I now allude, I generally make use of a terrestrial eye-piece of a considerable power, with a large field, the sun-glass is fixed at the end of a short tube which slides on the eye-piece, and permits the coloured glass to approach within a line or two of the lens next the eye, so that the whole field of the telescope is completely secured. The eye-piece alluded to carries a magnifying power of 95 times for a 46-inch telescope, and takes in about three fourths of the surface of the sun, so that the relative positions of all the spots may generally be perceived at one view. Such a power is, in most cases, quite sufficient for ordinary observations; and I have seldom found any good effect to arise from attempting very high powers, when minutely examining the solar spots.

But, the most pleasant mode of viewing the solar spots—especially when we wish to exhibit them to others—is to throw the image of the sun upon a white screen, placed in a room which is considerably darkened. It is difficult, however, when the sun is at a high altitude, to put this method into practice, on account of the great obliquity with which his rays then fall, which prevents a screen from being placed at any considerable distance from the eye-end of the telescope. The following plan, therefore, is that which I uniformly adopt as being both the easiest and the most satisfactory. A telescope is placed in a convenient position, so as to be directed to the sun. This telescope is furnished with a diagonal eye-piece, such as that represented, fig. 77, (p. 344.) The window-shutters of the apartment are all closed, excepting a space sufficient to admit the solar rays; and, when the telescope is properly adjusted, a beautiful image of the sun, with all the spots which then happen to diversify his surface, is thrown upon the ceiling of the room. This image may be from 12 to 20, or 30 inches or more in diameter, according to the distance of the ceiling from the diagonal eye-piece. The greater this distance is, the larger the image. If the sun is at a very high altitude, the image will be elliptical; if he be at no great distance from the horizon, the image will appear circular or nearly so; but in either case the spots will be distinctly depicted, provided the focus of the telescope be accurately adjusted. In this exhibition, the apparent motion of the sun, produced by the rotation of the earth, and the passage of thin fleeces of clouds across the solar disk, exhibit a very pleasing appearance.

By this mode of viewing the solar spots we may easily ascertain their diameter and magnitude, at least to a near approximation. We have only to take a scale of inches, and measure the diameter of any well-defined and remarkable spot, and then the diameter of the solar image; and, comparing the one with the other, we can ascertain the number of miles either lineal or square, comprehended in the dimensions of the spot. For example, suppose a spot to measure one half-inch in diameter, and the whole image of the sun 25 inches, the proportion between the diameter of the spot and that of the sun will be as 1 to 50, in other words, the one fiftieth part of the sun’s diameter. Now, this diameter being 880,000 miles, this number, divided by 50, produces a quotient of 17,600 = the number of miles which its diameter measures. Such a spot will therefore contain an area of 243,285,504, or more than two hundred and forty-three millions of square miles, which is 46 millions of miles more than the whole superficies of the terraquous globe. Again, suppose the diameter of a spot measures ³/₁₀ inch, and the solar image 23 inches, the proportion of the diameter of the spot to that of the sun is as 3 to 230 = the number of tenths in 23 inches. The number of miles in the spot’s diameter will therefore be found by the following proportion: 230 : 880,000 :: 3 : 11,478; that is, the diameter of such a spot measures eleven thousand four hundred and seventy-eight miles. Spots of such sizes are not unfrequently seen to transit the solar disk.

By this mode of viewing the image of the sun, his spots may be exhibited to twenty or thirty individuals at once without the least straining or injury to the eyes; and as no separate screen is requisite, and as the ceilings of rooms are generally white, the experiment may be performed in half a minute without any previous preparation, except screwing on and adjusting the eye-piece. The manner of exhibiting the solar spots, in this way, is represented in fig. 82.

figure 82.

5. On the space-penetrating power of telescopes.—The power of telescopes to penetrate into the profundity of space is the result of the quantity of light they collect and send to the eye in a state fit for vision. This property of telescopes is sometimes designated by the expression Illuminating Power.

Sir W. Herschel appears to have been the first who made a distinction between the magnifying power, and the space-penetrating power of a telescope; and there are many examples which prove that such a distinction ought to be made, especially in the case of large instruments. For example, the small star, or speck of light, which accompanies the pole-star, may be seen through a telescope of large aperture, with a smaller magnifying power than with a telescope of a small aperture furnished with a much higher power. If the magnifying power is sufficient to show the small star completely separated from the rays which surround the large one, this is sufficient in one point of view; but in order that this effect may be produced, so as to render the small star perfectly distinguishable, a certain quantity of light must be admitted into the pupil of the eye—which quantity depends upon the area of the object-glass or speculum of the instrument, or, in other words, on the illuminating power. If we compare a telescope of 2¾ inches aperture with one of 5 inches aperture, when the magnifying power of each does not exceed 50 times for terrestrial objects, the effect of illuminating power is not so evident; but if we use a power of 100 for day objects, and 180 for the heavenly bodies, the effects of illuminating power is so clearly perceptible, that objects not only appear brighter, and more clearly visible, in the larger telescope, but with the same magnifying power, they also appear larger, particularly when the satellites of Jupiter and small stars are the objects we are viewing.

Sir W. Herschel remarks, that ‘objects are viewed in their greatest perfection, when, in penetrating space, the magnifying power is so low as only to be sufficient to show the object well—and when, in magnifying objects, by way of examining them minutely, the space-penetrating power is no higher than what will suffice for the purpose; for in the use of either power, the injudicious overcharge of the other will prove hurtful to vision.’ When illuminating power is in too high a degree, the eye is offended by the extreme brightness of the object. When it is in too low a degree, the eye is distressed by its endeavours to see what is beyond its reach; and therefore it is desirable, when we wish to give the eye all the assistance possible, to have the illuminating and the magnifying powers in due proportion. What this proportion is, depends, in a certain degree, upon the brightness of the object. In proportion to its brightness or luminosity, the magnifying power may, to a certain extent, be increased. Sir W. Herschel remarks, in reference to a LyrÆ, ‘This star, I surmise, has light enough to bear being magnified, at least a hundred thousand times, with no more than six inches of aperture.’ However beautifully perfect any telescopes may appear, and however sharp their defining power, their performance is limited by their illuminating powers—which are as the squares of the diameters of the apertures of the respective instruments. Thus, a telescope whose object-glass is 4 inches diameter will have four times the quantity of light, or illuminating power, possessed by a telescope whose aperture is only 2 inches, or in the proportion of 16 to 4,—the square of 4 being 16, and the square of 2 being 4.

The nature of the space-penetrating power, to which we are adverting, and the distinction between it, and magnifying power, may be illustrated from a few examples taken from Sir W. Herschel’s observations.

The first observation which I shall notice refers to the nebula between ? and ? Ophiuchi, discovered by Messier in 1764. The observation was made with a 10 feet reflector, having a magnifying power of 250, and a space-penetrating power of 28.67. His note is dated May 3, 1783. ‘I see several stars in it, and make no doubt a higher power and more light will resolve it all into stars. This seems to me a good nebula for the purpose of establishing the connection between nebulÆ and clusters of stars in general.’—‘June 18, 1784. The same nebula viewed with a Newtonian 20 feet reflector; penetrating power 61, and a magnifying power of 157; a very large and a very bright cluster of excessively compressed stars. The stars are but just visible, and are of unequal magnitudes. The large stars are red, the cluster is a miniature of that near Flamstead’s forty-second ComÆ Berenices; Right ascension 17^h 6^m 32^s Polar distance 108° 18´´’ In this case, a penetrating power of about 28, with a magnifying power of 250, barely shewed a few stars; when in the second instrument the illuminating power of 60 with the magnifying power of only 157 showed them completely.

Subsequently to the date of the latter observation, the 20 feet Newtonian telescope was converted into an Herschelian instrument, by taking away the small speculum, and giving the large one the proper inclination for obtaining the front view; by which alteration the illuminating power was increased from 61 to 75, and the advantage derived from the alteration was evident in the discovery of the satellites of Uranus by the altered telescope, which before was incompetent in the point of penetration, or illuminating power. ‘March 14, 1798, I viewed the Georgian planet (or Uranus) with a new 25 feet reflector. Its penetrating power is 95.85, and having just before also viewed it with my 20 feet instrument, I found that with an equal magnifying power of 300, the 25 feet telescope had considerably the advantage of the former.’ The aperture of the 20 feet instrument was 18.8 inches, and that of the 25 feet telescope, 24 inches, so that the superior effect of the latter instrument must have been owing to its greater illuminating power. The following observations show the superior power of the 40 feet telescope as compared with the 20 feet.—‘Feb. 24, 1786, I viewed the nebula near Flamstead’s fifth Serpentis, with my 20 feet reflector, magnifying power 157. The most beautiful extremely compressed cluster of small stars; the greatest part of them gathered together into one brilliant nucleus, evidently consisting of stars, surrounded with many detached gathering stars of the same size and colour. R.A. 15^h 7^m 12^s. P.D. 87° 8´´’—‘May 27, 1791, I viewed the same object with my 40 feet telescope, penetrating power 191.69, magnifying power 370. A beautiful cluster of stars. I counted about 200 of them. The middle of it is so compressed, that it is impossible to distinguish the stars.’—‘Nov. 5, 1791, I viewed Saturn with the 20 and 40 feet telescopes. Twenty feet. The fifth satellite of Saturn is very small. The first, second, third, fourth and fifth, and the new sixth satellites are in their calculated places. Forty feet. I see the new sixth satellite much better with this instrument than with the 20 feet. The fifth is also much larger here than in the 20 feet, in which it was nearly the same size as a small fixed star, but here it is considerably larger than that star.’

