Sir Norman Lockyer

CHAPTER V.
THE REFRACTION OF LIGHT.

It is difficult to give the credit of the invention of the telescope to any one particular person, for, as in the case of most instruments, its history has been a history of improvements; and whether we should give the laurel to Jansen, Baptista Porta, Galileo or to others whose names are unknown, is an invidious task to decide; we will therefore not enter in any way into the question, interesting though it be, as to who was the inventor of the “optick tube,” as the telescope was called by its first users.

The telescope is not a thing in the ordinary sense—it is a combination of things, the things being certain kinds of lenses, concave and convex, known and used as spectacles long before they were combined to form the telescope.

The first telescopes depended on the refraction of light; others, to which attention will be called in a future chapter, depended on reflection.

Fig. 20.—View and Section of a Prism.

In order to understand the action of a lens, it is necessary to understand the action of a prism. By the aid of Fig. 20 the action of the lenses of which telescopes are constructed will be understood. A prism is a piece of glass, or other transparent substance, the sides of which are so inclined to each other that its section is a triangle, and its action on light passing through it is to change the direction of the course of the beam. If we examine Fig. 21 we shall understand the action clearly. It is a known law, that when a beam of light falls obliquely on the surface of a medium more dense than that through which it has been passing, its direction is changed to a new one, nearer the line drawn at right angles to that surface, railed the normal. For instance, the ray S, I, falling on the prism at I, is bent into the course I, E, which is in a direction nearer to that of N, I, produced inside the prism. On emerging, the reverse takes place, and the ray is bent away from the normal E, N´, and takes the course E, R. In the second diagram, Fig. 21, the ray S, I, called the incident ray, coincides with the normal to the surface, so it is not refracted until it reaches the second surface, when it has its path changed to E, R, instead of taking its direct course shown by the dotted line. This bending of the ray is very plainly shown with an electric lamp and screen. If a trough with parallel sides be placed so as to intercept part of the light coming from the electric lamp, so that part shall pass through it and part above, we have the image of the hole in the diaphragm of the lantern on the screen unchanged. Now, if the trough be filled with water, no difference whatever is made in the position of the light on the screen, because the water, which is denser than the air, is contained in a trough with parallel sides; but by opening the sides like opening a book, or by interposing another trough with inclined sides, shaped like a V, that parallelism is destroyed, and then the light passing through it will be deflected upwards from its original course, and will fall higher on the screen; by opening the sides more and more, one is able to alter the direction of the light passing through the prism, which has been constructed by destroying the parallelism of the two sides.

Fig. 21.—Deviation of Light in Passing at Various Incidences through Prisms of Various Angles.

The refraction of light then depends upon the density of the substance through which it passes, on the angle of incidence of the ray, on the angle of the prism, and also on the colour of the light, about which we shall have something to say presently.

Let us now pass from the prism to the lens; for having once grasped the idea of refraction there will be no difficulty in seeing what a lens really is.

With the prism just considered, placed so that a vertical section is represented by a V, a ray is thrown upwards; if another similar prism be placed with its base in contact with the base of the other, and its apex upwards, so that its section will be represented by a V reversed, ?, it is clear this will turn the rays downwards, so that the rays, on emerging from both prisms will tend to meet each other, as shown, in Fig. 22, where one ray is turned down to the same extent that the other is turned up; so that by the combination of two prisms the two rays are brought to a point, which is called a focus. Now, if instead of putting the prisms base to base, they are put apex to apex, a contrary action takes place, and by this means one is able to cause two rays of light to diverge instead of converging, so that the prisms, placed apex to apex, cause the rays to diverge, and when placed base to base they cause the light to converge.

Fig. 22.—Convergence of Light by Two Prisms Base to Base.

If instead of having two prisms merely, there be taken a system having different angles at their apices, and from each prism there be cut a section, beginning by cutting off the apex of the most powerful prism, a slice from below the apex of the next, and a slice below the corresponding part of the next, and so on; and then if these slices be laid on each other so as to form a compound prism, and another similar prism be placed with its base to this one, we get what is represented in Fig. 23. These different slices of prisms become more and more prismatic, that is, they form parts of prisms of greater angle, as they approach the ends. We can imagine a section of such a system as thin as we please. Suppose we had such a section and put it in a lathe, rotating it on the axis A B, we should describe a solid figure, and if we suppose all the angles rounded off, so that it is made thinner and thinner as we recede from the centre, the prism system is turned into a lens having the form represented in Fig. 24. In a similar manner, lenses thinner in the middle than at the edges, called concave lenses, can he constructed, some forms of which are represented in section in Fig. 25. It is also obvious that convex lenses of all curves and combinations of curves can be made, some of which appear in Fig. 26.

Fig. 23.—Formation of a Lens from Sections of Prisms.

Fig. 24.—Front View and Section of a Double Convex Lens.

Fig. 25.—Double Concave, Plane Concave, and Concavo-Convex Lenses.

The action of such lenses upon the light proceeding from any source may now be considered. If there is a parallel beam proceeding from a lamp, or from the sun, and it falls on the form of lens, called a convex lens, which bulges out in the middle, we learn from Fig. 27, that the upper part acts like the upper prism just considered and turns the light down, and the lower acts in the reverse manner and turns the light up, and the sides act in a similar manner; and as the inclination of the surfaces of the lens increases as we approach the edge, the rays falling on the parts near the edge are turned out of their course more than those falling near the centre, so that we have the rays converged to a point F, called the focus of the lens; and as the rays from an electric lamp are generally rendered parallel by means of the lenses in the lantern, called the condensers, the rays from such a lamp falling on a convex lens will come to a focus at just the same distance from the lens, called its principal focal length as they would do if they came from the sun or stars.

Fig. 26.—Double Convex, Plane Convex, and Concavo-Convex Lenses.

Fig. 27.—Convergence of Rays by Convex Lens to Principal Focus.

So far we have brought rays to a focus, and on holding a piece of paper at the focus of the convex lens, as just mentioned, there appears on it a spot of light; and every one knows that if this experiment be performed with the sun, one brings all the rays falling on the lens almost to a point, and the longer waves of light will set fire to the paper; and on this principle burning-glasses are constructed. If, however, the rays are not parallel when falling on the lens, but diverging, they are not brought to a focus so near the lens, and the nearer the luminous source or object is, the further off will the light be brought to a focus on the other side. If matters are reversed, and the luminous source be placed in the focus, the rays of light, when they leave the lens, will converge to the position of the original source; so that there are two points, one on either side of the lens, which are the foci of each other S, S´, Fig. 28, called conjugate foci; as one approaches the lens the other recedes, and vice versÂ, and it is obvious that when the one approaches the lens so as to coincide with the principal focus, the other recedes to an infinite distance, and the emergent rays are parallel.

Fig. 28.—Conjugate Foci or Convex Lens.

Fig. 29.—Conjugate Images.

Fig. 30.—Diagram explaining Fig. 29.

Now let us consider how images are formed. If we take a candle, Fig. 29, and hold the lens a little distance away from it, then, on placing a screen of paper just on the other side of the lens, there will be a small flame depicted on it, an exact representation of the real flame: and it is formed in this way: Consider the rays proceeding from the top of the flame, which are represented separately in Fig. 30, where A represents the top. One of these rays, A a, passing through the centre of the lens o, will he unaffected because the surfaces through which it passes are parallel to each other; and we know from the property of the lens that all the other rays from A will, on passing through it, be brought to a focus somewhere on A a, depending on the curvature of the lens, and in the case of our lens it is at a.

Fig. 31.—Dispersion of Rays by a Double Concave Lens.

In like manner also all the rays from B are brought to a focus at b, and so on with all other parts of A, B, which in this case represents the flame, each will have its corresponding focus; there being cones of rays from every point of the object and to every point of the image, having for their bases the convex lens, and we get an image or exact representation of our candle flame. It will further be noticed that the image a b is smaller than A B, in proportion as the distance a b is less than A B; so that if we increase the focal length of the lens till a b is twice the distance away from the lens, it will become double its present size.

If now the flame be brought nearer the lens, its image a b becomes indistinct; and we must move the screen further away in order to render the image again clear; hence the place of the focus depends on the distance of the object, and the candle and its image must correspond to two conjugate foci.

Fig. 32.—Horizontal Section of the Eyeball. Scl, the sclerotic coat; Cn, the cornea; R, the attachments of the tendons of the recti muscles; Ch, the choroid; Cp, the ciliary processes; Cm, the ciliary muscle; Ir, the iris; Aq, the aqueous humour; Cry, the crystalline lens; Vi, the vitreous humour; Rt, the retina; Op, the optic nerve; Ml, the yellow spot.

If now rays be passed from the lantern or sun through a concave lens, Fig. 31, they are not brought to a focus, but are dispersed and travel onwards, as if they came from a point, F, which is called its virtual focus; and if rays are first converged by a convex lens, and then, before they reach the focus are allowed to fall on a concave one, we can, by placing the lenses a certain distance apart, render the converging rays again parallel; or we can make them slightly divergent, as if they came, not from an infinite distance, but from a point a foot or two off. The application of this arrangement will appear hereafter.

What has now been said on the action of the convex lens will enable us to consider the optical action of the eye, without which we do little in astronomy. As to the way that the brain receives impressions from the eye we need say nothing, for that belongs to the domain of physiology, except indeed this, that an image is formed on the retina by a chemical decomposition, brought about by the dissociating action of certain rays of light in exactly the same way as on a photographic plate. Optically considered, the eye consists of nothing more than a convex lens, Cry, Fig. 32, and a surface, Rt, extending over the back of the eyeball, called the retina, on which the objects are focussed, but the rays of light falling on the cornea Cn, are refracted somewhat, so that it is not quite true to say that the crystalline lens does all the work, but for our present purpose it is sufficiently correct, and we shall consider their combined action as that of a single lens.

The outer coat of the eyeball, shown in section in Fig. 32, is called the sclerotic, with the exception of that more convex part in front of the eye, called the cornea; behind this comes the aqueous humour and then the iris, that membrane of which the colour varies in different people and races. In the centre of this is a circular aperture called the pupil, which contracts or expands according to the brightness of the objects looked at, so that the amount of light passing into the eye is kept as far as possible constant. Close behind the iris comes the crystalline lens, the thickness of which can be altered slightly by the ciliary muscle. In the space between the lens and the back of the eye is a transparent jelly-like substance called the vitreous humour. Finally comes the retina, a most delicate surface chiefly composed of nerve fibres. It is on this surface, that the image is formed by the curved surfaces of the anterior membranes, and through the back of the eyeball is inserted the mass of filaments of the optic nerve making communication with the brain; these filaments on reaching the inside of the eye spread out to receive the impressions of light.

Here then, we have a complete photographic camera; the crystalline lens and cornea, separated by the aqueous humour, representing the compound-glass camera lens, and the retina standing in the place of the sensitive plate.

Fig. 33.—Action of Eye in Formation of Images.

The path of the light forming an image on the retina is shown in Fig. 33, where A B is the object, and a b its image, formed in exactly the same way as the image of the candle-flame which we have just considered; in fact, the eye is exactly represented by a photographic camera, the iris acting in the same manner as the stops in the lens, limiting its available area, and by contracting, decreasing the amount of light from bright objects, and at the same time increasing the sharpness of definition, for in the case of the eye, the luminous rays obey the known laws of propagation of light in media of variable form and density, and we have only simple refraction to deal with. The next matter to be considered is that the nearer the object A B is to the eye, the larger is the angle A, o, B, and also a, o, b, and therefore the image on the retina is larger; but there is a limit to the nearness to which the object can be brought, for, as we found with the candle, the distance between the lens and the image must be increased as the object approaches, or the curvature of the lens itself must be altered, for if not the ray forming the rays from each point of the object will be too divergent for the lens to be able to bring them to a focus. Now in the eye there is an adjustment of this sort, but it is limited so that objects begin to get indistinct when brought nearer the eye than perhaps six inches, because the rays become too divergent for the lens to bring them to a focus on the retina, and they tend to come to a focus behind the retina, as in Fig. 34; but we may assist the eye lens by using a glass convex lens in front of it, between it and the object. It is for this reason that spectacle glasses are used to enable long-sighted persons to see clearly.

Fig. 34.—Action of a Long-sighted Eye.

We may also use a much stronger lens, and so get the object very near the lens and eye, as in Fig. 35, where a b is the object so near the eye that, if it were not for the lens L, its image would not come to a focus on the retina at all. The effect of the lens is to make the rays proceeding in a cone from a and b less divergent, so that after passing through it, they proceed to the eye-lens as if they were coming from the points A and B, a foot or so away from the eye, and so the object a b appears to be a much larger object at a greater distance from the eye.

Fig. 35.—1. Diagram showing path of rays when viewing an object at an easy distance. 2. Object brought close to eye when the lens L is required to assist the eye-lens to observe the image when it is magnified.

A convex lens then has the power of magnifying objects when brought near the eye, and its action is clearly seen in Fig. 35, where the upper figure shows the arrow at as short a distance from the eye as it can be seen distinctly with an ordinary eye, and the lower figure shows the same arrow brought close to the eye, and rendered distinctly visible by the lens when a magnified image is thrown on the retina, as if there was a real larger arrow somewhere between the dotted lines at the ordinary distance of distinct vision. It is also obvious that the nearer the object can be brought to the eye-lens the more magnified it is, just as an object appears larger the nearer it is brought to the unaided eye.

We have been hitherto dealing with the effect of a convex lens on the rays passing to the eye. We will now deal with a concave one.

We found that the power of adjustment of the normal eye was sufficient to bring parallel rays, or those proceeding from a very distant object, and also slightly diverging rays, to a focus on the retina. Parallel or slightly divergent rays are most easily dealt with, and slightly convergent rays can also be focussed on the retina; but if the eye-lens is too convex, as is the case with short-sighted people, Fig. 36, a concave lens of slight curvature is used to correct the eye-lens and bring the image to a focus on the retina instead of in front of it.

Fig. 36.—Action of Short-sighted Eye.

If the rays are very convergent, as those proceeding from a convex lens and coming to a focus, the lens of a normal eye will bring them to a focus far in front of the retina, as if the person were very short-sighted. But by interposing a sufficiently powerful concave lens the rays are made less convergent or parallel, and the eye-lens brings them to a focus on the retina, as if they came from a near object, so the use of convex and concave lenses placed close to the eye is to render divergent or convergent rays nearly parallel, so that the eye-lens can easily focus them, and therefore one of the conditions of the telescope is that the rays which come into our eye shall be parallel or nearly so.

