Thomas Dick

A micrometer is an instrument attached to a telescope, in order to measure small spaces in the heavens, such as the spaces between two stars, and the diameters of the sun, moon and planets—and by the help of which the apparent magnitude of all objects viewed through telescopes may be measured with great exactness.

There are various descriptions of these instruments, constructed with different substances, and in various forms, of which the following constitute the principal variety. The Wire micrometer—the Spider’s line micrometer—the Polymetric reticle—Divided object glass micrometer—Divided eye-glass micrometer—Ramsden’s Catoptric micrometer—Rochon’s crystal micrometer—Maskelyne’s Prismatic micrometer—Brewster’s micrometrical telescope—Sir W. Herschel’s Lamp micrometer—Cavallo’s Mother of Pearl micrometer, and several others. But, instead of attempting even a general description of these instruments, I shall confine myself merely to a very brief description of Cavallo’s Micrometer, as its construction will be easily understood by the general reader, as it is one of the most simple of these instruments, and is so cheap as to be procured for a few shillings; while some of the instruments now mentioned are so expensive, as to cost nearly as much as a tolerably good telescope.37

This micrometer consists of a thin and narrow slip of mother of pearl finely divided, which is placed in the focus of the eye-glass of a telescope, just where the image of the object is formed; and it may be applied either to a reflecting or a refracting telescope, provided the eye-glass be a convex lens. It is about the 20th part of an inch broad, and of the thickness of common writing paper, divided into equal parts by parallel lines, every fifth and tenth of which is a little longer than the rest. The simplest way of fixing it is to stick it upon the diaphragm which generally stands within the tube, and in the focus of the eye-glass. When thus fixed, if you look through the eye-glass, the divisions of the micrometrical scale will appear very distinct, unless the diaphragm is not exactly in the focus of the eye-glass, in which case it must be moved to the proper place;—or, the micrometer may be placed exactly in the focus of the eye-lens by the interposition of a circular piece of paper, card, or by means of wax. If a person should not like to see always the micrometer in the field of the telescope, then the micrometrical scale, instead of being fixed to the diaphragm, may be fitted to a circular perforated plate of brass, of wood, or even of paper, which may be occasionally placed upon the said diaphragm. One of these micrometers, in my possession, which contains 600 divisions in an inch, is fitted up in a separate eye-tube, with a glass peculiar to itself, which slides into the eye-piece of the telescope, when its own proper glass is taken out.

To ascertain the value of the divisions of this micrometer.—Direct the telescope to the sun, and observe how many divisions of the micrometer measure its diameter exactly. Then take out of the Nautical Almanack the diameter of the sun for the day on which the observation is made. Divide it by the above-mentioned number of divisions, and the quotient is the value of one division of the micrometer. Thus, suppose that 26½ divisions of the micrometer measure the diameter of the sun, and that the Nautical Almanack gives for the measure of the same diameter 31´: 22´´, or 1882´´. Divide 1882 by 26.5, and the quotient is 71´´ or 1´: 11´´, which is the value of one division of the micrometer; the double of which is the value of two divisions, and so on. The value of the divisions may likewise be ascertained by the passage of an equatorial star over a certain number of divisions in a certain time. The stars best situated for this purpose are such as the following—d in the Whale, R. A. 37°: 3?´, Dec. 37´: 50´´ S; d in Orion, R. A. 80°: 11´: 42´´, Dec. 28´: 40´´ S; ? in the Lion, R. A. 171°: 25´: 21´´, Dec. 23´: 22´´ N.; ? in Virgo R. A. 182°: 10´, Dec. 33´: 27´´ N. But the following is the most easy and accurate method of determining the value of the divisions:—

Mark upon a wall or other place the length of six inches, which may be done by making two dots or lines six inches asunder, or by fixing a six inch ruler upon a stand. Then place the telescope before it, so that the ruler or six-inch length may be at right angles with the direction of the telescope, and just 57 feet 3½ inches distant from the object-glass of the telescope; this done, look through the telescope at the ruler, or other extension of six inches, and observe how many divisions of the micrometer are equal to it, and that same number of divisions is equal to half a degree, or 30´; and this is all that is necessary for the required determination. The reason of which is, because an extension of six inches subtends an angle of 30´, at the distance of 57 feet, 3½ inches, as may be easily calculated from the rules of plane Trigonometry.

figure 85.

Fig. 85, exhibits this micrometer scale, but shows it four times larger than the real size of one which was adapted to a 3 feet achromatic telescope magnifying 84 times. The divisions upon it are the 200ths of an inch, which reach from one edge of the scale to about the middle of it, excepting every fifth and tenth division, which are longer. Two divisions of this scale are very nearly equal to one minute; and as a quarter of one of these divisions may be distinguished by estimation, therefore an angle of ¹/₈ of a minute, or of 7½´´ may be measured with it. When a telescope magnifies more, the divisions of the micrometer must be more minute. When the focus of the eye-glass of the telescope is shorter than half an inch, the micrometer may be divided with the 500ths of an inch; by means of which, and the telescope magnifying about 200 times, one may easily and accurately measure an angle smaller than half a second. On the other hand, when the telescope does not magnify above 30 times, the divisions need not be so minute. In one of Dollond’s pocket telescopes, which, when drawn out for use is only 14 inches long, a micrometer with the hundredths of an inch is quite sufficient, and one of its divisions is equal to little less than 3 minutes, so that an angle of a minute may be measured by it. Supposing 11½ of those divisions equal to 30´ or 23 to a degree—any other angle measured by any other number of divisions, is determined by proportion. Thus, suppose the diameter of the sun, seen through the same telescope, be found equal to 12 divisions, say As 11½ divisions : are to 30 minutes :: so are 12 divisions : to ((12 × 30)/11.5) 31.3, which is the required diameter of the sun.