These examples, and many others of a similar kind, explain sufficiently the nature and extent of that species of power that one telescope possesses over another, in consequence of its enlarged aperture; but the exact quantity of this power is in some degree uncertain. To ascertain practically the illuminating power of telescopes, we must try them with equal powers on such objects as the following,—the small stars near the pole-star, and near Rigel and e Bootis—the division in the ring of Saturn—and distant objects in the twilight or towards the evening. These objects are distinctly seen with a 5 feet achromatic of 3⁸/₁₀ inches aperture, and an illuminating power of 144, while they are scarcely visible in a 3½ feet with an aperture of 2¾ inches, and an illuminating power of 72, supposing the same magnifying power to be applied. The illuminating power of a telescope is best estimated, in regard to land objects, when it is tried on minute objects, and such as are badly lighted up; and the advantage of a telescope with a large aperture will be most obvious, when it is compared with another of inferior size in the close of the evening, when looking at a printed bill composed of letters of various sizes. As darkness comes on, the use of illuminating power becomes more evident. In a 5 feet telescope some small letters will be legible, which are hardly discernible in the 3½ feet, and in the 2½ feet are quite undefinable, though the magnifying powers be equal. Sir W. Herschel informs us, that in the year 1776, when he had erected a telescope of 20 feet focal length of the Newtonian construction, one of its effects by trial was, that when towards evening, on account of darkness, the natural eye could not penetrate far into space, the telescope possessed that power sufficiently to show, by the dial of a distant church steeple, what o’clock it was, notwithstanding the naked eye could no longer see the steeple itself.

In order to convey an idea of the numbers by which the degree of space-penetrating power is expressed, and the general grounds on which they rest, the following statements may be made. The depth to which the naked eye can penetrate into the spaces of the heavens, is considered as extending to the twelfth order of distances—in other words, it can perceive a star at a distance 12 times farther than those luminaries, such as Sirius, Arcturus or Capella, which, from their vivid light, we presume to be nearest to us. It has been stated above, that Herschel calculated his 10 feet telescope to have a space-penetrating power of 28.67, that is, it could enable us to descry a star 28 times farther distant than the naked eye can reach. His 20 feet Newtonian was considered as having a similar power of 61; his 25 feet, nearly 96, and his 40 feet instrument, a power of 191.69. If each of these numbers be multiplied by 12, the product will indicate how much farther these telescopes will penetrate into space than the nearest range of the fixed stars, such as those of the first magnitude. For instance, the penetrating power of the 40 feet reflector being 191.69, this number multiplied by 12, gives a product of 2,300, which shows, that were there a series of two thousand three hundred stars extended in a line beyond Sirius, Capella and similar stars—each star separated from the one beyond it, by a space equal to the distance of Sirius from the earth—they might be all seen through the 40 feet telescope. In short, the penetrating power of telescopes is a circumstance which requires to be particularly attended to in our observations of celestial phenomena, and in many cases, is of more importance than magnifying power. It is the effect produced by illuminating power that renders telescopes, furnished with comparatively small magnifying powers, much more efficient in observing comets and certain nebulÆ and clusters of stars, than when high powers are attempted. Every telescope may be so adjusted, as to produce different space-penetrating powers. If we wish to diminish such a power, we have only to contract the object-glass or speculum, by placing circular rims, or apertures of different degrees of breadth, across the mouth of the great tube of the instrument. But we cannot increase this illuminating power beyond a certain extent, which is limited by the diameter of the object-glass. When we wish illuminating power beyond this limit, we must be furnished with an object-glass or speculum of a larger size; and hence, the rapid advance in price of instruments which have large apertures, and consequently high illuminating powers. Mr. Tulley’s 3½ feet achromatics of 2¾ inches aperture, sell at £26 5s. When the aperture is 3¼ inches, the price is £42. When 3¾ inches, £68 5s. The following table contains a statement of the ‘comparative lengths, apertures, illuminating powers, and prices, of Achromatic Refractors, and Gregorian Reflectors,’ according to Dr. Kitchener.

The illuminating powers stated in the above table are only comparative. Fixing on the number 25 as the illuminating power of a 2 feet telescope, 1⁶/₁₀ inch aperture, that of a 2½ feet 2 inches inches aperture, will be 40, of a 5 feet 3⁸/₁₀ inch aperture, 144, &c. If the illuminating power of a Gregorian 1½ foot, and 3 inches aperture, be 90, a 5 feet, with 9 inches aperture, will be 810, &c.

6. On choosing Telescopes, and ascertaining their properties.

It is an object of considerable importance, to every astronomical observer, that he should be enabled to form a judgment of the qualities of his telescope, and of any instruments of this description which he may intend to purchase. The following directions may perhaps be useful to the reader in directing him in the choice of an achromatic refracting telescope.

Supposing that an achromatic telescope of 3½ feet focal length, and 3¼ inches aperture were offered for sale, and that it were required to ascertain whether the object-glass, on which its excellence chiefly depends—is a good one and duly adjusted;—some opinion may be formed by laying the tube of the telescope in a horizontal position, on a firm support, about the height of the eye,—and by placing a printed card or a watch glass vertically, but in an inverted position, against some wall or pillar, at 40 or 50 yards distant, so as to be exposed to a clear sky. When the telescope is directed to this object, and accurately adjusted to the eye—should the letters on the card, or the strokes and dots on the watch-glass appear clearly and sharply defined, without any mistiness or coloration, and if very small points appear well defined—great hopes may be entertained that the glass will turn out a good one. But a telescope may appear a good one, when viewing common terrestrial objects, to eyes unaccustomed to discriminate deviations from perfect vision, while it may turn out to be an indifferent one, when directed to certain celestial objects. Instead therefore of a printed card, fix a black board, or one half of a sheet of black paper, in a vertical position at the same distance, and a circular disk of white writing paper, about ¼ of an inch in diameter, on the centre of the black ground. Then having directed the telescope to this object, and adjusted for the place of distinct vision, mark with a black-lead pencil the sliding eye-tube, at the end of the main tube, so that this position can always be known; and if this sliding tube be gradually drawn out, or pushed in, while the eye beholds the disk, it will gradually enlarge and lose its colour, till its edges cease to be well-defined. Now, if the enlarged misty circle is observed to be concentric with the disk itself, the object-glass is properly centered, as it has reference to the tube; but if the misty circle goes to one side of the disk, the cell of the object-glass is not at right angles to the tube, and must have its screws removed and its holes elongated, by a rattailed file, small enough to enter the holes. When this has been done, the cell may be replaced, and the disk examined a second time, and a slight stroke on one edge of the cell, by a wooden mallet, will show by the alteration made in the position of the misty portion of the disk, how the adjustment is to be effected, which is known to be right when a motion in the sliding tube will make the diluted disk enlarge in a circle concentric with the disk itself. When the disk will enlarge so as to make a ring of diluted white light round its circumference, as the sliding tube holding the eye-piece is pushed in or drawn out, the cell may be finally fixed by the screws passing through its elongated holes.

When the object-glass is thus adjusted, it may then be ascertained whether the curves of the respective lenses composing the object-glass are well-formed and suitable for each other. If a small motion of the sliding tube of about ¹/₁₀th of an inch in a 3½ feet telescope, from the point of distinct vision, will dilute the light of the disk and render the appearance confused, the figure of the object-glass is good; particularly if the same effect will take place at equal distances from the point of distinct vision, when the tube is alternately drawn out and pushed in. A telescope that will admit of much motion in the sliding tube without sensibly affecting the distinctness of vision, will not define an object well at any point of adjustment, and must be considered as having an imperfect object-glass, inasmuch as the spherical aberration of the transmitted rays is not duly corrected. The due adjustment of the convex lens, or lenses, to the concave one, will be judged of by the absence of coloration round the enlarged disk, and is a property distinct from the spherical aberration; the achromatism depending on the relative focal distances of the convex and concave lenses, is regulated by the relative dispersive powers of the pieces of glass made use of; but the distinctness of vision depends on a good figure of the computed curves that limit the focal distances. When an object-glass is free from imperfection in both these respects, it may be called a good glass for terrestrial purposes.

It still, however, remains to be determined how far such an object-glass may be good for viewing a star or a planet, and can only be known by actual observations on the heavenly bodies. When a good telescope is directed to the moon or to Jupiter, the achromatism may be judged of, by alternately pushing in, and drawing out the eye-piece, from the place of distinct vision. In the former case, a ring of purple will be formed round the edge; and in the latter, a ring of light green, which is the central colour of the prismatic spectrum; for these appearances show, that the extreme colours red and violet are corrected. Again, if one part of a lens employed have a different refractive power from another part of it, that is, if the flint-glass particularly is not homogeneous, a star of the first and even of the second magnitude will point out the natural defect by the exhibition of an irradiation, or what is called a wing, at one side, which no perfection of figure or of adjustment will banish, and the greater the aperture the more liable is the evil to happen. Hence caps with different apertures are usually supplied with large telescopes, that the extreme parts of the glass may be cut off, in observations requiring a round and well-defined image of the body observed.

Another method of determining the figure and quality of an object-glass is by first covering its centre by a circular piece of paper, as much as one half of its diameter, and adjusting it for distinct vision of a given object, such as the disk above mentioned, when the central rays are intercepted—and then trying if the focal length remains unaltered when the paper is taken away, and an aperture of the same size applied, so that the extreme rays may in their turn be cut off. If the vision remains equally distinct in both cases, without any new adjustment for focal distance, the figure is good, and the spherical aberration cured, and it may be seen by viewing a star of the first magnitude successively in both cases, whether the irradiation is produced more by the extreme or by the central parts of the glass. Or, in case the one half be faulty and the other good, a semicircular aperture, by being turned gradually round in trial, will detect what semicircle contains the defective portion of the glass; and if such portion should be covered, the only inconvenience that would ensue, would be the loss of so much light as is thus excluded. When an object-glass produces radiations in a large star, it is unfit for the nicer observations of astronomy, such as viewing double stars of the first class. The smaller a large star appears in any telescope, the better is the figure of the object-glass, but if the image of the star be free from wings, the size of its disk is not an objection in practical observations.30

Some opticians are in the habit of inserting a diaphragm into the body of the large tube, to cut off the extreme rays coming from the object-glass when the figure is not good, instead of lessening the aperture by a cap. When this is the case, a deficiency of light will be the consequence beyond what the apparent aperture warrants. It is therefore proper to examine that the diaphragm be not placed too near the object-glass, so as to intercept any of the useful rays. Sometimes a portion of the object-glass is cut off by the stop in the eye-tube. To ascertain this, adjust the telescope to distinct vision, then take out the eye-glasses, and put your finger on some other object on the edge of the outside of the object-glass, and look down the tube; if you can see the tip of your finger, or any object in its place, just peeping over the edge of the object-glass, no part is cut off. I once had a 3½ feet telescope whose object-glass measured 3 inches diameter, which was neither so bright, nor did it perform in other respects nearly so well as another of the same length whose object-glass was only 2¾ inches diameter; but I found that a diaphragm was placed about a foot within the end of the large tube, which reduced the aperture of the object-glass to less than 2½ inches; and when it was removed the telescope was less distinct than before. The powers given along with this instrument were much lower than usual—none of them exceeding 100 times. This is a trick not uncommon with some opticians.