CHAPTER VI.
THE REFRACTOR.

In the telescope as first constructed by Galileo there are two lenses, so arranged that the first, a convex one, A B Fig. 37, converges the rays, while the second, C D, a concave one, diverges them, and renders them parallel, ready for the eye; the rays then, after passing through C D, go to the eye as if they were proceeding along the dotted lines from an object M M, closer to the eye instead of from a distant object, and so, by means of the telescope, the object appears large and close.

Fig. 37.—Galilean Telescope. A B, convex lens converging rays; C D, concave lens sending them parallel again and fit for reception by the eye.

It is this that constitutes the telescope. But nowadays we have other forms, as we are not content with the convex combined with the concave lens, and modern astronomy requires the eyepiece to be of more elaborate construction than those adopted by Galileo and the first users of telescopes, although this form is still used for opera-glasses and in cases where small power only is required. Having the power of converging the light and forming an image by the first convex lens or object glass, as we saw with the candle flame (Fig. 29), and an opportunity of enlarging this image by means of a magnifying or convex eyepiece, we can bring an image of the moon, or any other object, close to the eye, and examine it by means of a convex lens, or a combination of such lenses. So we get the most simple form of refracting telescopes represented in Fig. 38, in which the rays from all points of the object—let us take for instance an arrow—are brought to a focus by the object-glass A, forming there an exact representation of the real arrow. In the figure two cones of rays only are delineated, namely, those forming the point and feather of the arrow, but every other point in the arrow is built up by an infinite number of cones in the same way, each cone having the object-glass for its base. By means of the lens C we are able to examine the image of the arrow B, since the rays from it are thus rendered parallel, or nearly so, and to the eye they appear to come from a much larger arrow at a short distance away. We can draw their apparent direction, and the apparent arrow (as is done in Fig. 37 by the dotted lines), and so the object appears as magnified, or, what comes to the same thing, as if it were nearer.

The difference between this form and that contrived by Galileo is this: in the latter the rays are received by the eyepiece while converging, and rendered parallel by a concave lens, while in the former case the rays are received by the eyepiece on the other side of the focus, where they have crossed each other and are diverging, and are rendered parallel by a convex lens.

We may now sum up the use of the eye-lens. The image is brought to a focus on the retina, because the object is some distance off, and the rays from every point, (as from A and B, Fig. 35), on reaching the eye, are nearly parallel; but it is not necessary that they should be absolutely parallel, as the eye is capable of a small adjustment, but if one wishes to see an object much nearer (as in the lower figure), it is impossible to do it unless some optical aid is obtained, for the rays are too divergent, and cannot be brought to a focus on the retina. What does that optical aid effect? It enables us to place the object in the focus of another lens which shall make the rays parallel, and fit for the lens of the eye to focus on the retina, and since the object can by this means be brought close to the lens and eye, it forms a larger image on the retina. Dependent on this is the power of the telescope.

Fig. 38.—Telescope. A, object-glass, giving an image at B; C, lens for magnifying image B.

We shall refer later on to the mechanical construction of the telescope. Here it may be merely stated that the smaller ones consist of a brass tube, the object-glass held in a brass ring screwed in at one end of the tube and a smaller tube carrying the eyepiece sliding in and out of the large tube and sometimes moved by a rack and pinion motion, at the other. The larger ones as mounted for special uses will also be fully described farther on.

Fig. 39.—Diagram Explaining the Magnifying Power of Object-glass.

The power of the telescope depends on the object-glass as well as on the eyepiece; if we wish to magnify the moon, for instance, we must have a large image of the moon to look at, and a powerful lens to see that image. By studying Fig. 39 the fundamental condition of producing a large image by a lens will be seen. Suppose we wish to look at an object in the heavens, the diameter of which is one degree; if the lens throws an image of that body on to the circumference of a circle of 360 inches, then, as there are 360 degrees in a circle, that image will cover one inch; let the circle be 360 yards, and the image of a body of one degree will cover one yard; and to take an extreme case and suppose the circumference of the circle to be 360 miles, then the image will be one mile in diameter.

This is one of the principal conditions of the action of the object-glass in enabling us to obtain images which can be magnified by a lens, and by such magnification made to appear nearer to us than they are.

Galileo used telescopes which magnified four or five times, and it was only with great trouble and expense that he produced one which magnified twenty-three times.

Now, after what has been said of focal length, one will not be surprised to hear of those long telescopes produced in the very early days, a few of which are still extant; these show as well as anything the enormous difficulty which the early employers of telescopes had to deal with in the material they employed. One can scarcely tell one end of the telescope from the other; all the work was done in some cases by an object-glass not more than half an inch in effective diameter.

It might be supposed that those who studied the changes of places and the positions of the heavenly bodies would have been the first to gain by the invention of the telescope, and that telescopes would have been added to the instruments already described, replacing the pointers. For such a use as this a telescope of half an inch aperture would have been a great assistance. But things did not happen so, because the invention of the telescope gave such an impetus to physical astronomy that the whole heavens appeared novel to mankind. Groups of stars appeared which had never been seen before; Jupiter and Saturn were found to be attended by satellites; the sun, the immaculate sun, was determined after all to have spots, and the moon was at once set upon and observed with diligence and care; so that there was a very good reason why people should not limit the powers of the telescope to employing it to determine positions only. The number of telescopes was small, and they could not be better employed than in taking a survey of all the marvellous things which they revealed. It was at this time that the modern equatorial was foreshadowed. Galileo, and his contemporaries Scheiner and others, were observing sun-spots, and the telescope, Fig. 40, which Scheiner arranged, a very rough instrument, with its axis parallel to the earth’s axis, and allowed to turn so that Scheiner might follow the sun for many hours a day, was one of the first. This instrument is here reproduced, because it was one of the most important telescopes of the time, and gathered in to the harvest many of the earliest obtained facts.

Fig. 40.—Scheiner’s Telescope.

Since by means of little instruments like these, so much of beauty and of marvel could be discovered in the skies, it is no wonder that every one who had anything to do with telescopes strained his nerves to make them of greater power, by which more marvels could be revealed.

It was not long before those little instruments of Scheiner expanded into the long telescopes to which reference has been made. But there was a difficulty introduced by the length of the instrument. The length of the focus necessary for magnification spread the light over a large area, and therefore it was necessary to get an equivalent of light by increasing the aperture of the object-glasses in order that the object might be sufficiently bright to bear considerable magnification by the eyepiece,—and now arose a tremendous difficulty.

One part of refraction, namely, deviation, enables us to obtain, but the other half, dispersion, prevents our obtaining, except under certain conditions, an image we can make use of. By dispersion is meant the property of splitting up ordinary light into its component colours, of which we shall say more in dealing with spectrum analysis. If we wish to get more light by increasing the aperture of the telescope, the deviation of the light passing through the edge of the object-glass is increased, and with it the dispersion, the result of this increase of deviation. If the light of the sun be allowed to fall through a hole into a darkened chamber, and then through a prism, Fig. 41, it is refracted, and instead of having an exact reproduction of the bright circle we have a coloured band or spectrum. The white light when refracted is not only driven out of its original course—deviated—but it is also broken up—dispersed—into many colours. We have a considerable amount of colour; and this the early observers found when they increased the size of their telescopes, for it must be remembered that a lens is only a very complex prism.

Fig. 41.—Dispersion of Light by Prism.

First, they increased the size by enlarging the object-glasses, and not the focal length; but when they had done that they had that extremely objectionable colour which prevented them seeing anything well. The colour and indistinctness came from an overlapping of a number of images, as each colour had its own focus, owing to varying refrangibilities. They found, therefore, that the only effective way of increasing the power of the telescope was by increasing its focal length so as to reduce the dispersing action as much as possible, and so enlarging the size of the actual image to be viewed, without at the same time increasing the angular deviation of the rays transmitted through the edges of the lens. The size of the image corresponding to a given angular diameter of the object is in the direct proportion of the focal length, while the flexure of the rays which converge to form any point of it is in the same proportion inversely.

Fig. 42.—Diagram Showing the Amount of Colour Produced by a Lens.

To take an example. In the case of an object-glass of crown-glass, the space over which the rays are dispersed is one-fiftieth of the distance through which they are deviated, and it will be seen by reference to Fig. 42, that if the red rays are at R, and the blue at B, the distance A B is fifty times R B, and as these distances depend on the diameter of the lens only, we can increase the focal length, and so increase the size of the image without altering the dispersion R B, and so throw the work of magnifying on the object-glass instead of on the eyepiece, which would magnify R B equally with the image itself. So that in that time, and in the time of Huyghens, telescopes of 100, 200, and 300 feet focal length were not only suggested but made, and one enthusiastic stargazer finished an object-glass, the focal length of which was 600 feet. Telescopes of 100 and 150 feet focal length were more commonly used. The eyepiece was at the end of a string, and the object-glass was placed free to move on a tall pole, so that an observer on the ground, by pulling the string, might get the two glasses in a line with the object which he wished to observe.

So it went on till the time of Sir Isaac Newton, who considered the problem very carefully—but not in an absolutely complete way. He came to the conclusion, as he states in his Optics, that the improvement of the refracting telescope was “desperate;” and he gave his attention to reflecting telescopes, which are next to be noticed.

Let us examine the basis of Sir Isaac Newton’s statement, that the improvement of the refracting telescope was desperate. He came to the conclusion that in refraction through different substances there is always an unchanged relation between the amount of dispersion and the amount of deviation, so that if we attempt to correct the action of one prism by another acting in an opposite direction in order to get white light, we shall destroy all deviation. But Sir Isaac Newton happened to be wrong, since there are substances which, for equivalent deviations, disperse the light more or less. So by means of a lens of a certain substance of low dispersive power we can form an image slightly coloured, and we can add another lens of a substance having a high dispersive power and less curvature and just reverse the dispersion of the first lens without reversing all its deviating power.

The following experiments will show clearly the application of this principle. We first take two similar prisms arranged as in Fig. 43. The last through which the light passes corrects the deviation and dispersion of the first. We then take two prisms, one of crown glass and the other of flint glass, and since the dispersion of the flint is greater than that of the crown, we imagine with justice that the flint-glass prism may be of a less angle than the other and still have the same dispersive power, and at the same time, seeing that the angles of the prisms are different, we may expect to find that we shall get a larger amount of deviation from the crown-glass prism than from the other.

Fig. 43.—Decomposition and Recomposition of Light by Two Prisms.

If then a ray of light be passed through the crown-glass prism, we get the dispersion and deviation due to the prism A Fig. 44, giving a spectrum at D. And now we take away the crown glass and place in its stead a prism of flint glass inverted; the ray in this instance is deviated less, but there is an equal amount of colouring at D´. If now we use both prisms, acting in opposite directions, we shall be able to get rid of the colours, but not entirely compensate the deviation. We now place the original crown-glass prism in front of the lantern and then interpose the flint-glass prism, so that the light shall pass through both. The addition of this prism of flint, of greater dispersive power, combines, or as it were shuts off, the colour, leaving the deviation uncompensated, so that we get an uncoloured image of the hole in front of the lantern at D?. This is the foundation of the modern achromatic telescope.

Fig. 44.—Diagram Explaining the Formation of an Achromatic Lens. A, crown-glass prism; B, flint-glass prism of less angle, but giving the same amount of colour; C, the two prisms combined, giving a colourless yet deviated band of light at D?.

Another method of showing the same thing is to bring a V-shaped water-trough into the path of the rays from the lantern; then, while no water is in it, the beam of light passing through it is absolutely uncoloured and undeviated. In this case we have no water inclosed by these surfaces, and it is not acting as a prism at all. If, however, a prism of flint glass, a substance of high dispersive power, is introduced into it, with its refracting edge upwards, it destroys the condition we had before, and we have a coloured band on the screen, because the glass that the prism is made of has the faculty of strong dispersion in addition to its deviation. We can get rid of that dispersion by throwing dispersion in a contrary direction by filling up the trough with water, and so making, as it were, a water prism on either side of the glass one, water being a substance of low dispersive power. We have a colourless beam thrown on the screen, which is deviated from the original level, because the water prisms are together of a greater angle than the glass one.

The experiments of Hall and Dolland have resulted in our being able to combine lenses in the same way that we have here combined prisms, bearing in mind what has been said in reference to the action of lenses being like that of so many prisms; and we may consider two lenses, one of crown and the other of flint glass, Fig 45. The crown glass being of a certain curvature will give a certain dispersion; the flint glass, in consequence of its great dispersive power, will require less curvature to correct the crown glass. What will happen will be this: assuming the second lens to be away, the rays will emerge from the first (convex) lens and form a coloured image at A. But if the second flint-glass concave lens be interposed it will, by means of its action in a contrary direction, undo all the dispersion due to this first lens and a certain amount of deviation, so that we shall get the combination giving an almost colourless image at B.

Fig. 45.—Combination of Flint- and Crown-glass Lenses in an Achromatic Lens.

It will not be absolutely colourless, for the reasons which will be now explained. If light be passed through different substances placed in hollow prisms, or through prisms of flint and crown glass, and the spectra thus produced be observed, we find there are important differences. When we expand the spectra considerably, we see that the action of these different substances is not absolutely uniform, some colours extending over the spectrum further than others. In the case of one kind of glass the red end of the spectrum is crushed up, while in the other we have the red end expanded.

This is called the irrationality of the spectrum produced by prisms of different substances. The crown and the flint-glass lenses—and for telescopes we must use such glass—give irrational spectra, so that the achromatic telescope is not absolutely achromatic, in consequence of this peculiarity; for if R, G, B, Fig. 46, are the centres of the red, green, and violet in the spectrum given by a prism composed of the glass of which one lens is made, and R´, G´, B´, are those of the other, if the lenses are placed so as to counteract each other, and are of such curves that the reds and violets are combined, the greens will remain slightly outstanding. Suppose, as in the drawing, the second prism disperses the violet as much as the first one does, then, when these are reversed they will exactly compensate red and violet. But the second one acts more strongly on the green than the first, which will be over-compensated; and if we weaken the second prism so that the green and red are correct, then the violet will be slightly outstanding, which in practice is not much noticed, except with a very bright object when there is always outstanding colour.

Fig. 46.—Diagram Illustrating the Irrationality of the Spectrum.

This is, however, not a matter of any very great importance for ordinary work, since the visual rays all lie in the neighbourhood of the yellow, so that opticians take care to correct their lenses for the rays in this part of the spectrum, and at the same time, as a matter of necessity, over-correct for the violet rays, that is, reverse the dispersion of the exterior lens, so that the violet rays have a longer instead of a shorter focus than the red, and, therefore, in looking at a bright object, such as a first magnitude star, it appears surrounded by a violet halo; with fainter objects the blue light is not of sufficient intensity to be visible. It is, therefore, always preferable to correct for the most visible rays and leave the outstanding violet to take care of itself; but nevertheless various proposals have been made to get rid of it. Object-glasses containing fluids of different kinds have been tried, but they have never become of any practical value, and it does not seem probable that they ever will.

In order to get rid of the outstanding violet colour when the remainder of the spectrum was corrected, Dr. Blair constructed object-glasses the space between the lenses of which were filled with certain liquids, generally a solution of a salt of mercury or antimony, with the addition of hydrochloric acid; for in the spectrum given by the metallic solution the green is proportionally nearer the red than is the case with the spectrum produced by hydrochloric acid, so that by the adjustment of the different solutions he exactly destroyed the outstanding colour of the ordinary combination. In this way Sir John Herschel tells us he was able to construct lenses of three inches aperture and only nine inches focal length, free from chromatic and spherical aberration.

It was proposed by Mr. Barlow to correct a convex crown-glass lens for chromatic aberration by a hollow concave lens containing bisulphide of carbon, a highly dispersive fluid, having double the power of flint glass. This lens was placed in the cone of rays between the object-glass and the eyepiece. Its surfaces were concavo-convex, calculated to destroy spherical aberration, and its distance from the object-glass was varied until exact achromatism was obtained. A telescope of this principle of eight inches aperture was made by Mr. Barlow, which proved highly satisfactory. In the early part of the last century it was proposed by Wolfius to interpose between the object-glass and eyepiece a concave lens in order to give greater magnification of the image, with a slight increase of focal length; if an ordinary lens be used the achromatism of the images given by the object-glass will be destroyed. Messrs. Dolland and Barlow, however, proposed to make the concave lens achromatic, so that the image is as much without colour when the lens is used as without it. Mr. Dawes found such a lens to work extremely well. These lenses, usually called “Barlow lenses,” are generally made about one inch in diameter, and by varying their distance from the eyepiece the image is altered in size at pleasure.

In the reflecting telescope, with which we will now proceed to deal, there is an absence of colour; but the reflector is not without its drawbacks, for there are imperfections in it as great as those we have been considering in the case of the refractor.

CHAPTER VII.
THE REFLECTION OF LIGHT.

We have now dealt with the refraction of light in general, including deviation and dispersion, in order to see how it can assist us in the formation of the telescope; and we have shown how the chromatic effect of a single lens can be got rid of by employing a compound system composed of different materials, and so we have got a general idea of the refracting telescope. We have now to deal with another property of light, called reflection; and our object is to see how reflection can help us in telescopes.

In the case of reflection we get the original direction of the ray changed as in the case of refraction, but the deviation is due to a different cause. Take a bright light, a candle will do, and a mirror fixed so that the light falls on its surface and is thrown back to the eye, Fig. 47, we see the image of the candle apparently behind the mirror; the rays of light falling on the mirror are reflected from it at exactly the same angle at which they reach it. This brings us in the presence of the first and most important law of reflection; and it is this, at whatever angle the light falls on a mirror, at that angle will it be reflected. As it is usually expressed, the angle of incidence, which is the angle made by the incident ray with an imaginary line drawn at right angles to the mirror, called the normal, is equal to the angle of reflection, that is, the angle contained by the reflected ray, and the normal to the surface. In order, therefore, to find in what direction a ray of light will travel after striking a flat polished surface, we must draw a line at right angles to the surface at the point where the ray impinges on it, then the reflected ray will make an angle with the normal equal to that which the incident ray makes, or the angles of incidence and reflection will be equal.

Fig. 47.—Diagram Illustrating the Action of a Reflecting Surface.

Very simple experiments, which every one can make will show us the laws which govern the phenomena of reflection. Let us employ a bath of mercury for a reflecting surface, and for a luminous object a star, the rays of which, coming from a distance which is practically infinite, to the surface of the earth, may be considered exactly parallel. The direction of the beams of light coming from the star, and falling on the mirror formed by the mercury, is easily determined by means of a theodolite, Fig. 48. If we look directly at the star, the line I´ S´ of the telescope indicates the direction of the incident luminous rays, and the angle S´ I´ N´, equal to the angle S, I, N, is the angle of incidence, that is to say, that formed by the luminous ray with the normal to the surface at the point of incidence.

Fig. 48.—Experimental Proof that the Angle of Incidence = Angle of Reflection.

In order to find the direction of the reflected luminous rays, we must turn the telescope on its axis, until the rays reflected by the surface of the mercury bath enter it and produce an image of the star. When the image is brought to the centre of the telescope, it is found that the angle R´ I´ N´ is equal to the angle of reflection N, I, R. Thus, in reading the measure on the graduated circle of the theodolite the angle of reflection can be compared with the angle of incidence.

Now, whatever may be the star observed, and whatever its height above the horizon, it is always found that there is perfect equality between these angles. Moreover, the position of the circle of the theodolite which enables the star and its image to be seen evidently proves that the ray which arrives directly from the luminous point and that which is reflected at the surface of the mercury are both in the same vertical plane.

Now this demonstrates one of the most important laws of reflection. The laws of refraction do not deal directly with the angles themselves, but with the sines of the angles; in reflection the angles are equal; in refraction the sines have a constant relation to each other.

So far we have dealt with plane surfaces, but in the case of telescopes we do not use plane surfaces, but curved ones, so we will proceed at once to discuss these.

Fig. 49.—Convergence of Light by Concave Mirror.

Fig. 50.—Conjugate Foci of Convex Mirror.

In Fig. 49, A represents a curved surface, such as that of a concave mirror, the centre of curvature being C. Now we can consider that this curved surface is made up of an infinite number of small plane surfaces, and since all lines drawn from the centre, C, to the mirror, will be at right angles to the surface at the points where they meet it, we find, from our experiment with the plane mirror, that rays falling on the mirror at these points will be reflected so that the angles on either side of each of these lines shall be equal; so, for instance, in Fig. 49, we wish to find to what point the upper ray will be reflected, and we draw a line from the centre, C, to the point where it falls on the mirror, and then draw another line from that point making the angle of reflection equal to that made by the incident ray, and we can consider the small surface concerned in reflection flat, so that the ray will in this case be reflected to F. If now we take any other ray, and perform the same operation we shall find that it is also reflected nearly to F, and so on with all other parallel rays falling on the mirror; and this point, F, is therefore said to be the focus of the mirror. If now the rays, instead of falling parallel on the mirror, as if they came from the sun or a very distant object, are divergent, as if they came from a point S, Fig. 50, near the mirror, the rays approach nearer to the lines drawn from the centre to the mirror, one of which is represented by the dotted line; or, in other words, the angles of incidence become reduced, and so the angles of reflection will also be reduced, and the focus of the rays from S will approach the centre of the mirror, and be at s; just so it will be seen that if an illuminated point be at s, its focus will be at S, and these two points are therefore called conjugate foci.

Fig. 51.—Formation of Image of Candle by Reflection.

Fig. 52.—Diagram explaining Fig. 51.

If a candle is held at a short distance in front of a concave mirror, as represented in Fig. 51, its image appears on the paper between the candle and the mirror, so that the rays from every point of the flame are brought to a focus, and produce an image just as the image is produced by a convex lens. If we study Fig. 52 the formation of this image will be clearly understood. First we must note that the rays A, C, a, and B, C, b, which pass through the centre of curvature of the mirror C, will fall perpendicularly on the surface, and be reflected back on themselves, so that the focus of the part a of the arrow will be somewhere on A a, and that of B on B b, and by drawing another ray we shall find it reflected to a, which will be the focus of the point A, and so also by drawing another line from B, we shall find it is reflected to b, which is the focus of the part B; and we might repeat this process for every part of the arrow, and for every ray from those parts. We now see that since the rays A a and B b cross each other at C, the distance from a to b bears the same proportion to the distance from A to B as their respective distances from the point C; or, in other words, the image is smaller than the object in the same proportion as the distance from the image to C is smaller than the distance from the object to C. Now, in dealing with the stars, which are at a practically infinite distance, the rays are parallel, and will be brought to a focus half-way between the mirror and its centre of curvature. In this case, therefore, the distance from the image to the mirror is equal to that from the image to the centre, so that we can express the size of the image by saying that it is smaller than the object, in proportion as its distance from the mirror is smaller than the distance of the object from C; and as it makes little difference whether we measure the distance of the stars from C or from the mirror, and as C is not always known, we can take the relation of the distances of the object and image from the mirror as representing the proportionate sizes of the two.

We will now consider the case of rays falling on a mirror curved the other way, that is, a convex mirror. Let us consider the ray impinging at D, Fig. 53, which would go on to C, the centre of the mirror. Now, as C D is drawn from the centre, it is at right angles to the mirror at D, and the ray L D, being in the same straight line on the opposite side, will also be at right angles, and will be reflected back on itself. Now take the ray I A, draw C E through A, then E A will be perpendicular to the surface at A, and I A E will be the angle of incidence, and E A G the angle of reflection, so that this ray A G will be reflected away from L D, and so will all the other rays falling on the mirror as K B: and if we continue the lines G A and H B backwards, they will meet at M, and therefore the rays diverge from the mirror as if they came from a point at M, and this point is called the virtual focus.

Fig. 53.—Reflection of Rays by Convex Mirror.

So much for parallel rays. Next let us consider another case which happens in the telescope, namely, where converging rays fall on a convex mirror, as in Fig. 53, where we consider the light proceeding to the mirror from a converging lens along the lines H B and G A, these will be made parallel, at B K and A F, after reflection, and it is manifest that by making the mirror sufficiently convex, these rays, tending to come to a focus at M, could be rendered divergent; and if the curvature is decreased by making the centre of curvature at a certain distance beyond C, it will be seen at once by the diagram that these rays will after reflection, converge towards L and will come to a focus in front of the mirror at a point further in front than C is behind it, so that they have been rendered less convergent only by the mirror in this supposed case.

It will be seen from what has been stated here and in Chapter V., that we get nearly the same results from reflection as we did from refraction when we were considering the functions of glasses instead of mirrors; that a concave mirror acts exactly as a convex lens, and vice versÂ, so that they can be substituted the one for the other. If we take a mirror, and allow the light to fall on it from a lamp, no one will have any difficulty in seeing that the mirror grasps the beam, and forms an image which is seen distinctly in front of the mirror, just as one gets an image from a convex lens behind it.

CHAPTER VIII.
THE REFLECTOR.

The point we have next to determine is how we can utilise the properties of reflection for the purposes of astronomical observation. Many admirable plans have been suggested. The first that was put on paper was made by Gregory, who pointed out that if we had a concave mirror, we should get from this mirror an image of the object viewed at the focus in front of it, as in Fig. 51. Of course we cannot at once utilise this focal image by using an eyepiece in the same way as we do in a refractor, because the observer’s head would stop the light, and the mirror would be useless, and all the suggestions which have been made, have reference to obtaining the image in such a position that we are able to view it conveniently.

Gregory, the Scottish astronomer above referred to, in 1663 suggested a method, and it has turned out to be a good one, of utilizing reflection by placing a small mirror D C, Fig. 54, on the other side of the focus A of the large one, at such a distance that the image at A is again focussed at B by reflection from the small mirror; and at B we get of course an enlarged image of A. The rays of light proceeding to B would, however, be intercepted by the large mirror, unless an aperture were made in the large mirror of the size of the small one through which the rays could pass and be rendered parallel by means of an eyepiece placed just behind the large mirror. So that towards the object is the small mirror C, and there is an eyepiece E, which enables the image of the object to be viewed after two reflections, first from the large mirror and then from the small one. Mr. Short (who made the best telescopes of this construction, and did much for the optical science of the last century) altered the position of the small mirror with reference to the focus of the large one, by sliding it along the tube by a screw arrangement, F, and so was enabled to focus both near and distant objects without altering the eyepiece.

Fig. 54.—Reflecting Telescope (Gregorian).

But before this was put into practice, Sir Isaac Newton (in 1666) made telescopes on a totally different plan.

The eyepiece of the Newtonian telescope is at the side of the tube, and not at the end, as in Gregory’s. We have next to inquire how this arrangement is carried out, and, like most things, it is perfectly simple when one knows how it is done. There is a large mirror at the bottom of the tube as in the Gregorian, but not perforated, and the focus of the mirror would be somewhere just in front of the end of the tube. Now in this case we do not allow the beam to get to the focus at all in the tube or in front of it; but before it comes to the focus it is received on a small diagonal plane surface m, and thus it is at once thrown outwards at right angles through the side of the tube, and comes to a focus in front of an eyepiece, placed at the side, ready to be viewed the same as an image from a refractor (Fig. 55).

Fig. 55.—Newton’s Telescope.

The next arrangement is one which Mr. Grubb has recently rescued from obscurity, and it is called the Cassegrainian form. It will be seen on referring to that, Fig. 56, if the small mirror, C, were removed, the rays from the mirror A B would come to a focus at F.

In the Gregorian construction a concave reflector was used outside that focus (at C, Fig. 54), but Cassegrain suggested that if, instead of using a concave reflector outside the focus, a reflector with a convex surface were placed inside it, we should arrive at very nearly the same result, provided we retain the hole in the large mirror. The converging rays from A B will fall on the convex surface of the mirror C, which is of such a curvature and at such a distance from F, the focus of the large mirror, that the rays are rendered less converging, and do not come to a focus until they reach D, where an image is formed ready to be viewed by the eyepiece E. It appears from this, that the convex mirror is in this case acting somewhat in the same manner as the concave lens does in the Galilean telescope.

Fig. 56.—Reflecting Telescope (Cassegrain).

Fig. 57.—Front View Telescope (Herschel).

Then, lastly, we have the suggestion which Sir William Herschel soon turned into more than a suggestion. The mirror M in this arrangement is placed at the bottom of the tube as in the other forms, but, instead of being placed flat on the bottom it is slightly tipped, so that if the eyepiece is placed at the edge of the extremity of the tube all parallel rays falling on the mirror are reflected to the side of the tube at the top where the eyepiece is, instead of being reflected to a convex or other mirror in the middle.