Dr. Pearson mentions that an old Dollond’s telescope of 63 inches focal length, and 3¾ inches aperture, supposed to be an excellent one, was brought to Mr. Tulley, when he was present, and the result of the examination was that its achromatism was not perfect. The imperfection was thus determined by experiment. A small glass globe was placed at 40 yards distance from the object-end of the telescope when the sun was shining, and the speck of light seen reflected from this globe formed a good substitute for a large star, as an object to be viewed. When the focal length of the object-glass was adjusted to this luminous object, no judgment could be formed of its prismatic aberrations, till the eye-piece had been pushed in beyond the place of correct vision; but when the telescope was shortened a little, the luminous disk occasioned by such shortening was strongly tinged with red rays at its circumference. On the contrary, when the eye-piece was drawn out, so as to lengthen the telescope too much, the disk thus produced was tinged with a small circle of red at its centre, thereby denoting that the convex lens had too short a focal length; and Mr. Tulley observed, that if one or both of the curves of the convex lens were flattened till the total focal length should be about 4 inches increased, it would render the telescope quite achromatic, provided in doing this the aberration should not be increased.

The following general remarks may be added. 1. To make anything like an accurate comparison of telescopes, they must be tried not only at the same place, but as nearly as possible at the same time, and, if the instruments are of the same length and construction, if possible, with the same eye-piece. 2. A difference of 8 or 10 times in the magnifying power, will sometimes, on certain objects, give quite a different character to a telescope. It has been found by various experiments that object-glasses of two or three inches longer focus will produce different vision with the same eye-piece. 3. Care must be taken to ascertain that the eye-glasses are perfectly clean and free from defects. The defects of glass are either from veins—specks—scratches—colour, or an incorrect figure. To discover veins in an eye or an object-glass, place a candle at the distance of 4 or 5 yards; then look through the glass, and move it from your eye till it appear full of light—you will then see every vein, or other imperfection in it which may distort the objects and render vision imperfect. Specks or scratches, especially in object-glasses, are not so injurious as veins, for they do not distort the object, but only intercept a portion of the light. 4. We cannot judge accurately of the excellence of any telescope by observing objects with which we are not familiarly acquainted. Opticians generally try an instrument at their own marks, such as the dial-plate of a watch, a finely engraved card, a weather-cock, or the moon and the planet Jupiter, when near the meridian. Of several telescopes of the same length, aperture and magnifying power, that one is generally considered the best with which we can read a given print at the greatest distance, especially if the print consists of figures, such as a table of logarithms, where the eye is not apt to be deceived by the imagination, in guessing at the sense of a passage, when two or three words are distinguished.

There is a circumstance which I have frequently noticed, in reference to achromatic telescopes, particularly those of a small size, and which I have never seen noticed by any optical writer. It is this,—if the telescope, when we are viewing objects, be gradually turned round its axis, there is a certain position in which the objects will appear distinct and accurately defined; and if it be turned round exactly a semicircle from this point, the same degree of distinctness is perceived; but in all other positions, there is an evident want of clearness and defining power. This I find to be the case in more than ten 1 foot and 2 feet telescopes now in my possession; and therefore I have put marks upon the object-end of each of them, to indicate the positions in which they should be used for distinct observation.—This is a circumstance which requires, in many cases, to be attended to in the choice and the use of telescopical instruments, and in fixing and adjusting them on their pedestals. In some telescopes this defect is very striking, but it is in some measure perceptible in the great majority of instruments which I have had occasion to inspect. Even in large and expensive achromatic telescopes this defect is sometimes observable. I have an achromatic whose object-glass is 4¹/₁₀ inches diameter, which was much improved in its defining power, by being unscrewed from its original position, or turned round its axis—about one-eighth part of its circumference. This defect is best detected by looking at a large printed bill, or a sign-post at a distance, when, on turning round the telescope or object-glass, the letters will appear much better defined in one position than in another. The position in which the object appears least distinct is when the upper part of the telescope is a quadrant of a circle different from the two positions above-stated, or at an equal distance from each of them.

7. On the mode of determining the magnifying power of Telescopes.

In regard to refracting telescopes, we have already shown that, when a single eye-glass is used, the magnifying power may be found by dividing the focal distance of the object-glass by that of the eye-glass. But when a Huygenian eye-piece, or a four-glass terrestrial eye-piece such as is now common in achromatic telescopes, is used, the magnifying power cannot be ascertained in this manner; and in some of the delicate observations of practical astronomy, it is of the utmost importance to know the exact magnifying power of the instrument with which the observations are made, particularly when micrometrical measurements are employed to obtain the desired results.—The following is a general method of finding the magnifying powers of telescopes when the instrument called a dynameter is not employed; and it answers for refracting and reflecting telescopes of every description.

Having put up a small circle of paper, an inch or two in diameter, at the distance of about 100 yards, draw upon a card 2 black parallel lines, whose distance from each other is equal to the diameter of the paper circle. Then view through the telescope the paper circle with one eye, and the parallel lines with the other; and let the parallel lines be moved nearer to or further from, the eye, till they seem exactly to cover the small circle viewed through the telescope. The quotient obtained by dividing the distance of the paper circle by the distance of the parallel lines from the eye, will be the magnifying power of the telescope. It requires a little practice before this experiment can be performed with accuracy. The one eye must be accustomed to look at an object near at hand, while the other is looking at a more distant object through the telescope. Both eyes must be open at the same time, and the image of the object seen through the telescope must be brought into apparent contact with the real object near at hand. But a little practice will soon enable any observer to perform the experiment with ease and correctness, if the telescope be mounted on a firm stand, and its elevation or depression produced by rack-work.

The following is another method, founded on the same principle:—Measure the space occupied by a number of the courses, or rows of bricks in a modern building—which, upon an average, is found to have 8 courses in 2 feet, so that each course or row, is 3 inches. Then cut a piece of paper 3 inches in height, and of the length of a brick—which is about 9 inches—so that it may represent a brick, and fixing the paper against the brick wall, place the telescope to be examined at the distance of about 80 or 100 yards from it. Now, looking through the telescope at the paper with one eye, and at the same time, with the other eye, looking past the telescope, observe what extent of wall the magnified image of the paper appears to cover, then count the courses of bricks in that extent, and it will give the magnifying power of the telescope. It is to be observed, however, that the magnifying power determined in this way, will be a fraction greater than for very distant objects, as the focal distance of the telescope is necessarily lengthened in order to obtain distinct vision of near objects.

In comparing the magnifying powers of two telescopes, or of the same telescope, when different magnifying powers are employed, I generally use the following simple method. The telescopes are placed at 8 or 10 feet distant from a window, with their eye-ends parallel to each other, or at the same distance from the window. Looking at a distant object, I fix upon a portion of it whose magnified image will appear to fill exactly two or three panes of the window. Then putting on a different power, or looking through another telescope, I observe the same object, and mark exactly the extent of its image on the window-panes, and compare the extent of the one image with the other. Suppose for example, that the one telescope has been previously found to magnify 90 times, and that the image of the object fixed upon exactly fills three panes of the window, and that with the other power or the other telescope, the image fills exactly two panes, then the magnifying power is equal to two thirds of the former, or 60 times; and were it to fill only one pane, the power would be about 30 times. A more correct method is to place at one side of the window, a narrow board, two or three feet long, divided into 15 or 20 equal parts, and observe how many of these parts appear to be covered by the respective images, of the different telescopes. Suppose, in the one case, 10 divisions to be covered by the image, in a telescope magnifying 90 times, and that the image of the same object in another telescope, measures 6 divisions, then its power is found by the following proportion, 10 : 90 : 6 : 54 : that is, this telescope magnifies 54 times.

Another mode which I have used for determining, to a near approximation, the powers of telescopes, is as follows:—Endeavour to find the focus of a single lens which is exactly equivalent to the magnifying power of the eye-piece, whether the Huygenian or the common terrestrial eye-piece. This may be done by taking a small lens, and using it as an object-glass to the eye-piece. Looking through the eye-piece to a window and holding the lens at a proper distance, observe whether the image of one of the panes exactly coincides with the pane, as seen by the naked eye; if it does, then the magnifying power of the eye-piece is equal to that of the lens. If the lens be ½ inch focal length, the eye-piece will produce the same magnifying power, as a single lens when used as an eye-glass to the telescope, and the magnifying power will then be found by dividing the focal distance of the object-glass by that of the eye-glass. But if the image of the pane of glass does not exactly coincide with the pane as seen by the other eye, then proportional parts may be taken by observing the divisions of such a board as described above, or we may try lenses of different focal distances. Suppose, for example, that a lens 2 inches focal length had been used, and that the image of a pane covered exactly the space of two panes, the power of the eye-piece is then equal to that of a single lens 1 inch focal distance.

The following is another mode depending on the same general principle. If a slip of writing-paper one inch long, or a disk of the same material of one inch diameter, be placed on a black ground at from 30 to 50 yards distance from the object-end of the telescope, and a staff painted white, and divided into inches and parts by strong black lines, be placed vertically near the said paper or disk; the eye that is directed through the telescope when adjusted for vision, will see the magnified disk, and the other eye, looking along the outside of the telescope, will observe the number of inches and parts that the disk projected on it will just cover, and as many inches as are thus covered will indicate the magnifying power of the telescope—at the distance for which it is adjusted for distinct vision. The solar power, or powers for very distant objects, may be obtained by the following proportion:—As the terrestrial focal length, at the given distance: is to the solar focal length :: so is the terrestrial power, to the solar power. For example, a disk of white paper one inch in diameter, was placed on a black board, and suspended on a wall contiguous to a vertical black staff that was graduated into inches by strong white lines, at a distance of 33 yards 2½ feet, and when the adjustment for vision was made with a 42 inch telescope, the left eye of the observer viewed the disk projected on the staff, while the right eye observed that the enlarged image of the disk covered just 58½ inches on the staff, which number was the measure of the magnifying power, at the distance answering to 33 yards 2½ feet—which in this case exceeded the solar focus by an inch and a half. Then according to the above analogy, we have, as 43.5 : 42 :: 58.5 : 56.5 nearly. Hence the magnifying power due to the solar focal length of the telescope in question is 56.5, and the distance 33 yards 2½ feet, is that which corresponds to an elongation of the solar focal distance an inch and a half.31 If we multiply the terrestrial and the solar focal distances together, and divide the product by their difference, we shall again obtain the distance of the terrestrial object from the telescope. Thus, (43.5 + 42)/1.5 = 1218 inches = 101.5 feet, or 33 yards 2½ feet.

The magnifying power of a telescope is also determined, by measuring the image which the object-glass or the large speculum of a telescope forms at its solar focus. This is accomplished by means of an instrument called a Dynameter. This apparatus consists of a strip of mother-of-pearl, marked with equal divisions, from the ¹/₁₀₀th to the ¹/₁₀₀₀th of an inch apart, according to the accuracy required. This measure is attached to a magnifying lens in its focus, in order to make the small divisions more apparent. When the power of a telescope is required, the person must measure the clear aperture of the object-glass, then holding the pearl dynameter next the eye-glass, let him observe how many divisions the small circle of light occupies, when the instrument is directed to a bright object. Then by dividing the diameter of the object-glass by the diameter of this circle of light, the power will be obtained.32 The most accurate instrument of this kind is the Double Image Dynameter invented by Ramsden, and another on the same principle now made by Dollond, a particular description of which may be found in Dr. Pearson’s ‘Introduction to Practical Astronomy.’ The advantage attending these dynameters is that they do not require any knowledge of the thickness and focal lengths of any of the lenses employed in a telescope, nor yet of their number or relative positions; neither does it make any difference whether the construction be refracting or reflecting, direct or inverting. One operation includes the result arising from the most complicated construction.

I shall only mention farther the following method of discovering the magnifying power, which is founded on the same general principle as alluded to above. Let the telescope be placed in such a position opposite the sun, that the rays of light may fall perpendicularly on the object-glass; and the pencil of rays may be received on a piece of paper, and its diameter measured. Then, as the diameter of the pencil of rays is to that of the object-glass, so is the magnifying power of the telescope.

8.—On cleaning the lenses of telescopes.—

It is necessary, in order to distinct vision, that the glasses, particularly the eye-glasses of telescopes be kept perfectly clean, free of damp, dust, or whatever may impede the transmission of the rays of light. But great caution ought to be exercised in the wiping of them, as they are apt to be scratched, or otherwise injured by a rough and incautious mode of cleaning them. They should never be attempted to be wiped unless they really require it; and, in this case, they should be wiped carefully and gently with a piece of new and soft lamb’s-skin leather. If this be not at hand, a piece of fine silk paper, or fine clean linen may be used as a substitute. The lens which requires to be most particularly attended to is the second glass from the eye, or the field-glass; for if any dust or other impediment be found upon this glass, it is always distinctly seen, being magnified by the glass next the eye. The next glass which requires attention is the fourth from the eye, or that which is next the object. Unless the glass next the eye be very dusty, a few small spots or grains of dust are seldom perceptible. The object-glass of an achromatic should seldom be touched, unless damp adheres to it. Care should be taken never to use pocket handkerchiefs or dirty rags for wiping lenses. From the frequent use of such articles, the glasses of seaman’s telescopes get dimmed and scratched in in the course of a few years. If the glasses be exceedingly dirty, and if greasy substances are attached to them, they may be soaked in spirits and water, and afterwards carefully wiped. In replacing the glasses in their socket, care should be taken not to touch the surfaces with the fingers, as they would be dimmed with the perspiration: they should be taken hold of by the edges only, and carefully screwed into the same cells from which they were taken.

ON MEGALASCOPES, OR TELESCOPES FOR VIEWING VERY NEAR OBJECTS.

It appears to have been almost overlooked by opticians and others, that telescopes may be constructed so as to exhibit a beautiful and minute view of very near objects, and to produce even a microscopic effect, without the least alteration in the arrangement of the lenses of which they are composed. This object is effected simply by making the eye-tube of a telescope of such a length as to be capable of being drawn out 12 or 13 inches beyond the point of distinct vision for distant objects. The telescope is then rendered capable of exhibiting with distinctness all kinds of objects, from the most distant to those which are placed within 3 or 4 feet of the instrument—or not nearer than double the focal distance of the object-glass. Our telescopes, however, are seldom or never fitted with tubes that slide farther than an inch or two beyond the point of distinct vision for distant objects, although a tube of a longer size than usual, or an additional tube would cost but a very trifling expence.

The following, among many others, are some of the objects on which I have tried many amusing experiments with telescopes fitted up with the long tubes to which I allude. The telescope to which I shall more particularly advert is an achromatic, mounted on a pedestal, having an object-glass about 19 inches focal length, and 1? inch diameter, with magnifying powers for distant objects of 13 and 20 times. When this instrument is directed to a miniature portrait, 3½ inches in length, placed in a good light, at the distance of about 8 or 10 feet, it appears as large as an oil-painting four or five feet long, and represents the individual as large as life. The features of the face appear to stand out in bold relief: and perhaps there is no representation of the human figure that more resembles the living prototype, than in this exhibition, provided the miniature is finely executed. In this case the tube requires to be pulled out four or five inches from the point of distinct vision for distant objects, and consequently the magnifying power is proportionally increased. Another class of objects to which such a telescope may be applied is Perspective prints, either of public buildings, streets or landscapes. When viewed in this way they present a panoramic appearance, and seem nearly as natural as life—just in the same manner as they appear in the Optical Diagonal Machine, or when reflected in a large concave mirror—with this advantage, that, while in these instruments the left hand side of the print appears where the right should be,—the objects seen through the telescope appear exactly in their natural position. In this case, however, the telescope should have a small magnifying power, not exceeding 5 or 6 times, so as to take in the whole of the landscape. If an astronomical eye-piece be used, the print will require to be inverted.

Other kinds of objects which may be viewed with this instrument, are trees, flowers, and other objects in gardens immediately adjacent to the apartment in which we make our observations. In this way we may obtain a distinct view of a variety of rural objects, which we cannot easily approach, such as the buds and blossoms on the tops of trees, and the insects with which they may be infested. There are certain objects on which the telescope may be made to produce a powerful microscopical effect, such as the more delicate and beautiful kinds of flowers, the leaves of trees, and similar objects. In viewing such objects, the telescope may be brought within little more than double the focal distance of the object-glass from the objects to be viewed, and then the magnifying power is very considerably increased. A nosegay composed of a variety of delicate flowers, and even a single flower, such as the sea-pink, makes a splendid appearance in this way. A peacock’s feather, or even the fibres on a common quill, appear very beautiful, when placed in a proper light. The leaves of trees, particularly the leaf of the plane-tree, when placed against a window-pane, so that the light may shine through them—appear, in all their internal ramifications, more distinct, beautiful and interesting, than when viewed in any other way; and in such views a large portion of the object is at once exhibited to the eye. In this case, the eye-piece of such a telescope as that alluded to requires to be drawn out 12 or 14 inches beyond the point of distinct vision for objects at a distance—and the distance between these near objects and the object-end of the telescope, is only about 3½ feet.

A telescope having a diagonal eye-piece presents a very pleasant view of near objects in this manner. With an instrument of this kind, I have frequently viewed the larger kind of small objects alluded to above, such as the leaves of shrubs and trees, flowers consisting of a variety of parts, the fibres of a peacock’s feather and similar objects. In this case the object-glass of the instrument, which is 10½ inches focal length, was brought within 22 inches of the object, and the eye looked down upon it, in the same manner, as when we view objects in a compound microscope. A common pocket achromatic telescope may be used for the purposes now stated, provided the tube in the eye-piece containing the two lenses next the object, be taken out, in which case the two glasses next the eye form an astronomical eye-piece, and the tubes may be drawn out 5 or 6 inches beyond the focal point for distant objects, and will produce distinct vision for objects not farther distant than about 20 or 24 inches. But, in this case, the objects to be viewed must be inverted, in order that they may be seen in their natural positions when viewed through the instrument. Telescopes of a large size and high magnifying powers may likewise be used with advantage for viewing very near objects in gardens adjacent to the room in which the instruments are placed, provided the sliding-tube next the eye has a range of two or three inches beyond the point of vision for distant objects. In this case, a magnifying power of 100 times on a 3½ or a 5 feet achromatic produces a very pleasant effect. In making the observations to which I have now alluded, it is requisite in order to distinct vision, and to obtain a pleasing view of the objects, that the instrument should be placed on a pedestal, and capable of a motion in every direction. The adjustment for distinct vision may be made either by the sliding-tube, or by removing the telescope nearer to or farther from the object.

REFLECTIONS ON LIGHT AND VISION—AND ON THE NATURE AND UTILITY OF TELESCOPES.