This is called the front view telescope, and it enabled Sir William Herschel to make his discoveries with the forty-feet reflector. With small telescopes this form could not be adopted, as the observer’s head would cover some part of the tube and obstruct the light, but with large telescopes the amount of light stopped by the head is small in proportion to what would be lost by using a small mirror.

These are in the main the four methods of arranging reflecting telescopes—the Gregorian, the Cassegrainian, the Newtonian, and the Herschelian.

In order to make large reflectors perfect—large telescopes of short focus, because that is one of the requirements of the modern astronomer—we have to battle against spherical aberration.

We have already seen that the power of substances to refract light differs for different colours, and we have seen the varied refraction of different parts of the spectrum, and the necessity of making lenses achromatic. Now there is one enormous advantage in favour of the reflector. We do not take our light to bits and put it together again as with an achromatic lens. But curiously enough, there is a something else which quite lowers the position of the reflector with regard to the refractor. Although, in the main all the light falling in parallel lines on a concave surface is reflected to a focus, this is only true in a general sense, because, if we consider it, we find an error which increases very rapidly as the diameter of the mirror increases or as the focal length diminishes. For instance, D I, Fig. 58, is the segment of a circle, or the section of a sphere—if we deal with a solid figure. D C, E G and H I, are three lines representing parallel rays falling on different parts of it. According to that law which we have considered, we can find where the ray E G will fall. We draw a line L, G, from the centre to the point of reflection, and make the angle F G L, equal to the angle of incidence E G L; then F will be the focus, so far as this part of the mirror is concerned. Now let us repeat the process for the ray H I, and we shall find that it will be reflected to K, a point nearer the mirror than F, and it will be seen that the further the rays are from the axis D C, the further from the point F is the light reflected; so that if we consider rays falling from all parts of the reflecting surface, a not very large but a distinctly visible surface is covered with light, so that a spherical surface will not bring all the rays exactly to a point, and with a spherical mirror we shall get a blurred image. We can compare this imperfection of the reflector, called spherical aberration, with the chromatic aberration of the object-glass.

Fig. 58.—Diagram Illustrating Spherical Aberration.

Fig. 59.—Diagram Showing the Proper Form of Reflector to be an Ellipse.

Newton early calculated the ratio of imperfection depending upon these properties of light, first of dispersion and then of spherical aberration, and he found that in the refracting telescope the chromatic aberration was more difficult to correct and get rid of than the spherical aberration of the reflector, so that in Newton’s time, before achromatic lenses were constructed, the reflector with its aberration had the advantage. It must now be explained how this difficulty is got over. What is required to produce a mirror capable of being used for astronomical purposes, is to throw back the edges of the mirror to the dotted line A C I, Fig. 58, which will make the margin of the mirror a part of a less concave mirror, and so its focus will be thrown further from itself—to F, instead of to K. Now let us consider what curve this is, that will throw all the rays to one point. It is an ellipse, as will be seen by reference to Fig. 59, in which, instead of having a spherical surface the section of which is a circle, we deal with a surface whose section is an ellipse.

It will be seen in a moment, that by the construction of an ellipse any light coming in any direction from the point A, which represents one of the foci of the curve, must necessarily be reflected back to the other focus, B, of the curve, for it is a well-known property of this curve that the angles made with a tangent C D, by lines from the foci are equal; and the same holds good for the angles made at all other tangents; and it will be seen at once that this is better than a circular curve, because by making the distance between the foci almost infinite we shall have the star or object viewed at one focus and its image at the other; if we use any portion of the reflecting surface we shall still get the rays reflected to one point only. It must also be noticed, that unless we have an ellipse so large that one focus shall represent the sun or a particular star we want to look at, this curve will not help us in bringing the light to one point, but if we use the curve called the parabola, which is practically an ellipse with one focus at an infinite distance, we do get the means of bringing all the rays from a distant object to a point. Hence the reflector, especially when of large diameter, is of no use for astronomical purposes without the parabolic curve.

That it is extremely difficult to give this figure may be gathered from Sir John Herschel’s statement, that in the case of a reflecting telescope, the mirror of which is forty-eight inches in diameter and the focal distance of which is forty feet, the distance between the parabolic and the spherical surface, at the edges of the mirror, will be represented by something less than a twenty-one thousandth part of an inch, or, more accurately, 1
21333 inch. In Fig. 58 the point A represents the extreme edge of the curve of the parabolic mirror, and D that of the circular surface before altered into a parabola.

At the time of Sir William Herschel the practical difficulties in constructing large achromatic lenses led to the adoption by him of reflectors beginning with small apertures of six inches to a foot, and increasing till he obtained one of four feet in diameter and forty-six feet focal length. This has been surpassed by Lord Rosse, whose well-known telescope is six feet diameter, and fifty-three feet focal length. Mr. Lassell, Mr. De La Rue, M. Foucault and Mr. Grubb, have also more recently succeeded in bringing reflectors to great perfection.

How the work has been done will be fully stated in the sequel.

CHAPTER IX.
EYEPIECES.

We have considered the telescope as a combination of an object-glass and eyepiece in the one case, and of a speculum and eyepiece in the other; that is to say, we have discussed the optical principles which are applied in the construction of refracting and reflecting telescopes, the telescope being taken as consisting of an object-glass or speculum and an eyepiece of the most simple form, viz., a simple double convex lens.

We must now go into detail somewhat on the subject of eyepieces, and explain the different kinds.

It will be recollected that when we spoke of the object-glass, its aberration, both chromatic and spherical, was mentioned. Now every ordinary lens has these errors, and eyepieces must be corrected for them, but this is not done in exactly the same way as with object-glasses.

In the case of eyepieces the error is corrected by using two lenses of such focal lengths or at such a distance apart that each counteracts the defects of the other; not by using two kinds of glass as in the case of the object-glass, but by so arranging the lenses that the coloured rays produced by the first lens shall fall at different angles of incidence on the second and become recombined.

Fig. 60.—Huyghens’ Eyepiece.

Let us take the case of a well-known eyepiece, called the Huyghenian eyepiece, after its inventor. It consists of two plano-convex lenses, A and B Fig. 60, with their convexities turned towards the object-glass, and having their focal lengths in the proportion of three to one. The strongest lens, A, being next the eye, the lens B is placed inside the focus of the object-glass, so that it assists in bringing the image, say of a double star, to a focus at F, half way between the lenses, and nearer to the object-glass than it would have been without the lens. This image is then viewed by the eye-lens, A, and a magnified image of it seen apparently at F´, as has been before explained. Now let us see how the fieldlens renders this combination achromatic. Let us consider the path of a ray falling on the lens near B, shown in section in Fig. 61: it is there refracted, but, the blue rays being refracted more than the red, there will be two rays produced, r and v, giving of course a coloured edge to the image; but when this image is viewed by the eye-glass, A, it no longer appears coloured, for the ray v, falling nearer the axis of A, is less bent than r, and they are rendered nearly parallel and appear to proceed from the point F´ where the whole image appears without colour. In order to get the best result with this form of eyepiece the focal length of the fieldlens should be three times that of the eye-lens and they should be placed at a distance of half their joint focal lengths apart.

Fig. 61.—Diagram Explaining the Achromaticity of the Huyghenian Eyepiece.

The next eyepiece which comes under consideration is that called Ramsden’s, Fig. 62. It consists of two plano-convex lenses of the same focus, A and B, placed at a distance of two-thirds of the focal length of either apart; they are both on the eye side of the focus of the telescope, and act together, to render the rays parallel and give a magnified virtual image of F´F.

This eyepiece is not strictly achromatic, but it suffers least of all lenses from spherical aberration; it also has the advantage of being placed behind the focus of the object-glass, which makes it superior to others in instruments of precision, as we shall presently see.

Fig. 62.—Ramsden’s Eyepiece.

It must be remembered that these eyepieces give an inverted image—or rather the object glass gives an inverted image, and the eyepiece does not right it again; but there are eyepieces that will erect the image, and Rheita’s is one of this kind. It is, as will be seen from Fig. 63, merely a second application of the same means that first inverts the object, namely, a second small telescope. A is the object-glass, a b the image inverted in the usual way; B is an ordinary convex lens sending the rays from a and b parallel. Now, instead of placing the eye at C, as in the ordinary manner, another small lens, acting as an object-glass, is placed in the path of the rays, bringing them to a focus at a´, b´, and forming there an erect image which is viewed by the eye-lens D. This is the erecting eyepiece or “day eyepiece,” of the common “terrestrial telescope.” Dollond substituted an Huyghenian eyepiece for the eye-lens D, and so made what is called his four-glass eyepiece.

Dr. Kitchener devised and Mr. G. Dollond made an alteration in this eyepiece in order to vary its power at pleasure. It is done in this way: The size of the image a´ b´ depends upon the relation of the distances a B and E a´, which can be varied by altering the distance of the combination of the lenses B and E, from the image a b, and so making a´ b´ larger and at a focus further from E; the tube carrying d slides in and out, so that it can be focussed on a´ b´ at whatever distance from E it may be. This arrangement is called Dollond’s Pancratic eyepiece.

Fig. 63.—Erecting or day eyepiece.

On the sliding tube carrying the lens D, or rather the Huyghenian eyepiece in place of the single lens, are marked divisions, showing the power of the eyepiece when drawn out to certain lengths, so that if we want the eyepiece to magnify say 100 times, the tube carrying the eye-lens is drawn out to the point marked 100, and the whole eyepiece moved in or out of the telescope tube by the focussing screw, until the image of the object viewed is focussed in the field of the eyepiece D. To increase the power, we have only to draw out the eyepiece D, and move the whole combination nearer to the object-glass so as to throw the image a´ b´ further from the lens E. This eyepiece, though so convenient for changing powers, is little used, owing perhaps chiefly to four lenses being required instead of two, hence a loss of light, so a stock of eyepieces of various powers is generally found in observatories. When very high powers are required, a single plano-convex lens is sometimes used, but although there is less loss of light in this case, the field of view is so contracted in comparison with that given with other eyepieces that the single lens is seldom used. This form is, however, adopted in Dawes’ solar eyepiece, to be hereafter mentioned, and a number of lenses are in this case fixed in holes near the circumference of a disc of metal which turns on its centre, so that by rotating the disc the lenses come in succession in front of the focus of the object-glass, and the power can be changed almost instantaneously.

In order that objects near the zenith may be observed with ease, a diagonal reflector is sometimes used, so that the eye looks sidewise into the telescope tube instead of directly upwards. This reflector may take the form of two short pieces of tube joined together at right angles, and having a piece of silvered glass or a right-angled prism at the angle, so that when one tube is screwed into the telescope, the rays of light falling on the reflector are sent up the other, in which the ordinary eyepiece is placed.

The eyepieces just described are suitable, without further addition, for observing all ordinary objects, but when the sun has to be examined a difficulty presents itself. The heat rays are brought to a focus along with those of light, and with an object-glass of more than one or two inches aperture there is great danger of the heat cracking the lenses, but with such telescopes the interposition—and neglect of this may cost an eye—of smoked or strongly-coloured glass in front of the eye is generally sufficient to protect it from the intense glare. With larger telescopes, however, dark glasses are apt to split suddenly and allow the full blaze of sunlight to enter the eye and do infinite mischief, and some other method of reducing the heat and light is required. Perhaps the most simple method of effecting this object is to allow the light to fall on a diagonal plane glass reflector at an angle of 45°, which lets the greater part of the light and heat pass through, reflecting only a small portion onwards to the eyepiece and thence to the eye; a coloured glass is, however, required as well, and the glass reflector must form part of a prism of small angle, otherwise there will be two images, one produced by each surface.

Another arrangement is to reflect the rays from the surfaces of two plates of glass inclined to them at the polarizing angle, so that by turning the second plate, or a Nicols’ prism, in its place round the ray as an axis, the amount of light allowed to pass to the eye can be varied at pleasure.

The late Mr. Dawes constructed a very convenient solar eyepiece, depending on the principle of viewing a very small portion of the sun’s image at one time, and thereby diminishing the total quantity of heat passing through the eye-lens. The details of the eyepiece are as follows: very minute holes of varying diameters are made in a brass disc near its circumference, and as this is turned each successive hole is brought into the centre of the field of view and the common focus of the eye-lens and object-glass. Small areas on the sun of different sizes can thus be examined at pleasure. A number of eye-lenses of different powers arranged in a disc of metal can be successively brought to bear, giving a means of quickly varying the power, while coloured glasses of different shades can be passed in front of the eye in the same manner. The surface of the disc of brass containing the holes is covered on one side—that on which the sun’s image falls—with plaster of Paris, which, being a bad conductor, prevents the heat from affecting the whole apparatus.

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The true magnifying power of the eyepiece is found by dividing the focal length of the object-glass by that of the eyepiece; in practice it is found approximately by comparing the diameter of the object-glass with that of its image formed by the eyepiece when the telescope is in its usual adjustment; the former divided by the latter giving the power required. The diameter of the image can be measured by a small compound microscope carrying a transparent scale in its focus, when the image of the object-glass is brought to a focus and enlarged on the scale and then viewed, together with the divisions, by the microscope; or the image can be measured with tolerable accuracy by Mr. Berthon’s dynameter, consisting of a plate of metal traversed longitudinally by a wedge-shaped opening. This is placed close to the eye-lens in the case of the Huyghenian eyepiece, or at the point where the image of the object-glass is focussed with other forms of eyepieces, and the plate moved until the sides of the wedge-shaped opening are exactly tangential to the image; the point of the opening at which this occurs is read off on a scale, which gives the width of opening at this point and therefore the diameter of the image.

CHAPTER X.
PRODUCTION OF LENSES AND SPECULA.

Before we go on to the use and various mountings of telescopes, the optical principles of which have been now considered, a few words may be said about the materials used and the method of obtaining the necessary and proper curves. Object-glasses, of course, have always been made of glass, and till a few years ago specula were always made of metal; but so soon as Liebig discovered a method of coating glass with a thin film of metallic silver, Steinheil, and after him the illustrious Foucault, so well known for his delicate experiments on the velocity of light and his invention of the gyroscope, suggested the construction of glass mirrors coated by Liebig’s process with an exceedingly thin film of silver, chemically deposited.

This arrangement much reduced the price of reflectors and rendered their polishing extremely easy, and at the present time discs of glass up to four feet in diameter are being thus produced and formed into mirrors, though in the opinion of competent judges this size is likely to be the limit for some time. But there is this important difference, that although glass is now used both for reflectors and refractors, almost any glass, even common glass, will do, if we wish to use it for a speculum; but if we wish to grind it into lenses it is impossible to overrate the difficulty of manufacture and the skill and labour required in order to prepare it for use, first in the simple material, and then in the finished form in which it is used by the astronomer. In a former chapter we considered some chefs-d’oeuvre of the early opticians, some specimens of a quarter or half-an-inch in diameter, with extremely long focus; and as we went on we found object-glasses gradually increasing in diameter, but they were limited to the same material, namely, crown glass.

Dollond, whose name we have already mentioned in connection with that of Hall, gave us the foundation of the manufacture of the precious flint glass, the connection of which with crown glass he had insisted upon as of critical importance. The existence of a piece of flint glass two inches in diameter was then a thing to be devoutly desired, that is to say, flint glass of sufficient purity for the purpose; it could not be made of a size larger than that, and not only was the material wanted, but the material in its pure state.

In the year 1820 we hear of a piece of flint glass six inches in diameter, and in 1859 Mr. Simms reported that a piece of flint glass of seven and three-quarter inches was produced, six inches of which were good for astronomical purposes. But even at this time they did these things better in Germany and Switzerland, where M. Guinand made large discs at the beginning of the present century. He was engaged by Fraunhofer and Utzschneider at their establishment in Bavaria in 1805, and by his process achromatics of from six to nine inches in diameter were constructed. Afterwards Merz, the successor of Fraunhofer, succeeded in obtaining flint glass of the then unprecedented diameter of fifteen inches.

Now we have in part turned the tables, and Mr. Chance, of Birmingham, owing to the introduction of foreign talent, has since constructed discs of glass of a workable diameter of twenty-five inches for Mr. Newall’s telescope, and for the American Government he has completed the large discs used in constructing the refractor of 26 inches’ diameter for the observatory at Washington (the Americans are never content till they go an inch beyond their rivals), while M. Feil of Paris, a descendant of the celebrated Guinand, has also made one of nearly 28 inches’ diameter for the Austrian Government.

Messrs. Chance and Feil, however, have the monopoly of this manufacture, and the production of these discs is a secret process. What we know is that the glass is prepared in pots in large quantities, it is then allowed to cool, and is broken up in order that it may be determined which portions of the glass are worth using for optical purposes. These are gathered together and fused at a red heat into a disc, and it is this disc which, after being annealed with the utmost care, forms the basis of the optician’s work.

For the glass used for reflectors, purity is of little moment, as we only require a surface to take a polish, since we look on to it, and not through it; but in the case of the glass that has to be shaped into a lens the purity is of the utmost importance. The practical and scientific optician, on his commencement to make an object-glass, will grind the two surfaces of both flint and crown as nearly parallel as possible, and polish them. In this state he can the better examine them as to veins, striÆ, and other defects, which would be fatal to anything made out of it. He has next to see that the annealing is perfectly done by examining the discs with polarized light, to see by the absence of the “black cross” that there is no unequal tension. It is so difficult to run the gauntlet through all these difficulties when the aperture is considerable that refractors of forty inches’ aperture may be perhaps despaired of for years to come, though the glassmaker is willing to try his part.

Next, as to metallic specula. As we are dealing with the instruments that are now used, we will be content with considering the compounds that have been made successfully, and omit the variations which have never been brought into practice. To put it roughly, the metal used for Lord Rosse’s reflector consisted of two parts of copper and one part of tin; but here we have an idea of the Scylla and the Charybdis which are always present in these inquiries. If we use too much tin, which tends to give a surface of brilliancy to the speculum, a few drops of hot water poured on it will be enough to shiver it to atoms. This brittleness is objectionable, and what we have to do is to reduce the quantity of tin. But then comes the Charybdis. If we do this, the colour is no longer white, but it is yellow, and in addition we have introduced a surface that quickly tarnishes instead of a surface which remains bright. The proportions which seem to answer best are copper sixty-four parts and tin twenty-nine. Lord Rosse, we believe, uses 31·79 per cent, of tin; or very nearly the above proportions. Mr. Grubb in the Melbourne mirrors used copper and tin in the proportion of 32 to 14·77.

Having the metal, we have roughly to cast it in the shape of a speculum, but if an ordinary casting is made in a sand mould the speculum metal is so spongy that we can do nothing with it. If it is put in a close mould it will probably be cast very well, but it will shiver to atoms with a very slight change of temperature. The difficulty was got over by Lord Rosse, using an open mould called a “bed of hoops;” the bottom of the mould being composed of strips of iron set edgeways, held together by an iron ring and turned to the proper convexity; sand is then placed round the iron to form the edges, the metal is then poured in, and the bubbles and vapours run down through the small apertures at the bottom of the mould, so that the speculum is fairly cast. Mr. Lassell proposed a different method, which was introduced by Mr. Grubb in his arrangements for the Melbourne telescope. Instead of having the bottom of the bed of hoops perfectly horizontal it is slightly inclined; the crucible, which contains the metal of which the speculum is to be cast, is then brought up to it—the amount of metal being something under two tons in the case of the Melbourne telescope—and the bed of the mould is kept tipped up as the metal is poured into it, and so arranged as to keep the melted metal in contact with one side; and as it gets full it is brought into a perfectly horizontal position.

Having cast the speculum, the next thing is to put it in an annealing oven, raised to a temperature of 1,000°, where it is allowed to cool slowly for weeks till it has acquired nearly the ordinary temperature. On being removed from the oven the speculum is placed on several thicknesses of cloth and rough ground on front, back, and edge.

Having got the material roughly into form we now pass on to see what is done next.

In the case of the reflector, whether of metal or glass, the optician next attempts to get a perfectly spherical surface of the proper curvature for the required focus.

In the case of the refractor matters are somewhat more complicated; we have there four spherical surfaces to deal with, and the optician has work to do of quite a different kind before he even commences to grind.

Presuming the refractive and dispersive properties of the glass not known, it will be necessary to have a small bit of glass of the same kind to experiment with. That the optician may make no mistake in this important matter, some glass manufacturers make the discs with projecting pieces to be cut off; these the object-glass maker works into prisms to determine the exact refraction and dispersion, including the position in the spectrum of the Fraunhofer lines C and G, for both the crown and flint glass. With these numbers and the desired focal length he has all the necessary data for the mathematical operation of calculating the powers to be given to the two lenses—flint and crown, and the radii of curvature of the four surfaces in order that the object-glass may be aplanatic or free from aberration both spherical and chromatic. The problem is what mathematicians call an indeterminate one, as an infinite number of different curvatures is possible. Assume, however, the radius of curvature of one surface, and all the rest are limited. In assuming the radius of curvature on one of the crown-glass surfaces, it is well to avoid deep ones. It is better to divide the refraction of the four surfaces as equally as the nature of the problem will admit, as any little deviation from a true spherical figure in the polishing will produce less effect in injuring the performance of the object-glass from surfaces so arranged than if the curves were deep.

But whatever curves he chooses he goes to work so that the spherical aberration of the compound lens shall be eliminated as far as possible, and the chromatism in one lens shall be corrected by the other, or in other words, that what is called the secondary spectrum shall be as small as possible; and it is to be feared that this will never be abolished.^[6]

Fig. 64.—Images of planet produced by short and long focus lenses of the same aperture giving images of different size, but with the same amount of colour round the edges.

This matter requires a somewhat detailed treatment in order that it may be seen how the four surfaces to which reference has been made are determined.

The chromatic dispersion, in the case of the object-glass, may be roughly stated to be measured by about one fiftieth of the aperture. Suppose for instance the discs, Fig. 64, to represent the image of any object, say the planet Jupiter. Then round that planet we should have a coloured fringe, and the dimensions of that coloured fringe, that is, the joint thickness of colour at A and D, will be found by dividing the diameter of the object-glass used by fifty. Now this is absolutely independent of the focal length of the telescope; therefore one way of getting rid of it is to increase the focal length of telescopes; and as the size of the image depends on focal length, and has nothing whatever to do with aperture, we may imagine that with the same sized object-glass, instead of having a little Jupiter as on the left of Fig. 64, we may have a very large Jupiter, due to the increased focal length of the telescope. Then, it may be asked, how about the chromatic aberration? It will not be disturbed. The aperture of the object-glass remains unaltered, and there is no more chromatic aberration here than in the first case; so that the relation between the visible planet Jupiter and the colour round it is changed by altering the focal length. But as we have seen, we are able by means of a combination of flint and crown glass to counteract this dispersion to a very great extent. How then about spherical aberration?

Up to the present we have assumed that all rays falling on a convex lens are brought to a point or focus, but this is not strictly true, for the edges of a lens turn the rays rather too much out of their course, so that they will not come to a point; just as the rays reflected from a spherical mirror do not form a single focus. The marginal rays will be spread over a certain circular surface, just as the colour due to chromatic aberration covered a surface surrounding the focus. It was explained that for the same diameter of lens the circle of colour remained the same, irrespective of focal length, but in the case of spherical aberration this is not so; it diminishes as the square of the focal length increases; that is to say, if we double the focal length we shall not only halve, but half-halve, or quarter the aberration. Newton calculated the size of the circle of aberration in comparison with that due to colour, and he found that in the case of a lens of four inches diameter and ten feet focus, the spherical aberration was eighty-one and a half times less than that of colour. It is found that by altering the relative curvatures of the surfaces of the lens, this aberration can be corrected without altering the focal length; for any number of lenses can be made of different curvatures on each side but of the same thickness in the middle, so that they have all the same focal length, but the one, having one surface about three times more convex than the other, will have least aberration, so that it is the adaptation of the surfaces of lenses to each other that exercises the art of the optician.

So far we have got rid of this aberration in a single lens; it can also be done in the case of achromatic lenses. The foci of the two lenses in an achromatic combination must bear a certain relation to each other, and the curvatures of the surfaces must also have a certain relation for spherical aberration. In the achromatic lens there are four surfaces, two of which can be altered for one aberration and two for the other. For instance, in the case of the lens, Fig. 45, where the interior surfaces of the lenses are cemented together, although shown separate for clearness, we find that if the exterior surface of the crown double convex lens be of a curvature struck by a radius 672 units in length, and the exterior surface of the flint glass lens to a curvature due to a radius of 1,420 units, the lens will be corrected for spherical aberration, and these conditions leave the interior surfaces to be altered so that the relation between the powers of the lenses is such as to give achromatism.

The flint is as useful in correcting the spherical aberration as the chromatic aberration; for although the relative thicknesses of the flint and crown are fixed in order to get achromatism, still we have by altering both the curvatures of each lens equally, and keeping the same foci, the power of altering the extent of spherical aberration; and it is in the applications of these two conditions that much of the higher art of our opticians is exercised. We have now therefore practically got rid of both aberrations in the modern object-glass, and hence it is that lenses of the large diameter of twenty-five and twenty-six inches are possible.

The nearest approach to achromatism is known to be made when looking at a star of the first or second magnitude, the eyepiece being pushed out of focus towards the object-glass, the expanded disc has its margin of a claret colour. When the eyepiece is pushed beyond the focus outwards the margin of the expanded disc is of a light green colour.

If the object-glass is well corrected for spherical aberration, the expanded discs both within and without the focus will be constituted of a series of rings equally dense with regard to light throughout, with the exception of the marginal ring, which will be a little stronger than the rest.

Having determined the radius of curvature of surface, both he who grinds the speculum, whether of speculum metal or glass, and he who grinds the object-glass, starts fair; only one has four times the work to do that the other has. The grinding is managed in a simple way, and the process of grinding or polishing an object-glass or speculum, either of glass or of metal, is the same.

Supposing we wish to make a reflecting telescope of six feet focus, or a surface of an object-glass of twelve feet radius, all we have to do is to get a long rod, a little more than twelve feet long, and pin it to a wall at its upper end so that it can swing, pendulum fashion; then at a distance of twelve feet below the point of suspension a pin is stuck through the rod and its point made to scratch a line on a sheet of metal laid against the wall; then this line will be part of a circle struck with a radius of twelve feet. If then the plate be cut along this line we get a convex and a concave surface of the desired radius, and then we can take a block of iron or brass and turn its surface, convex or concave, to fit the sheet of metal or template. For a reflector we should make a convex tool, and for a refractor a concave one.

Generally this grinding tool is divided into squares or furrows all over it, in order that the emery which is used in rough grinding may flow freely about with the water. A disc of glass is then laid on the tool, or the tool on the glass, the two being pressed together by a weight or spring; emery powder, with water, is strewn between them, and one is rubbed over the other by a machine similar to those used for polishing, which we shall explain presently. This operation is continued until the glass is ground all over, and in this process of rough grinding the rough emery is used between the tool and the glass, so that whatever irregularities the glass or tool may have they are got rid of, and it is easy to obtain a spherical surface, and indeed, it is the only surface that can be obtained. Then finer and finer emery is used, till it ceases to be a sufficiently fine substance to use, and a surface of iron or lead is also too hard a surface. Now the polishing begins, and the optician and amateur avail themselves of a suggestion due to Sir Isaac Newton, who always saw much further through things than other people.

Even when he first began to make the first reflector, he used pitch, a substance not too hard, nor yet too soft, and one that can be regulated by temperature; therefore for polishing, instead of having a tool made of metal, pitch laid on glass or wood and supplied with rouge and water is used. This polisher of pitch is divided into squares by channels to allow free flow of rouge and water, and is laid on the mirror or object-glass, or vice versÂ, and moved about over it.

When the maximum of polish is attained the work is done, and the object-glass finished, as here we have to do with a spherical surface. In the grinding of the two discs for Mr. Newall’s telescope 1,560 hours were consumed, the thickness of the crown disc having been reduced one inch in the process.

In the case of specula, however, there is more to be done; and it is in this polishing of specula that the curve is altered from a circle to a parabola by using a certain length of stroke, size of polisher, consistency of pitch, and numbers of other smaller matters, the proper proportionment of which constitutes the practical skill of the optician, and it is in accomplishing this that the finest niceties of manipulation come into play, and the utmost patience is required. 1,170 hours were occupied in the grinding and polishing of the four-feet Melbourne speculum. This was equivalent to 2,050,000 strokes of the machine at 33 per minute for rough and 24 for fine grinding. Dr. Robinson, in his description of the grinding operations, states that at the edge of one of the four-feet specula the distance of its parabola from the circle was only 0·000106?.