Light is one of the most wonderful and beneficial, and at the same time one of the most mysterious agents in the material creation. Though the sun from which it flows to this part of our system is nearly a hundred millions of miles from our globe, yet we perceive it as evidently, and feel its influence as powerfully, as if it emanated from no higher a region than the clouds. It supplies life and comfort to our physical system, and without its influence and operations on the various objects around us, we could scarcely subsist and participate of enjoyment for a single hour. It is diffused around us on every hand from its fountain the sun; and even the stars, though at a distance hundreds of thousands of times greater than that of the solar orb, transmit to our distant region a portion of this element. It gives beauty and fertility to the earth, it supports the vegetable and animal tribes, and is connected with the various motions which are going forward throughout the system of the universe. It unfolds to us the whole scenery of external nature—the lofty mountains and the expansive plains, the majestic rivers and the mighty ocean; the trees, the flowers, the crystal streams, and the vast canopy of the sky adorned with ten thousands of shining orbs. In short there is scarcely an object within the range of our contemplation, but what is exhibited to our understanding through the medium of light, or at least bears a certain relation to this enlivening and universal agent. When we consider the extreme minuteness of the rays of light, their inconceivable velocity, the invariable laws by which they act upon all bodies, the multifarious phenomena produced by their inflections, refractions and reflections, while their original properties remain the same; the endless variety of colours they produce on every part of our terrestrial creation, and the facility with which millions of rays pass through the smallest apertures, and pervade substances of great density, while every ray passes forward in the crowd without disturbing another, and produces its own specific impression—we cannot but regard this element as the most wonderful, astonishing and delightful part of the material creation. When we consider the admirable beauties and the exquisite pleasures of which light is the essential source, and how much its nature is still involved in mystery, notwithstanding the profound investigations of modern philosophers, we may well exclaim with the Poet:—

The eye is the instrument by which we perceive the beautiful and multifarious effects of this universal agent. Its delicate and complicated structure, its diversified muscles, its coats and membranes, its different humours possessed of different refractive powers, and the various contrivances for performing and regulating its external and internal motions, so as to accomplish the ends intended—clearly demonstrate this organ to be a master-piece of Divine mechanism—the workmanship of Him whose intelligence surpasses conception, and whose Wisdom is unsearchable. ‘Our sight (says Addison) is the most perfect and delightful of all our senses. It fills the mind with the largest variety of ideas, converses with its objects at the greatest distance, and continues the longest in action, without being tired or satiated with its proper enjoyments. The sense of feeling can indeed give us a notion of extension, shape, and all other ideas that enter the eye, except colours; but at the same time it is very much strained, and confined in its operation to the number, bulk and distance of its particular objects. Our sight seems designed to supply all these defects, and may be considered as a more delicate and diffusive kind of touch that spreads itself over an infinite multitude of bodies, comprehends the largest figures, and brings into our reach some of the more remote parts of the universe.’

Could we suppose an order of beings endued with every human faculty but that of sight, it would appear incredible to such beings—accustomed only to the slow information of touch—that by the addition of an organ consisting of a ball and socket, of an inch diameter, they might be enabled, in an instant of time, without changing their place, to perceive the disposition of a whole army, the order of a battle, the figure of a magnificent palace, or all the variety of a landscape. If a man were by feeling to find out the figure of the Peak of Teneriffe, or even of St. Peter’s church at Rome, it would be the work of a lifetime. It would appear still more incredible to such beings as we have supposed, if they were informed of the discoveries which may be made by this little organ in things far beyond the reach of any other sense—that, by means of it we can find our way in the pathless ocean—that we can traverse the globe of the earth, determine its figure and dimensions, and delineate every region of it—yea, that we can measure the planetary orbs, and make discoveries in the sphere of the fixed stars. And, if they were farther informed that, by means of this same organ, we can perceive the tempers and dispositions, the passions and affections of our fellow-creatures, even when they want most to conceal them—that when the tongue is taught most artfully to lie and dissemble, the hypocrisy should appear in the countenance to a discerning eye—and that by this organ we can often perceive what is straight and what is crooked in the mind as well as in the body—would it not appear still more astonishing to beings such as we have now supposed?33

Notwithstanding these wonderful properties of the organ of vision, the eye, when unassisted by art, is comparatively limited in the range of its powers. It cannot ascertain the existence of certain objects at the distance of three or four miles, nor perceive what is going forward in nature or art beyond such a limit. By its natural powers we perceive the moon to be a globe about half a degree in diameter, and diversified with two or three dusky spots, and that the sun is a luminous body of apparently the same size—that the planets are luminous points, and that about a thousand stars exist in the visible canopy of the sky. But the ten thousandth part of those luminaries, which are within the reach of human vision, can never be seen by the unassisted eye. Here the TELESCOPE interposes, and adds a new power to the organ of vision, by which it is enabled to extend its views to regions of space immeasurably distant, and to objects, the number and magnitude of which could never otherwise have been surmised by the human imagination. By its aid we obtain a sensible demonstration that space is boundless—that the universe is replenished with innumerable suns and worlds—that the remotest regions of immensity, immeasurably beyond the limits of unassisted vision, display the energies of Creating Power, and that the Empire of the Creator extends far beyond what eye hath seen or the human imagination can conceive.

The telescope is an instrument of a much more wonderful nature than what most people are apt to imagine. However popular such instruments now are, and however common a circumstance it is to contemplate objects at a great distance which the naked eye cannot discern, yet, prior to their invention and improvement, it would have appeared a thing most mysterious, if not impossible, that objects at the distance of ten miles could be made to appear as if within a few yards of us, and that some of the heavenly bodies could be seen as distinctly as if we had been transported by some superior power, hundreds of millions of miles beyond the bounds of our terrestrial habitation. Who could ever have imagined—reasoning a priori—that the refraction of light in glass—the same power by which a straight rod appears crooked in water, by which vision is variously distorted, and by which we are liable to innumerable deceptions—that that same power, or law of nature, by the operation of which the objects in a landscape appear distorted when seen through certain panes of glass in our windows, that that power should ever be so modified and directed as to extend the boundaries of vision, and enable us clearly to distinguish scenes and objects at a distance a thousand times beyond the natural limits of our visual organs? Yet such are the discoveries which science has achieved, such the powers it has brought to light, that by glasses ground into different forms, and properly adapted to each other, we are enabled as it were to contract the boundaries of space, to penetrate into the most distant regions, and to bring within the reach of our knowledge the most sublime objects in the universe.

When Pliny declared in reference to Hipparchus, the ancient astronomer, ‘Ausus rem Deo improbam annumerare posteris stellas,’—that ‘he dared to enumerate the stars for posterity, an undertaking forbidden by God,’ what would that natural historian have said, had it been foretold that in less than 1600 years afterwards, a man would arise who should enable posterity to perceive, and to enumerate ten times more new stars than Hipparchus ever beheld—who should point out higher mountains on the moon than on the earth, who should discover dark spots, as large as our globe, in the sun, the fountain of light—who should descry four moons revolving in different periods of time around the planet Jupiter, and could show to surrounding senators the varying phases of Venus? and that another would soon after arise who should point out a double ring of six hundred thousand miles in circumference, revolving around the planet Saturn, and ten hundreds of thousands of stars which neither Hipparchus nor any of the ancient astronomers could ever descry? Yet these are only a small portion of the discoveries made by Galileo and Herschel, by means of the telescope. Had any one prophetically informed Archimedes, the celebrated geometrician of Syracuse, that vision would, in after ages, be thus wonderfully assisted by art—and further, that one manner of improving vision would be to place a dark opake body directly between the object and the eye—and that another method would be, not to look at the object, but to keep the eye quite in a different, and even in an opposite direction, or to stand with the back directly opposed to it, and to behold all the parts of it, invisible to the naked eye, most distinctly in this way—he would, doubtless have considered the prophet as an enthusiastic fool or a raving madman. Yet these things have been realized in modern times in the fullest extent. In the Gregorian reflecting telescope an opake body, namely the small speculum near the end of the tube, interposes directly between the eye and the object. In the Newtonian Reflector, and in the diagonal eye-pieces formerly described, the eye is directed in a line at right angles to the object, or a deviation of 90 degrees from the direct line of vision. In Herschel’s’ large telescopes, and in the Aerial Reflector formerly described (in pp. 311-325) the back is turned to the object, and the eye in an opposite direction.

These circumstances should teach us humility and a becoming diffidence in our own powers; and they should admonish us not to be too dogmatical or peremptory in affirming what is possible or impossible in regard either to nature or art, or to the operations of the Divine Being. Art has accomplished, in modern times, achievements, in regard to locomotion, marine and aËrial navigation, the improvement of vision, the separation and combinations of invisible gases, and numerous other objects, of which the men of former ages could not have formed the least conception. And even yet, we can set no boundaries to the future discoveries of science and the improvements of art; but have every reason to indulge the hope that, in the ages to come, scenes of Divine mechanism in the system of nature will be unfolded, and the effects of chemical and mechanical powers displayed, of which the human mind, in its present state of progress, cannot form the most imperfect idea. Such circumstances likewise should teach us not to reject any intimations which have been made to us in relation to the character, attributes, and dispensations of the Divine Being, and the moral revelations of his will given in the Sacred Records, because we are unable to comprehend every truth and to remove every difficulty, which relates to the moral government of the Great Ruler of the universe. For, if we meet with many circumstances in secular science, and even in the common operations of nature, which are difficult to comprehend—if even the construction of such telescopes as we now use, would have appeared an incomprehensible mystery to ancient philosophers—we must expect to find difficulties almost insurmountable to such limited minds as ours, in the eternal plans and moral arrangements of the “King Immortal and Invisible,” as delineated only in their outlines, in the Sacred Oracles—particularly those which relate to the origin of physical and moral evil, the ultimate destiny of man, and the invisible realities of a future world.

The UTILITY of the telescope may be considered in relation to the following circumstances.

In the first place, it may be considered as an instrument or machine which virtually transports us to the distant regions of space. When we look at the moon through a telescope which magnifies 200 times, and survey its extensive plains, its lofty peaks, its circular ranges of mountains, throwing their deep shadows over the vales, its deep and rugged caverns, and all the other varieties which appear on the Lunar surface, we behold such objects in the same manner as if we were standing at a point 238,800 miles from the earth in the direction of the moon, or only twelve hundred miles from that orb, reckoning its distance to be 240,000 miles. When we view the planet Saturn with a similar instrument, and obtain a view of its belts, and satellites, and its magnificent rings, we are transported, as it were, through regions of space, to a point in the heavens more than nine hundred millions of miles from the surface of our globe, and contemplate those august objects, as if we were placed within five millions of miles of the surface of that planet.34 Although a supernatural power, sufficient to carry us in such a celestial journey, a thousand miles every day, were exerted—it would require more than two thousand four hundred and sixty years, before we could arrive at such a distant position; yet the telescope, in a few moments, transports our visual powers to that far distant point of space. When we view, with such an instrument, the minute and very distant clusters of stars in the Milky Way, we are carried in effect through the regions of space to the distance of five hundred thousand millions of miles from the earth; for we behold those luminaries through the telescope nearly as if they were actually viewed from such a distant point in the spaces of the firmament. These stars cannot be conceived as less than a hundred billions of miles from our globe, and the instrument we have supposed brings them within the two hundredth part of this distance. Suppose we were carried forward by a rapid motion towards this point, at the rate of a thousand miles every hour, it would require more than fifty-seven thousand years, before we could reach that very distant station in space to which the telescope, in effect, transports us. So that this instrument is far more efficient in opening to our view the scenes of the universe than if we were invested with powers of locomotion to carry us through the regions of space, with the rapidity of a cannon ball at its utmost velocity; and all the while we may sit at ease in our terrestrial apartments.

In the next place, the telescope has been the means of enlarging our views of the sublime scenes of creation, more than any other instrument which art has contrived. Before the invention of this instrument the universe was generally conceived as circumscribed within very narrow limits. The earth was considered as among the largest bodies in creation; the planets were viewed as bodies of a far less size than what they are now found to be; no bodies similar to our moon were suspected as revolving around any of them; and the stars were supposed to be little more than a number of brilliant lamps hung up to emit a few glimmering rays, and to adorn the canopy of our earthly habitation. Such a wonderful phenomenon as the Ring of Saturn was never once suspected, and the sun was considered as only a large ball of fire. It was suspected, indeed, that the moon was diversified with mountains and vales, and that it might possibly be a habitable world; but nothing certainly could be determined on this point, on account of the limited nature of unassisted vision. But the telescope has been the means of expanding our views of the august scenes of creation to an almost unlimited extent. It has withdrawn the veil which formerly interposed to intercept our view of the distant glories of the sky. It has brought to light five new planetary bodies, unknown to former astronomers, one of which is more than eighty times larger than the earth—and seventeen secondary planets which revolve around the primary. It has expanded the dimensions of the solar system to double the extent which was formerly supposed. It has enabled us to descry hundreds of comets which would otherwise have escaped our unassisted vision, and to determine some of their trajectories and periods of revolution.

It has explored the profundities of the Milky Way, and enabled us to perceive hundreds of thousands of those splendid orbs, where scarcely one is visible to the naked eye. It has laid open to our view thousands of NebulÆ, of various descriptions, dispersed through different regions of the firmament—many of them containing thousands of separate stars. It has directed our investigations to thousands of double, treble and multiple stars—suns revolving around suns, and systems around systems, and has enabled us to determine some of the periods of their revolutions. It has demonstrated the immense distances of the starry orbs from our globe, and their consequent magnitudes; since it shows us that, having brought them nearer to our view by several hundreds or thousands of times, they still appear only as so many shining points. It has enabled us to perceive that mighty changes are going forward throughout the regions of immensity—new stars appearing, and others removed from our view, and motions of incomprehensible velocity carrying forward those magnificent orbs through the spaces of the firmament. In short, it has opened a vista to regions of space so immeasurably distant, that a cannon ball impelled with its greatest velocity, would not reach tracts of creation so remote in two thousand millions of years, and even light itself, the swiftest body in nature, would require more than a thousand years before it could traverse this mighty interval. It has thus laid a foundation for our acquiring an approximate idea of the infinity of space, and for obtaining a glimpse of the far distant scenes of creation, and the immense extent of the universe.

Again, the telescope, in consequence of the discoveries it has enabled us to make, has tended to amplify our conceptions of the attributes and the Empire of the Deity. The amplitude of our conceptions of the Divine Being bears a certain proportion to the expansion of our views in regard to his works of creation, and the operations he is incessantly carrying forward throughout the universe. If our views of the works of God, and of the manifestations he has given of himself to his intelligent creatures, be circumscribed to a narrow sphere, as to a parish, a province, a kingdom, or a single world, our conceptions of that Great Being, will be proportionably limited. For it is chiefly from the manifestation of God in the material creation that our ideas of his Power, his Wisdom, and his other natural attributes, are derived. But in proportion to the ample range of prospect we are enabled to take of the operations of the Most High, will be our conceptions of his character, attributes, and agency. Now, the telescope—more than any other invention of man—has tended to open to our view the most magnificent and extensive prospects of the works of God. It has led us to ascertain that, within the limits of the solar system, there are bodies which, taken together, comprise a mass of matter nearly two thousand five hundred times greater than that of the earth—that these bodies are all constituted and arranged in such a manner as to fit them for being habitable worlds—and that the sun, the centre of this system, is five hundred times larger than the whole. But, far beyond the limits of this system, it has presented to our view a universe beyond the grasp of finite intelligences, and to which human imagination can assign no boundaries. It has enabled us to descry suns clustering behind suns, rising to view in boundless perspective, in proportion to the extent of its magnifying and illuminating powers—the numbers of which are to be estimated, not merely by thousands, and tens of thousands, and hundreds of thousands, but by scores of millions—leaving us no room to doubt that hundreds of millions more, beyond the utmost limits of human vision, even when assisted by art, lie hid from mortal view’s in the unexplored and unexplorable regions of immensity.

Here, then, we are presented with a scene which gives us a display of Omnipotent Power which no other objects can unfold, and which, without the aid of the telescope, we should never have beheld—a scene which expands our conceptions of the Divine Being, to an extent which the men of former generations could never have anticipated—a scene which enables us to form an approximate idea of Him who is the “King Eternal, Immortal, and Invisible,” who “created all worlds, and for whose pleasure they are, and were created.” Here we behold the operations of a Being whose power is illimitable and uncontrollable, and which far transcends the comprehension of the highest created intelligences—a power, displayed not only in the vast extension of material existence, and the countless number of mighty globes which the universe contains—but in the astonishingly rapid motions with which myriads of them are carried along through the immeasurable spaces of creation,—some of those magnificent orbs moving with a velocity of one hundred and seventy thousand miles an hour. Here, likewise, we have a display of the infinite Wisdom and Intelligence of the Divine Mind, in the harmony and order with which all the mighty movements of the universe are conducted—in proportionating the magnitudes, motions and distances of the planetary worlds—in the nice adjustment of the projectile velocity to the attractive power—in the constant proportion between the times of the periodical revolution of the planets and the cubes of their mean distances—in the distances of the several planets from the central body of the system, compared with their respective densities—and in the constancy and regularity of their motions, and the exactness with which they accomplish their destined rounds—all which circumstances evidently show that He who contrived the universe is “the only Wise God,” who is “wonderful in counsel and excellent in working.” Here, in fine, is a display of boundless benevolence. For we cannot suppose, for a moment, that so many myriads of magnificent globes, fitted to be the centres of a countless number of mighty worlds, should be nothing else than barren wastes, without the least relation to intelligent existence. And if they are peopled with intellectual beings of various orders—how vast must be their numbers, and how overflowing that Divine Beneficence which has provided for them all, every thing requisite to their existence and happiness!

In these discoveries of the telescope, we obtain a glimpse of the grandeur and the unlimited extent of God’s universal empire. To this empire no boundaries can be perceived. The larger, and the more powerful our telescopes are, the further are we enabled to penetrate into those distant and unknown regions; and however far we penetrate into the abyss of space, new objects of wonder and magnificence still continue rising to our view—affording the strongest presumption, that were we to penetrate ten thousand times farther into those remote spaces of immensity, new suns, and systems, and worlds would be disclosed to our view. Over all this vast assemblage of material existence, and over all the sensitive and intellectual beings it contains, God eternally and unchangably presides; and the minutest movements, either of the physical or the intelligent system, throughout every department of those vast dominions, are at every moment “naked and open” to his Omniscient eye. What boundless Intelligence is implied in the Superintendence and arrangement of the affairs of such an unlimited empire! and what a lofty and expansive idea does it convey of Him who sits on the throne of Universal Nature, and whose greatness is unsearchable! But without the aids of the telescopic tube, we could not have formed such ample conceptions of the greatness, either of the Eternal Creator himself, or of the universe which he hath brought into existence.

Besides the above, the following uses of the telescope, in relation to science and common life, may be shortly noticed:—

In the business of astronomy, scarcely any thing can be done with accuracy without the assistance of the telescope. 1. It enables the astronomer to determine with precision the transits of the planets and stars, across the meridian; and on the accuracy with which these transits are obtained, a variety of important conclusions and calculations depend. The computation of astronomical and nautical tables for aiding the navigator in his voyages round the globe, and facilitating his calculations of latitude and longitude, is derived from observations made by the telescope, without the use of which instrument, they cannot be made with precision. 2. The apparent diameters of the planets can only be measured by means of this instrument, furnished with a micrometer. By the naked eye no accurate measurements of the diameters of these bodies can be taken; and without knowing their apparent diameters, in minutes or seconds, their real bulk cannot be determined, even although their exact distances be known. The differences, too, between their polar and equatorial diameters cannot be ascertained without observations made by powerful telescopes. For example, the equatorial diameter of Jupiter is found to be in proportion to the polar as 14 to 13, that is, the equatorial is more than 6000 miles longer than the polar diameter, which could never have been determined by observations made by the naked eye. 3. The parallaxes of the heavenly bodies can only be accurately ascertained by the telescope; and it is only from the knowledge of their parallaxes, that their distances from the earth or from the sun can be determined. In the case of the fixed stars, nothing of the nature of a parallax could ever be expected to be found without the aid of a telescope. It was by searching for the parallax of a certain fixed star, that the important fact of the Aberration of light was discovered. The observations, for this purpose, were made by means of a telescope 24 feet long, fixed in a certain position. 4. The motions and revolutionary periods of Sidereal systems, can only be determined by observations made by telescopes of great magnifying and illuminating powers. Without a telescope the small stars which accompany double or treble stars cannot be perceived, and much less their motions or variation of their relative positions. Before the invention of the telescope such phenomena—now deemed so wonderful and interesting—could never have been surmised. 5. The accurate determination of the longitude of places on the earth’s surface is ascertained by the telescope, by observing with this instrument the immersions and emersions of the satellites of Jupiter. From such observations, with the aid of a chronometer, and having the time at any known place, the situation of any unknown place is easily determined. But the eclipses of Jupiter’s moons can be perceived only by telescopic instruments of considerable power. 6. By means of a telescope, with cross hairs in the focus of the eye-glass, and attached to a Quadrant, the altitude of the sun or of a star, particularly the pole-star, may be most accurately taken; and, from such observations, the latitude of the place may be readily and accurately deduced.