In the early times of specula the polishing was invariably done by hand, a handle being cemented by pitch to the back of the speculum to work it with. Mudge tells us that at first, when the mirror was rough from the emery grinding, it was worked round and round on the pitch, which was supplied with rouge and water and cut by channels into small squares, carrying the edge but little over the polisher, an occasional cross stroke being made. The effect of this was to press the pitch towards the centre where the polish always commenced, and gradually spread to the circumference. As soon as the polishing was complete the speculum was worked by short straight strokes across the centre, tending to bring it back to a sphere; then the circular strokes were recommenced to restore the paraboloid form: these were continued for a short time only, otherwise it would pass the proper curve and require reworking with straight strokes again. By this method some small mirrors of first-class definition were constructed.

When Sir W. Herschel began his labours he constructed a machine for working the speculum over the polisher; the polisher was a little larger than the mirror, the proportion given by him from a number of trials being 1·06 to 1.

The speculum was held in a circular frame, which was free to turn round in another ring or frame; this frame was moved backwards and forwards by a vibrating lever to which it was attached by rods, carrying the speculum over the polisher. This motion he designates the stroke. Besides this there was the side motion produced by a rod attached to the side of the frame opposite to that to which the rods giving it the stroke were attached and at right angles to the direction of stroke: this rod was in connection, by means of intermediate levers, with a pin on a rachet wheel, which was turned a tooth at a time by a rod in connection with the lever giving the stroke motion, so that the rod giving the side motion was pushed and pulled back by the pin on the rachet wheel every time it turned round, which it did every twenty or thirty strokes. There were also teeth on the ring fastened round the edge at the back of the speculum, into which claws worked which were attached by rods to a point on the lever a little distance from the attachment of the rod giving the stroke, so that the claws had a less motion than the speculum and its ring, and consequently pulled the ring, and with it the speculum, round a tooth or more at each stroke. The polisher was also turned round in the same manner in a contrary direction to the motion of the speculum. The speculum had therefore three motions, a revolving one on its centre, a stroke, and a side motion, making its centre describe a number of parallel lines over the polisher on each side of its centre. Sir W. Herschel gives as a good working length of stroke, 0·29, and 0·19 side motion measured from side to side, the diameter of the speculum being 1. To produce a seven-inch mirror with this instrument he would work continuously for sixteen hours, his sister “putting the victuals by bits into his mouth.”

Lord Rosse adopted a similar arrangement; the polisher, K L, Fig. 65, was worked over the speculum in straight strokes with side motion, the requisite straight motion being given by a crank-pin and rod and the side motion by the continuation of this latter rod on the other side of the polisher working in a guide on another crank-pin, which threw it from side to side as the wheel carrying the pin revolved. The trough E F carrying the speculum also revolved slowly, and the requisite motions were given by pulleys and straps of various sizes under the table on which the machine rested; the weight of the polisher was in a great measure counterpoised by strings from its upper surface to a weighted lever M above. The polisher was free to turn in its ring, which it did once in about twenty strokes, and for the six feet speculum the velocity of working was about eight strokes a minute, the length of stroke being one-third of the diameter of the speculum, and that of the side motion one-fifth.

The speculum was polished on the same system of levers that were afterwards to support it, in order that no change of form might be produced in moving it to a different mounting. The consistency of the pitch is a matter of importance, Mr. Lassell’s test of the requisite hardness being the number of impressions left by a sovereign standing on edge on it; this should leave three complete impressions of the milled edge in one minute at the ordinary temperature of the atmosphere.

Fig. 66 represents the machine contrived by Mr. Lassell for his method of polishing, and shows what a complicated arrangement is essential in order to arrive at any good result in these matters.

The speculum is placed on a bed, and above it is a train of wheels terminating in a crank-pin that gives motion to the polisher, which is made to take a very devious path by the motion of the wheels above. The pin giving motion to the polisher G at its centre can be set at a variable distance from the axis of the lowest pinion F to which it is attached, by moving it in its slide, so that when the pinion is turned, the pin and centre of the polisher describe a circle. The pinion in question is carried on a slide C above it, attached to the main vertical driving shaft A, so that as the shaft revolves the centre of the pinion describes a circle of a diameter variable at pleasure by moving it in the slide C, the result of the two motions being that the centre of the polisher describes circles about a moving centre, and consequently in constantly varying positions on the speculum. Motion is given to the vertical shaft by the cog-wheel and endless screw above, worked by some prime mover, and as the cogwheels on the shaft E parallel to the main shaft are carried round the latter by the arm D holding them, they are caused to revolve by gearing into the fixed wheel B, through the centre of which the main shaft passes, and they in their turn impart motion to the pinion carrying the pin giving motion to the polisher. The speculum is also maintained in slow rotation by the wheel and endless screw below it. The speculum and its supports are surrounded by water contained in a circular trough not shown in the engraving, so that the consistency of the pitch shall be constant.

This arrangement, pure and simple, was found to bring on the polish in rings over the speculum, and as an improvement, the speculum, or rather the system of levers supporting it, was carried on a plate which had the power of sliding backwards and forwards on the wheel turning it round; the edges of this plate pressed against a fixed roller, and it was made of such a shape that as it revolved it was forced to take a side motion as its edges passed by the fixed roller, so that the speculum had a side motion in addition to the rotatory one.

Mr. De La Rue improved on this by giving the speculum a rotatory motion irrespective of that of the sliding plate, so that the side motion should not always be along the same diameter of the speculum. This was done by allowing the speculum to turn freely on a pivot on the sliding plate, and giving it a rotatory motion by means of a cord going round the plate carrying the speculum supports. As a further improvement Mr. De La Rue controls the motion of the polisher on the central pin, giving it motion by a crank carrying a system of wheels in place of the lowest crank, so that the pin gets a rotatory motion in addition to these.

Mr. Grubb’s arrangement for polishing is different. The speculum is made to rotate, the polisher is made to execute curves variable at pleasure by altering the throw of the cranks which move rods attached to the centre of the polisher, giving it a motion similar to that of Mr. Lassell’s machine. The polisher moves a little off the edge, so that the edge is worn down more than the centre, thus giving the parabolic form.

M. Foucault, of whom we have already spoken, proceeds in a different manner in parabolising his glass mirrors. He first obtains a spherical surface, fairly reflective, by grinding. He then alters the surface to a paraboloid form by handwork, only testing the surface from time to time to ascertain the parts requiring reduction by the polishing pad. The method of testing is as beautiful as it is simple. The approximate estimate of the curvature of the speculum is made by placing a small and well-defined object, such as the point of a pin, close to the centre of curvature and examining its image formed close by its side with a lens. As a nicer test, he places an object having parallel sides, say a flat ruler, near the centre of curvature, and views its image with the naked eye at the distance of distinct vision, then each point of the edge is seen by rays converging only from a small portion of the surface of the mirror, the remainder of the diverging cone from each point of the edge passes on beside the eye, and by moving the eye about, any point of the edge can be seen formed by rays proceeding from any particular part of the mirror, viz., that part in line with the eye and point of the edge examined; if the curvature be not uniform the edge will appear distorted, and points on it will appear in different positions, as rays from different parts of the mirror are received by the eye as it is moved, making the edge appear to move in waves. Finally, he allows light from a very small hole in a metal plate near the centre of curvature to fall on the mirror, and places the eye just on the side opposite to the point where the image is formed, so as to receive the rays as they diverge after having come to a focus. The whole of the light thus passes into the eye, and the mirror is seen illuminated in every part. A sharp edge of metal is then gradually brought into the focus, when the illumination of the mirror decreases, and just before the light disappears the irregularities will plainly appear, showing themselves by patches of light, which prove that those parts still bright are so inclined as to reflect the rays by the side of the true focus. By moving the metallic edge so as to advance upon the focus from all sides, a very good idea of the irregularities may be obtained. If, however, the surface be truly spherical, the light will disappear regularly over the whole surface.

M. Foucault commences by making the surface truly spherical, and then by polishing off in concentric circles, increasing the polishing from the centre, an elliptic and at last a parabolic curve is attained. The ellipse is tested from time to time by removing the perforated plate further and further away from the mirror until the ellipse becomes practically a parabola. The great advantage of this method is, that the effect of the polishing can be examined as it proceeds, and the work can always be applied wherever necessary, and the test is entirely independent of hot-air currents which are seen to fluctuate over the mirror as waves of light, leaving the irregularities of form permanently marked. It further appears that the method may be varied to form a first-rate test of a finished mirror already mounted; for one has nothing to do but bring a star into the field of view, and remove the eyepiece, and bring the eye into such a position as to receive the diverging rays from the focus of the star. A knife is then gradually moved across in front of the eye, say from the right; then if the mirror commences to get darkened on the right side distinctly before the left the knife is on the mirror side of the focus; if, however, the left side of the mirror becomes darkened first it is on the eye side of the focus. After a few trials it can be got to cut across the focus and darken the mirror at all points at once, and show up all irregularities.

We have now, then, by one system or another, got our mirror, either of speculum metal or of glass, and if of the latter substance we have to silver it; processes have been published by Mr. Browning, and M. Martin,^[7] by which, on the plan proposed in the first instance by Liebig, an extremely thin coating of silver is deposited on the glass. This film is susceptible of taking a high polish, which, in the case of small mirrors, can be renewed as often as is wished without repolishing the mirror; the resilvering of one of large aperture however is a most formidable affair. To those who wish to silver their own mirrors, let us say that it should be done in summer, or in a room kept by a stove at an equable summer heat, and the silvering solution should be kept for a day or more to settle, and for probably some chemical change to take place before the reducing solution is added. It will be found easy enough to silver the small planes for Newtonian reflectors, but large mirrors require much greater care and trouble.

Having now obtained the lenses and specula we come, in order to complete our consideration of the purely optical portion of the subject, to the question of mounting these lenses and specula in tubes and thus connecting them with the eyepieces so as to become of practical utility. We will first consider the adjustment of lenses in a tube, the combination forming a simple telescope that can be supported, in any manner desirable, by mountings we shall presently consider, according to the purpose for which it is required. The adjustment of specula will be considered as we advance further.

The smaller telescopes consist of a brass tube, the object-glass, held in a brass ring, being screwed in at one end of the tube: a smaller tube sliding in and out of the other end of the large tube, generally moved by a rack and pinion motion, carries the eyepiece. In larger telescopes the mounting is similar, only somewhat more elaborate, the object-glass being carried in a brass cell, or a steel one if the dimensions are very large. This screws into the ring at the end of the tube, and this ring can be slightly tipped on either side by set screws, so that the object-glass can be brought exactly at right angles to the axis of the tube.

It is important, in order that an object-glass shall perform its best, that the lenses forming it shall be properly centred: this is generally done by the maker once and for ever. Wollaston pointed out an ingenious method of centring them; it is as follows:—The eyepiece is removed, and a lighted candle put in its place: the object-glass is then examined from the opposite side, when, if all the lenses are correctly placed, the images of the candle produced by the successive reflections of the candle from the surfaces of the lenses will be concentric, and in a straight line from the candle through the centre of the system of lenses, a fact easily judged of, by moving the eye slightly from side to side, and if they are not, they are easily corrected by tipping the lens in fault slightly in the cell. In case the lenses are cemented together, this method of course is applicable in setting the object-glass at right angles to the axis of the tube. The adjustment of an object-glass can also be judged of by examining a star as it is thrown in and out of focus by the focusing screw; the disc of the star should be perfectly round in and out of focus, and the rings produced by interference should also be circular when in focus, and the disc of light, when out of focus, must be circular. Any elongation of the disc or rings, or a “flare” appearing, shows a want of a slight alteration of the setting screw, on the same side of the object-glass as the “flare” or elongation appears.

In some object-glasses the curves of the two interior surfaces are such that three pieces of tin foil are placed at equal distances round the edge to prevent the central portions from coming in contact.

The flexure of small object-glasses by their own weight is of little importance, because every surface is affected alike; but when the aperture is large special precautions have to be taken. The late Mr. Cooke when he had completed the 25-inch object-glass for Mr. Newall’s telescope, introduced a system of counterpoise levers just within the edge which helped to support the object-glass in all positions. Mr. Grubb states that with an aperture of 15 inches, supported on three points, there is decided evidence of flexure, and he proposes, in the 27-inch Vienna refractor, not only to introduce six intermediate supports, thereby following in the footsteps of Mr. Cooke, but with larger apertures to introduce boldly a central support, or to hermetically seal the tube and fill it with compressed air. He has calculated that in the case of an object-glass 40 inches aperture, weighing 600 lbs., two-thirds of its weight could be supported by an air pressure of one-third of a pound to the square inch.

The tube of the telescope when of large size is usually made of iron or wood, and a tube of the latter substance may be made very light and yet sufficiently strong, by wrapping layers of veneer round a central core and fastening the layers firmly with glue. There are generally two or more tubes sliding inside each other at the eye end of the telescope, to carry the eyepiece so as to give plenty of power of adjustment of the length of the tube to suit the different eyepieces, or other instruments used in their place. The tube then is ready to be adapted to any of the mountings to be hereafter considered.

We now come to the mounting of specula, and when we recollect the enormous weights of some of the specimens to which we have referred, it will be obvious that some additional precautions, which are not at all necessary in the case of a refractor, must be taken to insure success.

In reflecting telescopes, the speculum is carried at the bottom of a tube in a sort of tray or cell, which can be adjusted by screws at the back, so as to set the mirror at right angles to the tube, and the conditions of support should be such that the mirror should be as free from strain as if it were floating in mercury. A system of lateral supports in all positions is also necessary.

The action of the telescope depends greatly on the backing of the speculum, and numerous methods of carrying specula on soft backing and systems of levers have been suggested, all aiming at carrying them so that they are free from all possible strain and flexure occasioned by their own weight. For smaller mirrors a soft back of flannel or cloth can be used, and a leather strap placed round the mirror and its back, so as to form the side of a sort of circular tray, will give it sufficient support when inclined to the horizontal. Mr. Browning adopts the plan of making the back of the mirror and its support perfectly flat, so as not to require levers or soft backing; this arrangement would probably fail for mirrors larger than one foot in diameter, although answering admirably for those of less size.