Again, in the Surveying of land, the telescope is particularly useful; and for this purpose it is mounted on a stand with a horizontal and vertical motion, pointing out by divisions the degrees and minutes of inclination of the instrument. For the more accurate reading of these divisions, the two limbs are furnished with a Nonius, or Vernier’s scale. The object here is to take the angular distances between distant objects on a plane truly horizontal; or else the angular elevation or depression of objects above or below the plane of the horizon. In order to obtain either of those kinds of angles to a requisite degree of exactness, it is necessary that the surveyor should have as clear and distinct a view as possible of the objects, or station-staves, which he fixes up for his purpose, that he may with the greater certainty determine the point of the object which exactly corresponds with the line he is taking. Now, as such objects are generally at too great a distance for the surveyor to be able to distinguish with the naked eye, he takes the assistance of the telescope, by which he obtains, 1. A distinct view of the object to which his attention is directed, and 2. he is enabled to determine the precise point of the object aimed at, by means of the cross hairs in the focus of the eye-glass. A telescope mounted for this purpose is called a Theodolite, which is derived from two Greek words ?e?a? to see, and ?d??, the way or distance.

In the next place, the telescope is an instrument of special importance, in the conducting of Telegraphs, and in the conveyance of signals of all descriptions. Without its assistance telegraphic dispatches could not be conveyed with accuracy to any considerable distance, nor in quadruple the time in which they are now communicated, and the different stations would need to be exceedingly numerous. But by the assistance of the telescope information may be communicated, by a series of telegraphs, with great rapidity. Twenty-seven telegraphs convey information from Paris to Calais—a distance of 160 miles—in 3 minutes; twenty-two from Paris to Lisle in 2 minutes; forty-six from Strasburg to Paris in 4½ minutes; and eighty from Paris to Brest in 10 minutes. In many other cases which occur both on land and on sea, the telescope is essentially requisite for descrying signals. The Bell-Rock Light House, for example, is situated 12 miles from Arbroath, and from every other portion of land, so that the naked eye could not discern any signal which the keepers of that light could have it in their power to make; but by means of a large telescope in the station-house in Arbroath, the hoisting of a ball every morning at 9 A.M.—which indicates that ‘All is well’—may be distinctly recognised.

Many other uses of this instrument, in the ordinary transactions of life, will readily occur to the reader; and therefore I shall only mention the following purpose to which it may be applied, namely,—

To measure the distance of an object from one station. This depends upon the increase of the focal distance of the telescope in the case of near objects. Look through a telescope at the object whose distance is required, and adjust the focus till it appear quite distinct; then slide in the drawer, till the object begins to be obscure, and mark that place of the tube precisely. Next draw out the tube till the object begins to be again obscured, and then make another mark as before. Then take the middle point between these two marks, and that will be the point where the image of the object is formed most distinctly; which is to be nicely measured from the object lens, and compared with the solar focus of the lens or telescope, so as to ascertain their difference. And the rule for finding the distance is,—‘As the difference between the focal distance of the object, and the solar focal distance : Is to the solar focal distance :: So is the focal distance of the object : To its true distance from the object lens.’ An example will render this matter more perspicuous.

Let AB (fig. 84.) be the object lens, EY the eye-glass, FC the radius, or focus of the lens AB, and Cf the focal distance of the object OB, whose distance is to be measured. Now suppose CF = 48 inches, or 4 feet, and that we find by the above method that Cf is 50 inches, then Ff is 2 inches; and the analogy is:—As Ff = 2, is to CF = 48, so is Cf = 50, to CQ = 1200 inches, or 100 feet. Again, suppose Cf = 49 inches, then will Ff = 1 inch; and the proportion is, 1 : 48 :: 49 : 2352 = QC, or 196 feet. A telescope of this focal length, however, will measure only small distances. But, suppose AB a lens whose solar focus is 12 feet, or 144 inches; and that we find, by the above method, that Cf, or the focal distance of the object, is 146 inches; then will Ff be 2 inches, and the proportion will be, as 2 : 144 :: 146 : 21024 inches, or 1752 feet = the distance QC. If with such a large telescope, we view an object OB, and find Ff but ¹/₁₀th of an inch, this will give the distance of the object as 17292 feet or nearly 3? miles.

Since the difference between the radius of the object lens and the focal distance of the object is so considerable as 2 inches in a tube of 4 feet, and more than 12 inches in one of 12 feet, a method might be contrived for determining the distance of near objects by the former, and more distant objects by the latter, by inspection only. This may be done by adjusting or drawing a spiral line round the drawer or tube, through the two inch space in the small telescope, and by calculation, graduate it for every 100 feet, and the intermediate inches, and then, at the same time we view an object, we may see its distance on the tube. In making such experiments, a common object-glass of a long focal length, and a single eye-glass, are all that is requisite; since the inverted appearance of the object can cause no great inconveniency.

CHAPTER VII.

ON THE METHOD OF GRINDING AND POLISHING OPTICAL LENSES AND SPECULA.

I originally intended to enter into particular details on this subject, for the purpose of gratifying those mechanics and others who wish to amuse themselves by constructing telescopes and other optical instruments for their own use; but, having dwelt so long on the subject of telescopes, in the preceding pages, I am constrained to confine myself to a very general sketch.

1. To grind and polish lenses for eye-glasses, microscopes, &c.

First provide an upright spindle, at the bottom of which a pulley is fixed, which must be turned by a wheel by means of a cord and handle. At the top of the spindle make a screw the same as a lathe-spindle, on which you may screw chocks of different sizes, to which the brass tool in which the lens is to be ground, may be fixed. Having fixed upon the breadth and focal length of the lens, and whether it is to be a plano, or a double convex—take a piece of tin-plate or sheet copper, and, with a pair of compasses, draw an arch upon its surface, near one of its extremities, with a radius equal to the focal distance of the lens, if intended to be double convex, or with half that distance, if it is to be plano-convex. Remove with a file that part of the copper which is without the circular arch, and then a convex gage is formed. With the same radius strike another arch, and having removed that part of the copper which is within it, a concave gage will be obtained. The brass tool, in which the glass is to be ground, is then to be fixed upon a turning-lathe, and turned into a portion of a concave sphere, so as to correspond to the convex gage. In order to obtain an accurate figure to the concave tool, a convex tool of exactly the same radius is generally formed, and they are ground one upon another with flour emery; and when they exactly coincide, they are fit for use. The convex tool will serve for grinding concave glasses of the same radius—and it should be occasionally ground in the concave tool to prevent it from altering its figure.

The next thing to be attended to is, to prepare the piece of glass which is to be ground, by chipping it in a circular shape, by means of a large pair of scissors, and removing the roughness from its edges by a common grind-stone. The faces of the glass near the edges should likewise be ground on the grind-stone, till they nearly fit the concave gage, by which the labour of grinding in the tool will be considerably saved. The next thing required is to prepare the emery for grinding, which is done in the following manner. Provide four or five clean earthen vessels; fill one of them with water, and put into it a pound or half a pound of fine emery, and stir it about with a stick; after which let it stand 3 or 4 seconds, and then pour it into another vessel, which may stand about 10 seconds; then pour it off again into the several vessels till the water is quite clear; and by this means, emery of different degrees of fineness is obtained, which must be kept separate from each other, and worked in their proper order, beginning at the first, and working off all the marks of the grind-stone; then take of the second, next of the third, &c.,—holding the glass upon the pan or tool with a light hand, when it comes to be nearly fit for polishing. The glass in this operation should be cemented to a wooden handle, by means of pitch or other strong cement. After the finest emery has been used, the roughness which remains may be taken away, and a slight polish given by grinding the glass with pounded pumice-stone. Before proceeding to the polishing, the glass should be ground as smooth as possible, and all the scratches erased, otherwise the polishing will become a tedious process. The polishing is performed as follows: Tie a piece of linen rag or of fine cloth about the tool, and with fine putty, (calcined tin), or colcothar of vitriol (a very fine powder, sometimes called the red oxide of iron) moistened with water, continue the grinding motion, and in a short time there will be an excellent polish.

In order to grind lenses very accurately for the finest optical purposes, particularly object-glasses for telescopes—the concave tool is firmly fixed to a table or bench, and the glass wrought upon it by the hand with circular strokes so that its centre may never go beyond the edges of the tool. For every 6 or 7 circular strokes, the glass should receive 2 or 3 cross ones along the diameter of the tool, and in different directions; and while the operation is going on, the convex tool should, at the end of five minutes, be wrought upon the concave one for a few seconds, in order to preserve the same curvature to the tools and to the glass. The finest polish is generally given in the following way. Cover the concave tool with a layer of pitch hardened by the addition of a little rosin, to the thickness of ¹/₁₅th of an inch. Then, having taken a piece of thin writing paper, press it upon the surface of the pitch with the convex tool, and pull the paper quickly from the pitch before it has adhered to it; and if the surface of the pitch is marked every where with the lines of the paper, it will be truly spherical. If any paper remains on the surface of the pitch, it may be rubbed off by soap and water, and if the marks of the paper should not appear on any part of it, the operation must be repeated, till the polisher or bed of pitch is accurately spherical. The glass is then to be wrought on the polisher by circular and cross strokes with the putty or colcothar, till it has received a complete polish. When one side is finished, the glass must be separated from its handle, by inserting the point of a knife between it and the pitch, and giving it a gentle stroke. The pitch which remains upon the glass may be removed by rubbing it with a little oil or spirits of wine. The operation of polishing on cloth is slower, and the polish less perfect than on pitch; but it is a mode best fitted for those who have little experience, and who would be apt, in the first instance, to injure the figure of the lens by polishing it on a bed of pitch.

2. On the method of casting and grinding the Specula of Reflecting Telescopes.

The first thing to be considered in the formation of reflecting telescopes, is the composition of the metal of which the specula are made. The qualities required are—a sound uniform metal, free from all microscopic pores—not liable to tarnish by absorption of moisture from the atmosphere—not so hard as to be incapable of taking a good figure and polish—nor so soft as to be easily scratched, and possessing a high reflecting power. Various compositions have been used for this purpose, of which the following are specimens:—Take good Swedish copper 32 ounces, and when melted, add 14½ ounces of grain tin to it; then, having taken off the scoria, cast it into an ingot. This metal must be a second time melted to cast a speculum; but it will fuse in this compound state with a small heat, and therefore will not calcine the tin to putty. It should be poured off as soon as it is melted, giving it no more heat than is absolutely necessary. The best method for giving the melted metal a good surface is this: the moment before it is poured off, throw into the crucible a spoonful of charcoal-dust; immediately after which the metal must be stirred with a wooden spatula and poured into the moulds.—The following is another composition somewhat similar. Take 2 parts copper as pure as it is possible to procure; this must be melted in a crucible by itself. Then put, in another crucible, 1 part of pure grain tin. When they are both melted, mix and stir them with a wooden spatula, keeping a good flux on the melted surface to prevent oxidation, and then pour the metal quickly into the moulds, which may be made of founder’s loam.

The composition suggested, more than half a century ago, by the Rev. Mr. Edwards, has often been referred to with peculiar approbation. This gentleman took a great deal of pains to discover the best composition, and to give his metals a fine polish and the true parabolical figure. His telescopes were tried by Dr. Maskelyne, the Astronomer Royal, who found them greatly to excel in brightness, and to equal in other respects those made by the best artists. They showed a white object perfectly white, and all objects of their proper colour. He found, after trying various combinations, the following to be the best: namely 32 ounces of copper, with 15 or 16 ounces of grain tin, (according to the purity of the copper) with the addition of one ounce of brass, one of silver, and one ounce of arsenic. This, he affirms, will form a metal capable, when polished in a proper manner, of reflecting more light than any other metal yet made public.

The Rev. J. Little, in his observations on this subject in the ‘Irish Transactions,’ proposes the following composition, which he found to answer the purpose better than any he had tried, namely—32 parts of best bar copper, previously fluxed with the black flux, of two parts tartar and one of nitre, 4 parts brass, 16 parts tin, and 1¼ arsenic. If the metal be granulated, by pouring it, when first melted, into water, and then fused a second time, it will be less porous than at first. In this process, the chief object is, to hit on the exact point of the saturation of the copper, &c., by the tin. For, if the latter be added in too great quantity, the metal will be dull coloured and soft; if too little, it will not attain the most perfect whiteness, and will certainly tarnish.35

When the metal is cast, and prepared by the common grind-stone for receiving its proper figure—the gages and grinding-tools are to be formed in the same manner as formerly described for lenses, with this difference, that the radius of the gages must always be double the focal length of the speculum, as the focus of parallel rays by reflection is at one half the radius of concavity. In addition to the concave and convex tools—which should be only a little broader than the metal itself—a convex elliptical tool of lead and tin should be formed with the same radius, so that its transverse should be to its conjugate diameter as 10 to 9, the latter being exactly equal to the diameter of the metal. The grinding of the speculum is then to be commenced, on this tool, with coarse emery powder and water, when the roughness is taken off, by moving the speculum across the tool, in different directions, walking round the post on which the tool is fixed, holding the speculum by the wooden handle to which it is cemented. It is then to be wrought with great care on the convex brass tool, with circular and cross strokes, and with emery of different degrees—the concave tool being sometimes ground upon the convex one, to keep them all of the same radius, and when every scratch is removed from its surface, it will be fit for receiving the final polish.

When the metal is ready for polishing, the elliptical tool is to be covered with black pitch about ¹/₂₀th of an inch thick, and the polisher formed in the same way as in the case of lenses, either with the concave brass tool or with the metal itself. The colcothar of vitriol should then be triturated between two surfaces of glass, and a considerable quantity of it applied at first to the surface of the polisher. The speculum is then to be wrought, in the usual way, upon the polishing tool, till it has received a brilliant lustre, taking care to use no more of the colcothar, if it can be avoided, and only a small quantity of it, if it should be found necessary. When the metal moves stiffly on the polisher, and the colcothar assumes a dark muddy hue, the polish advances with great rapidity. The tool will then grow warm, and would probably stick to the speculum, if its motion were discontinued for a moment. At this stage of the process, therefore, we must proceed with great caution, breathing continually on the polisher, till the friction is so great, as to retard the motion of the speculum. When this happens, the metal is to be slipped off the tool at one side, cleaned with soft leather, and placed in a tube for the purpose of trying its performance; and if the polishing has been conducted with care, it will be found to have a true parabolic figure.36

It was formerly the practice, before the speculum was brought to the polisher, to smooth it on a bed of hones, or a convex tool made of the best blue stone, such as clockmakers use in polishing their work, which was made one fourth part larger than the metal which was to be ground upon it, and turned as true as possible to a gage. But this tool is not generally considered as absolutely necessary, except when silver and brass enter into the composition of the metal, in order to remove the roughness which remains after grinding with the emery.

To try the figure of the metal.—In order to this, the speculum must be placed in the tube of the telescope for which it is intended; and, at about 20 or 30 yards distant, there should be put up a watch-paper, or similar object, on which there are some very fine strokes of an engraver. An annular kind of diagram should be made with card-paper, so as to cover a circular portion of the middle part of the speculum, between the hole and the circumference, equal in breadth to about ¹/₈ of its diameter. This paper ring should be fixed in the mouth of the telescope, and remain so during the whole experiment. There must likewise be two other circular pieces of card-paper cut out, of such sizes, that one may cover the centre of the metal, by completely filling the hole in the annular piece now described: and the other such a round piece as shall exactly fill the tube, and so broad as that the inner edge just touches the outward circumference of the middle annular piece. All these pieces together will completely shut up the mouth of the telescope. Let the round piece which covers the centre of the metal be removed, and adjust the instrument so that the image may be as sharp and distinct as possible. Then replace the central piece, and remove the outside annular one, by which means the circumference only of the speculum will be exposed; and the image now formed will be from the rays reflected from the exterior side of the metal. If the two images formed by these two portions of the metal be perfectly sharp and equally distinct, the speculum is perfect and of the true parabolic curve. If, on the contrary, the image from the outside of the metal should not be distinct and that it should be necessary to bring the little speculum nearer by the screw, the metal is not yet brought to the parabolic figure; but if, in order to procure distinctness, we be obliged to move the small speculum farther off, then the figure of the great speculum has been carried beyond the parabolic, and has assumed the hyperbolic form.

To adjust the eye-hole of Gregorian Reflectors.—If there is only one eye-glass, then the distance of the small hole should be as nearly as possible equal to its focal length. But in the compound Huygenian eye-piece, the distance of the eye-hole may be thus found:—Multiply the difference between the focal distance of the glass next to the speculum, and the distance of the two eye-glasses, by the focal distance of the glass nearest the eye; divide the product by the sum of the focal distances of the two lenses, lessened by their distance, and the quotient will be the compound focal distance required. Thus, if the focal distance of the lens next the speculum be 3 inches, that of the lens next the eye 1 inch, and their distance 2 inches, then the compound focal distance from the eye-glass will be (3 - 2 × 1)/(3 × 1 - 2) = ½ inch.—The diameter of the eye-hole is always equal to the quotient obtained by dividing the diameter of the great speculum by the magnifying power of the telescope. It is generally from ¹/₂₅th to ¹/₅₀th of an inch in diameter. It is necessary, in many cases, to obtain, from direct experiment, an accurate determination of the place and size of the eye-hole, as on this circumstance depends, in a certain degree, the accurate performance of the instrument.

To center the two specula of Gregorian Reflectors.—Extend two fine threads or wires across the aperture of the tube at right angles, so as to intersect each other, exactly in the axis of the telescope. Before the arm is finally fastened to the slider, place it in the tube, and through the eye-piece (without glasses) the intersection of the cross wires must be seen exactly in the centre of the hole of the arm. When this exactness is obtained, let the arm be firmly riveted and soldered to the slider.

To centre lenses.—The centering of lenses is of great importance, more especially for the object-glasses of achromatic instruments. The following is reckoned a good method:—Let the lens to be centered be cemented on a brass chuck, having the middle turned away so as not to touch the lens, but near the edge, which will be hid when mounted. This rim is very accurately turned flat where it is to touch the glass. When the chuck and cement is warm it is made to revolve rapidly: while in motion a lighted candle is brought before it, and its reflected image attentively watched. If this image has any motion, the lens is not flat or central; a piece of soft wood must therefore be applied to it in the manner of a turning tool, till such time as the light becomes stationary. When the whole has cooled, the edges of the lens must be turned by a diamond, or ground with emery.

For more particular details in reference to grinding and polishing specula and lenses, the reader is referred to Smith’s ‘Complete system of Optics’—Imison’s ‘School of Arts’—Huygenii Opera—Brewster’s Appendix to ‘Ferguson’s Lectures’—‘Irish Transactions,’ vol. X., or ‘Nicholson’s Journal,’ vol. XVI., Nos. 65, 66, for January and February, 1807.