We will now consider the methods of mounting specula of larger size, and will take as an instance the mounting of some of the largest specula in existence which must act so as to prevent flexure in any position of the speculum. The speculum is, in the case of the Melbourne telescope, of the weight of something like two tons. When it is inclined at any considerable angle to the horizon, it is apt to bend over at the top, and thus destroy its proper curvature; and when horizontal, if not equally supported, it will also bend, and unless some measures are taken to prevent this flexure it will so entirely alter its figure by its own weight as to render minute observations of any delicate stars absolutely impossible.

Mr. Lassell was the first to suggest an arrangement for preventing this flexure. Through the back of the speculum case—the case which holds and supports the speculum, which we shall have to speak about presently—he inserts a large number of very small levers, the centres of which are fixed to the exterior part of this case, the forward part of each resting against a small aperture made in the back of the speculum. The ends of the levers furthest from the speculum are crowned with small weights, the weights varying on different parts of the speculum. Now so long as the speculum is perfectly horizontal, i.e. so long as the zenith is being observed, these levers will have no action whatever; but the moment the reflector is brought into any other position, as, for instance, when we wish to observe a star near the horizon, the more the mirror is inclined to the horizon the greater will be the power of these small levers, and at length their total effect comes into action when a star close to the horizon is being observed. Then the whole weight of the mirror is carried by these levers acting at points all over its back.

In the Melbourne reflector, which has recently been finished, Mr. Grubb manages this somewhat differently, as will be seen by Figs. 73-76.

In Fig. 73 the speculum is in a vertical position. It is supported in a frame, B B, all round it, which consists of a slightly flexible hoop of metal a little larger than the speculum. This in its turn is supported by a large fixed hoop, A A, having a hook-shaped section. This hoop is attached to the tube of the telescope C C. The hoop, B B, is rather larger than the part of A on which it hangs, so that it can adjust itself to the form of the mirror; and not only is the mirror supported in the hoop B B, like as in a strap in the position shown, but in every other position of the tube the speculum still hangs evenly supported.

As we have already seen, there is another point to consider. Not only must we be able to support the mirror when inclined to the horizon, but we must support it bodily at the end of the tube when it is horizontal. We will next examine an arrangement adopted by Mr. Grubb, similar to that adopted by others, for supporting the Melbourne speculum, and we cannot do better than quote Mr. Grubb’s own explanation of it. He says:—

“To understand it, suppose the speculum to be divided into forty-eight portions, as in Fig. 74, each of them being exactly equal in area, and consequently in weight. Now, if the centre of gravity of each of these pieces rested on points which would bear up with a force = the weight of each segmental piece, it is evident that there would be no strain in the mass from segment to segment.

“This is exactly what is accomplished by this system; in fact, if when the speculum is resting on these supports it could be divided up into segments corresponding to those lines, they would have no inclination to leave their places, showing a perfect absence of strain across those lines. Suppose now the points representing the centres of gravity of these segments were supported on levers and triangles, so as to couple them together, as at A, Fig. 75, and each of these couplings to be supported from a point a, representing the centre of gravity of the sum of the segments supported by that particular couple, and it is evident that there can be no strain between the components of these couples. Again, let these points, a, be coupled together by the system shown at B, Fig. 75, and their centres of gravity, b, coupled as at C, and it is evident that the whole weight of the speculum ultimately condensed by this system into these points is supported on forty-eight points of equal support being the centres of gravity of the forty-eight segments at Fig. 75. In Fig. 76 is seen the whole system complete. It consists of three screws passing through the back of the speculum box (which serve for levelling the mirror), the points of which carry levers (primary system) supporting triangles on their extremities (secondary system), from the vertices of which are hung two triangles and one lever (tertiary system). All the joints of this apparatus are capable of a small rocking motion, to enable them to take their positions when the speculum is laid upon them.

“In the system of levers made by Lord Rosse for his six-feet speculum, the primary, secondary, and tertiary systems were piled up one over the other, so that the distance from the support of the primary to the back of the speculum was about fifteen inches. This, as will be readily seen on consideration, introduced a new strain when the telescope was turned off the zenith, and had to be counterpoised by another very complicated system of levers. But in the Melbourne telescope, by the substitution of cast-steel for cast-iron, and by hanging the tertiary system from the secondary, and allowing it (the tertiary) to act in some places through the secondary, the whole system is reduced to three and a half inches in height, and the distance from the support of the primary lever to the back of the speculum is only one and three-quarter inch, by which means this cumbersome apparatus is entirely done away with.

“The ultimate points of the tertiary system are gunmetal cups, which hold truly ground cast-iron balls with a little play, and when the speculum is laid on these it can be moved about a little by a person’s finger with such ease as to seem to be floating in some liquid.”

It may perhaps be thought that it would be better to support these great specula on a flat surface, and it might be, if we could do so without extreme difficulty; but Lord Rosse has stated that if we attempt to support a large speculum on a surface extremely flat, a thread placed across that surface, or even a piece of dust, is quite enough to bend the mirror and render it absolutely useless. That will show the extreme importance of the support of the speculum.

Let us then assume that we have the speculum and the tube perfectly adjusted. The next thing, in all constructions except the Herschelian, is to apply the second small reflector, concave in the case of the Gregorian, convex in the case of the Cassegrainian, and plane in the case of the Newtonian.

This small mirror is generally supported by a thin strip of metal firmly fastened to the side of the tube, with power of movement parallel to the axis of the telescope, in the case of the Gregorian and Cassegrainian, for the purpose of focussing. In the Newtonian, the reflecting diagonal prism or plane mirror, inclined at an angle of 45° to the axis, is preferably supported in the manner suggested by Mr. Browning. See Figs. 77 and 78.

In these B B B represent strips of strong chronometer spring steel, placed edgewise towards the speculum; by these the prism or small mirror D is suspended.

The mirror thus mounted, does not produce such coarse rays on bright stars as when it is fixed to a single stout arm; it is also less liable to vibration, which is very injurious to distinct vision, or to flexure, which interferes with the accuracy of the adjustments.

Fig. 77.—Support of diagonal plane mirror (Front view).

The most usual form of reflector is the Newtonian, large numbers of which kind are now made; and just as the object-glasses of refractors require adjusting, so do not only the large mirror, but also the “flat” or diagonal mirror of this form. In the Newtonian the flat must be adjusted first; to do this, first place the large mirror in its cell in the tube, and secure it by turning it in the bayonet joint, with the cover on the mirror. Then remove the glasses from one of the eyepieces, insert it into the eyetube, and fix the diagonal mirror loosely in its position.

Then, looking through the eyetube, move the diagonal mirror, by means of the motions which are provided, until the reflected image of the cover of the speculum is seen in the centre of it.

This is accomplished by first loosening the milled-headed screw behind the mirror, and turning the mirror until the image of the speculum cover appears central in one direction. The screw at the back of the mirror enables the reflected image to be brought central in the other direction.

Next comes the turn of the large mirror. Take off the cover by screwing off the side opening and place the eye at the eyetube after having removed the eyepiece; the reflection of the diagonal mirror will be seen in the reflected image of the speculum. The adjusting screws, at the back of the speculum, must then be moved until the diagonal mirror is seen in the centre of the speculum. The adjustment should then be complete.

This may be judged of by bringing a star to the centre of the field, and sliding the focussing-tube in or out, when the circle of light should expand equally, and its centre should remain central in the field. As another test a bright star should be viewed with a high power, and the image examined; if it is round and the circles of light round it are concentric without rays in any one direction, then all is correct; but if a flare is seen, it is evidence that the part of the diagonal mirror towards which the flare extends must be moved from the eye by the setting-screws at the back.

The gain to astronomy from the discovery of the telescope has been twofold. We have first, the gain to physical astronomy from the magnification of objects, and secondly, the gain to astronomy of position from the magnification, so to speak, of space, which enables minute portions of it to be most accurately quantified.

Looking back, nothing is more curious in the history of astronomy than the rooted objection which Hevel and others showed to apply the telescope to the pointers and pinnules of the instruments used in their day; but doubtless we must look for the explanation of this not only in the accuracy to which observers had attained by the old method, but in the rude nature of the telescope itself in the early times, before the introduction of the micrometer. We shall show in a future chapter how the modern accuracy has step by step been arrived at; in the present one we have to see what the telescope does for us in the domain of that grand physical astronomy which deals with the number and appearances of the various bodies which people space.

Let us, to begin with, try to see how the telescope helps us in the matter of observations of the sun. The sun is about ninety millions of miles away; suppose, therefore, by means of a telescope reflecting or refracting, whichever we like, we use an eyepiece which will magnify say 900 times, we obviously bring the sun within 100,000 miles of us; that is to say, by means of this telescope we can observe the sun with the naked eye as if it were within 100,000 miles of us. One may say, this is something, but not much; it is only about half as far as the moon is from us. But when we recollect the enormous size of the sun, and that if the centre of the sun occupied the centre of our earth the circumference of the sun would extend considerably beyond the orbit of the moon, then one must acknowledge we have done something to bring the sun within half the distance of the moon. Suppose for looking at the moon we use on a telescope a power of 1,000, that is a power which magnifies a thousand times, we shall bring the moon within 240 miles of us, and we shall be able to see the moon with a telescope of that magnifying power pretty much as if the moon were situated somewhere in Lancashire—Lancaster being about 240 miles from London.

It might appear at first sight possible in the case of all bodies to magnify the image formed by the object-glass to an unlimited extent by using a sufficiently powerful eyepiece. This, however, is not the case, for as an object is magnified it is spread over a larger portion of the retina than before; the brightness, therefore, becomes diminished as the area increases, and this takes place at a rate equal to the square of the increase in diameter. If, therefore, we require an object to be largely magnified we must produce an image sufficiently bright to bear such magnification; this means that we must use an object-glass or speculum of large diameter. Again, in observing a very faint object, such as a nebula or comet, we cannot, by decreasing the power of the eyepiece, increase the brightness to an unlimited extent, for as the power decreases, the focal length of the eyepiece also increases, and the eyepiece has to be larger, the emergent pencil is then larger than the pupil of the eye, and consequently a portion of the rays of the cone from each point of the object is wasted.

We get an immense gain to physical astronomy by the revelations of the fainter objects which, without the telescope, would have remained invisible to us; but, as we know, as each large telescope has exceeded preceding ones in illuminating power, the former bounds of the visible creation have been gradually extended, though even now we cannot be said to have got beyond certain small limits, for there are others beyond the region which the most powerful telescope reveals to us; though we have got only into the surface we have increased the 3,000 or 6,000 stars visible to the naked eye to something like twenty millions. This space-penetrating power of the telescope, as it is called, depends on the principle that whenever the image formed on the retina is less than sufficient to appear of an appreciable size the light is apparently spread out by a purely physiological action until the image, say of a star, appears of an appreciable diameter, and the effect on the retina of such small points of light is simply proportionate to the amount of light received, whether the eye be assisted by the telescope or not; the stars always, except when sufficiently bright to form diffraction rings, appearing of the same size. It, therefore, happens that as the apertures of telescopes increase, and with them the amount of light, (the eyepieces being sufficiently powerful to cause all the light to enter the eye,) smaller and smaller stars become visible, while the larger stars appear to get brighter and brighter without increasing in size, the image of the brightest star with the highest power, if we neglect rays and diffraction rings, being really much smaller than the apparent size due to physiological effects, and of this latter size every star must appear.

The accompanying woodcuts of a region in the constellation of Gemini as seen with the naked eye and with a powerful telescope will give a better idea than mere language can do of the effect of this so-called space-penetrating power.

With nebulÆ and comets matters are different, for these, even with small telescopes and low powers, often occupy an appreciable space on the retina. On increasing the aperture we must also increase the power of the eyepiece, in order that the more divergent cones of light from each point of the image shall enter the pupil, and therefore increase the area on the retina, over which the increased amount of light, due to greater aperture, is spread; the brightness therefore is not increased, unless indeed we were at the first using an unnecessary high power. On the other hand, if we lengthen the focus of the object-glass, and increase its aperture, the divergence of the cones of light is not increased and the eyepiece need not be altered, but the image at the focus of the object-glass is increased in size by the increase of focal length, and the image on the retina also increases as in the last case. We may, therefore conclude that no comet or nebula of appreciable diameter, as seen through a telescope having an eyepiece of just such a focal length as to admit all the rays to the eye, can be made brighter by any increase of power, although it may easily be made to appear larger.

Very beautiful drawings of the nebula of Orion and of other nebulÆ, as seen by Lord Rosse in his six-foot reflector, and by the American astronomers with their twenty-six inch refractor, have been given to the world.

The magnificent nebula of Orion is scarcely visible to the naked eye; one can just see it glimmering on a fine night; but when a powerful telescope is used, it is by far the most glorious object of its class in the Northern hemisphere, and surpassed only by that surrounding the variable star ? ArgÛs in the Southern. And although, of course, the beauty and vastness of this stupendous and remote object increase with the increased power of the instrument brought to bear upon it, a large aperture is not needed to render it a most impressive and awe-inspiring object to the beholder. In an ordinary 5-foot achromatic, many of its details are to be seen under favourable atmospheric conditions.

Those who are desirous of studying its appearance, as seen in the most powerful telescopes, are referred to the plate in Sir John Herschel’s “Results of Astronomical Observations at the Cape of Good Hope,” in which all its features are admirably delineated, and the positions of 150 stars which surround ? in the area occupied by the Nebula, laid down. In Fig. 82 it is represented in great detail, as seen with the included small stars, all of which have been mapped with reference to their positions and brightness. This then comes from that power of the telescope which simply makes it a sort of large eye. We may measure the illuminating power of the telescope by a reference to the size of our own eye. If one takes the pupil of an ordinary eye to be something like the fifth of an inch in diameter, which in some cases is an extreme estimate, we shall find that its area would be roughly about one-thirtieth part of an inch. If we take Lord Rosse’s speculum of six feet in diameter the area will be something like 4,000 inches: and if we multiply the two together we shall find, if we lose no light, we should get 120,000 times more light from Lord Rosse’s telescope than we do from our unaided eye, everything supposed perfect.

Let us consider for a moment what this means; let us take a case in point. Suppose that owing to imperfections in reflection and other matters two-thirds of the light is lost so that the eye receives 40,000 times the amount given by the unaided vision, then a sixth magnitude star—a star just visible to the naked eye—would have 40,000 times more light, and it might be removed to a distance 200 times as great as it at present is and still be visible in the field of the telescope, just as it at present is to the unaided eye. Can we judge how far off the stars are that are only just visible with Lord Rosse’s instrument? Light travels at the rate of 185,000 miles a second, and from the nearest star it takes some 3½ years for light to reach us, and we shall be within bounds when we say that it will take light 300 years to reach us from many a sixth magnitude star.

But we may remove this star 200 times further away and yet see it with the telescope, so that we can probably see stars so far off that light takes 60,000 years to reach us, and when we gaze at the heavens at night we are viewing the stars not as they are at that moment, but as they were years or even hundreds of years ago, and when we call to our assistance the telescope the years become thousands and tens of thousands—expressed in miles these distances become too great for the imagination to grasp; yet we actually look into this vast abyss of space and see the laws of gravitation holding good there, and calculate the orbit of one star about another.

Whether the telescope be of the first or last order of excellence, its light-grasping powers will be practically the same; there is therefore a great distinction to be drawn between the illuminating and defining power. The former, as we have seen, depends upon size (and subsidiarily upon polish), the latter depends upon the accuracy of the curvature of the surface.

If the defining power be not good, even if the air be perfect, each increase of the magnifying power so brings out the defects of the image, that at last no details at all are visible, all outlines are blurred, or stellar character is lost.

The testing of a glass therefore refers to two different qualities which it should possess. Its quality as to material and the fineness of its polish should be such that the maximum of light shall be transmitted. Its quality, as to the curves, should be such that the rays passing through every part of its area shall converge absolutely to the same point, with a chromatic aberration not absolutely nil, but sufficient to surround objects with a faint violet light.

In close double stars therefore, or in the more minute markings of the sun, moon, or planets, we have tests of its defining power; and if this is equally good in the instruments examined, the revelations of telescopes as they increase in power are of the most amazing kind.

A 3¾-inch suffices to show Saturn with all the detail shown in Fig. 83, while Fig. 84 shows us the further minute structure of the rings which comes out when the planet is observed with an aperture of 26 inches.

In the matter of double stars, a telescope of 2 inches aperture, with powers varying from 60 to 100, should show the following stars double:—

A 4-inch aperture, powers 80-120, reveals the duplicity of—

A 6-inch, powers 240-300—

An 8-inch—

The “spurious disk,” which a fixed star presents, as seen in the telescope, is an effect which results from the passage of the light through the object-glass; and it is this appearance which necessitates the use of the largest apertures in the observation of close double stars, as the size of the star’s disk varies, roughly speaking, in the inverse ratio of the aperture of the object-glass.

In our climate, which is not so bad as some would make it, a 6- to an 8-inch glass is doubtless the size which will be found the most constantly useful; a larger aperture being frequently not only useless, but hurtful. Still, 4 or 3¾ inches are apertures by all means to be encouraged; and by object-glasses of these sizes, made of course by the best makers, views of the sun, moon, planets, and double stars may be obtained, sufficiently striking to set many seriously to work as amateur observers, and with a prospect of securing good, useful results.

Observations should always be commenced with the lowest power, gradually increasing it until the limit of the aperture, or of the atmospheric condition at the time, is reached. The former may be taken as equal to the number of hundredths of inches which the diameter of the object-glass contains. Thus, a 3¾-inch object-glass, if really good, should bear a power of 375 on double stars where light is no object; the planets, the Moon, &c., will be best observed with a much lower power. (See chapter on eyepieces.)

Care should be taken that the object-glass is properly adjusted. And we may here repeat that this may be done by observing the image of a large star out of focus. If the light be not equally distributed over the image, or the diffraction rings are not circular, the screws of the cell should be carefully loosened, and that part of the cell towards which the rings are thrown very gently tapped with wood, to force it towards the eyepiece, or the same purpose may be effected by means of the setscrews always present on large telescopes, until perfectly equal illumination is arrived at. This, however, should only be done in extreme cases; it is here especially desirable that we should let well alone.

The convenient altitude at which Orion culminates in these latitudes renders it particularly eligible for observation; and during the first months of the year our readers who would test their telescopes will do well not to lose the opportunity of trying the progressively difficult tests, both of illuminating and separating power, afforded by its various double and multiple systems, which are collected together in such a circumscribed region of the heavens that no extensive movement of their instruments—an important point in extreme cases—will be necessary.

Beginning with d, the upper of the three stars which form the belt, the two components will be visible in almost any instrument which may be used for seeing them, being of the second and seventh magnitudes, and well separated. The companion to , though of the same magnitude as that to d, is much more difficult to observe, in consequence of its proximity to its bright primary, a first-magnitude star. Quaint old Kitchener, in his work on telescopes, mentions that the companion to Rigel has been seen with an object-glass of 2¾-inch aperture; it should be seen, at all events, with a 3-inch. ?, the bottom star in the belt, is a capital test both of the dividing and space-penetrating power, as the two bright stars of the second and sixth magnitudes, of which the close double is composed, are exactly 2½? apart, while there is a companion to one of these components of the twelfth magnitude about ¾? distant. The small star below, which the late Admiral Smyth, in his charming book, “The Celestial Cycle,” mentions as a test for his object-glass of 5·9 inches in diameter, is now plainly to be seen in a 3¾. The colours of this pair have been variously stated; Struve dubbing the sixth magnitude—which, by the way, was missed altogether by Sir John Herschel—“olivaceasubrubicunda.”

That either our modern opticians contrive to admit more light by means of a superior polish imparted to the surfaces of the object-glass, or that the stars themselves are becoming brighter, is again evidenced by the point of light preceding one of the brightest stars in the system composing s. This little twinkler is now always to be seen in a 3¾-inch, while the same authority we have before quoted—Admiral Smyth—speaks of it as being of very difficult vision in his instrument of much larger dimensions. In this very beautiful compound system there are no less than seven principal stars; and there are several other faint ones in the field. The upper very faint companion of ? is a delicate test for a 3¾-inch, which aperture, however, will readily divide the closer double of the principal stars which are about 5? apart.

These objects, with the exception of ?, have been given more to test the space-penetrating than the dividing power; the telescope’s action on 52 Orionis will at once decide this latter quality. This star, just visible to the naked eye on a fine night, to the right of a line joining a and d, is a very close double. The components, of the sixth magnitude, are separated by less than two seconds of arc, and the glass which shows a good wide black division between them, free from all stray light, the spurious disk being perfectly round, and not too large, is by no means to be despised.

Then, again, we have a capital test object in the great nebula to which reference has already been made.

The star, to which we wish to call especial attention, is situate (see Fig. 82) opposite the bottom of the “fauces,” the name given to the indentation which gives rise to the appearance of the “fish’s mouth.” This object, which has been designated the “trapezium,” from the figure formed by its principal components, consists, in fact, of six stars, the fifth and sixth (?´ and a´) being excessively faint. Our previous remark, relative to the increased brightness of the stars, applies here with great force; for the fifth escaped the gaze of the elder Herschel, armed with his powerful instruments, and was not discovered till 1826, by Struve, who, in his turn, missed the sixth star, which, as well as the fifth, has been seen in modern achromatics of such small size as to make all comparison with the giant telescopes used by these astronomers ridiculous.

Sir John Herschel has rated ?´ and a´ of the twelfth and fourteenth magnitudes—the latter requires a high power to observe it, by reason of its proximity to a. Both these stars have been seen in an ordinary 5-foot achromatic, by Cooke, of 3¾-inches aperture, a fact speaking volumes for the perfection of surface and polish attained by our modern opticians.

Let us now try to form some idea of the perfection of the modern object-glass. We will take a telescope of eight inches aperture, and ten feet focal length. Suppose we observe a close double star, such as ? UrsÆ, then the images of these two stars will be brought to a focus side by side, as we have previously explained, and the distance by which they will be separated will be dependent on the focal length of the object-glass. If we refer once again to Fig. 39 we shall see that this distance depends on the focal length and on the angle subtended by the images of the stars at the object-glass, which is of course the same as the angle made by the real stars at the object-glass, which is called their angular distance, or simply their distance, and is expressed in seconds of arc.

If we take a telescope ten feet long and look at two stars 1° apart, the angle will be 1°; and at ten feet off the distance between the two images will be something like 2? inches, and therefore, if the angle be a second, the lines will be the 1
3600th part of that, or about 1
1700th part of an inch apart, so that in order to be able to see the double star ? UrsÆ, which is a 1? star, by means of an eight-inch object-glass, all the surfaces, the 50 square inches of surface, of both sides of the crown, and both sides of the flint glass, must be so absolutely true and accurate, that after the light is seized by the object-glass, we must have those two stars absolutely perfectly distinct at the distance of the seventeen hundredth part of an inch, and in order to see stars ½? apart, their images must be distinct at one-half of this distance or at 1
3400th part of an inch from each other.

We know that both with object-glasses and reflectors a certain amount of light is lost by imperfect reflection in the one case, and by reflection from the surfaces and absorption in the other; and in reflectors we have generally two reflections instead of one. This loss is to the distinct disadvantage of the reflector, and it has been stated by authorities on the subject, that, light for light, if we use a reflector, we must make the aperture twice as large as that of a refractor in order to make up for the loss of light due to reflection. But Dr. Robinson thinks that this is an extreme estimate; and with reference to the four-foot reflector which has recently been constructed, and of which mention has already been made, he considers that a refractor of 33·73 inches aperture would be probably something like its equivalent if the glass were perfectly transparent, which is not the case, and when the thickness of such a lens came to be considered, it was calculated that instead of its being equal to the four-foot reflector, it would only be equal to one of 37¼ of similar construction, and that even a refractor of 48 inches aperture, if such could be made, would not come up to the same sized reflector just referred to in illuminating power.

On the assumption, therefore, that no light is lost in transmission through the object-glass, Dr. Robinson estimates that the apertures of a refractor and a reflector of the Newtonian construction must bear the relation to each other of 1 to 1·42. In small refractors the light absorbed by the glass is small, and therefore this ratio holds approximately good, but we see from the example just quoted how more nearly equal the ratio becomes on an increase of aperture, until at a certain limit the refractor, aperture for aperture, is surpassed by its rival, supposing Dr. Robertson’s estimate to be correct. But with specula of silvered glass the reflective power is much higher than that of speculum metal; the silvered glass, being estimated to reflect about 90 per cent.^[8] of the incident light, while speculum metal is estimated to reflect about 63 per cent.; but be these figures correct or not, the silvered surface has undoubtedly the greater reflective power; and, according to Sir J. Herschel, a reflector of the Newtonian construction utilizes about seven-eighths of the light that a refractor would do.

Speaking generally, refractors of sizes usually obtainable are preferable to reflectors of equal and even greater aperture for ordinary work; as in addition to the want of illuminating power of reflectors, the absence of rigidity of the mounting of the speculum militates against its comfort of manipulation.

In treating of the question of the future of the telescope, we are liable to encroach on the domain of opinion and go beyond the facts vouched for by evidence, but there are certain guiding principles which are well worthy of discussion. There are the two classes of telescopes, the refractors and reflectors, each possessing advantages over the other. We may set out with observing that the light-grasping power of the reflector varies as the square of the aperture multiplied by a certain fraction representing the proportion of the amount of reflected light to that of the total incident rays. On the other hand, the power of the refractor varies as the square of the aperture multiplied by a certain fraction representing the proportion of transmitted light to that of the total incident rays. Now in the case of the reflector the reflecting power of each unit of surface is constant whatever be the size of the mirror, but in that of the refractor the transmitting power decreases with the thickness of the glass, rendered requisite by increased size, although for small apertures the transmitting power of the refractor is greater than the reflecting power of the reflector; still it is obvious that on increasing the size a stage must be at last reached when the two rivals become equal to each other. This limit has been estimated by Dr. Robinson to be 35·435 inches, a size not yet reached by our opticians by some 10 inches, but object-glasses are increasing inch by inch, and it would be rash to say that this size cannot be reached within perhaps the lifetime of our present workers, but up to the present limit of size produced, refractors have the advantage in light-grasping power.

The next point worthy of attention is the question of permanence of optical qualities. Here the refractor undoubtedly has the advantage. It is true that the flint glass of some objectives gets attacked by a sort of tarnish, still, that is not the case generally, while, on the other hand, metallic mirrors often become considerably tarnished after a few years of use, and although repolishing is not a matter of any great difficulty in the hands of the maker, still it is a serious drawback to be obliged to return mirrors every few years to be repolished. There are, however, some exceptions to this, for there are many small mirrors in existence whose polish is good after many years of continuous use, just as on the other hand there are many object-glasses whose polish has suffered in a few years, but these are exceptions to the rule. The same remarks apply to the silvered glass reflectors, for although the silvering of small mirrors is not a difficult process, the matter becomes exceedingly difficult with large surfaces, and indeed at present large discs of glass, say of four or six feet diameter, cannot be produced. If, however, a process should be discovered of manufacturing these discs satisfactorily and of silvering them, there are objections to them on the grounds of the bad conductivity of glass, whereby changes of temperature alter the curvature to a fatal extent, and there is also a great tendency for dew to be deposited on the surface.

The next point to be considered is the general suitability for observatory work, and this depends upon the quality of the work required, whether for measuring positions, as in the case of the transit instrument, where permanency of mounting is of great importance, or for physical astronomy, when a steady image for a time is only required. For the first purpose the refractor has decidedly the advantage, as the object-glass can be fixed very nearly immovably in its cell, whereas its rival must of necessity, at least with present appliances, have a small, yet in comparison considerable, motion.

Again, the refractor has the advantage over the other in not being of so large aperture when of equal power, so that the disturbing effects of air currents is considerably less, but the method of making the tubes of open lattice-work materially reduces this objection.

We have mentioned the difficulty of mounting mirrors, especially of large size, but this has now been got over very perfectly. This difficulty does not occur in the mounting of object-glasses of sizes at present in use, but when we come to deal with lenses of some 30 inches diameter, the present simple method will in all probability be found insufficient.

On the other hand the cost of mirrors is of course much less than that of object-glasses, a matter of considerable importance. The late M. Merz, on being asked as to price of a 30-inch object-glass, estimated that, if it were possible to make it, its cost would be between £8,500 and £9,000.

There is one great point of advantage in the use of the reflector in physical work,—the absence of secondary spectrum; but it is by no means certain that stellar photography will not be more easy with refractors.