Practical uses of this Micrometer.—This micrometer may be applied to the following purposes:—1. For measuring the apparent diameters of the sun, moon, and planets. 2. For measuring the apparent distances of the satellites from their primaries. 3. For measuring the cusps of the moon in eclipses. 4. For measuring the apparent distances between two contiguous stars—between a star and a planet—between a star and the moon—or between a comet and the contiguous stars, so as to determine its path. 5. For finding the difference of declination of contiguous stars, when they have nearly the same R. Ascension. 6. For measuring the small elevations or depressions of objects above and below the horizon. 7. For measuring the proportional parts of buildings, and other objects in perspective drawing. 8. For ascertaining whether a ship at sea, or any moving object is coming nearer or going farther off; for if the angle subtended by the object appears to increase, it shows that the object is coming nearer, and if the angle appears to decrease, it indicates that the object is receding from us. 9. For ascertaining the real distances of objects of known extension, and hence to measure heights, depths, and horizontal distances. 10. For measuring the real extensions of objects when their distances are known. 11. For measuring the distance and size of an object when neither of them is known.

When the micrometer is adapted to those telescopes which have four glasses in the eye-tube—and when the eye-tube only is used, it may be applied to the following purposes:—1. For measuring the real or lineal dimensions of small objects, instead of the angles. For if the tube be unscrewed from the rest of the telescope, and applied to small objects, it will serve for a microscope, having a considerable magnifying power, as we have already shown, (p. 348); and the micrometer, in that case, will measure the lineal dimensions of the object, as the diameter of a hair, the length of a flea, or the limbs of an insect. In order to find the value of the divisions for this purpose, we need only apply a ruler, divided into tenths of an inch, to the end of the tube, and, looking through the tube, observe how many divisions of the micrometer measure one tenth of an inch on the ruler, which will give the required value. Thus, if 30 divisions are equal to ¹/₁₀th of an inch, 300 of them must be equal to 1 inch, and one division is equal to the 300dth part of an inch. 2. For measuring the magnifying power of other telescopes. This is done by measuring the diameter of the pencil of light at the eye-end of the telescope in question. For, if we divide the diameter of the object lens by the diameter of this pencil of light, the quotient will express how many times that telescope magnifies in diameter. Thus, suppose that 300 divisions of the micrometer are equal to the apparent extension of 1 inch—that the pencil of light is measured by 4 of these divisions—and that the diameter of the object lens measures 1 inch and 2 tenths:—Multiply 1.2 by 300, and the product 360, divided by 4, gives 90 for the magnifying power of the telescope.

Problems which may be solved by this micrometer. I. The angle—not exceeding one degree—which is subtended by an extension of 1 foot, being given, to find its distance from the place of observation:—Rule 1. If the angle be expressed in minutes, say, as the given angle : is to 60 :: so is 687.55 : to a fourth proportional, which gives the answer in inches. 2. If the angle be expressed in seconds, say, As the given angle : is to 3600 :: so is 687.55 to a fourth proportional, which expresses the answer in inches. 3. If the angle be expressed in minutes and seconds, turn it all into seconds, and proceed as above. Example, at what distance is a globe of 1 foot in diameter, when it subtends an angle of 2 seconds? 2 : 3600 :: 687.55 : (3600 × 687.55)/2 = 1237596 inches, or 103132½ feet = the answer required. II. The angle which is subtended by any known extension being given, to find its distance from the place of observation. Rule, Proceed as if the extension were of one foot, by Problem I, and call the answer B; then if the extension in question be expressed in inches, say, as 12 inches : are to that extension :: so is B : to a fourth proportional, which is the answer in inches. But if the extension in question be expressed in feet, then we need only multiply it by B, and the product is the answer in inches.—Example, At what distance is a man 6 feet high, when he appears to subtend an angle of 30´´? By Problem I, if the man were 1 foot high, the distance would be 82506 inches; but as he is 6 feet high, therefore multiply 82506 by 6, and the product is the required distance, namely 495036 inches, or 41253 feet.

For greater conveniency, especially in travelling, when one has not the opportunity of making such calculations, the following two tables have been calculated; the first of which shows the distance answering to any angle from one minute to one degree, which is subtended by a man whose height is considered an extension of 6 feet, because at a mean, such is the height of a man when dressed with hat and shoes on. These tables may be transcribed on a card, and may be kept always ready with a pocket telescope furnished with a micrometer. Their use is to ascertain distances without any calculations; and they are calculated only to minutes, because with a pocket telescope and micrometer, it is not possible to measure an angle more accurately than to a minute. Thus, if we want to measure the extension of a street, let a foot ruler be placed at the end of the street; measure the angular appearance of it, which suppose to be 36´, and in the table we have the required distance against 36´, which is 95½ feet. Thus also a man who appears to be 49´ high, is at the distance of 421 feet. Again, Suppose the trunk of a tree which is known to be 3 feet in diameter be observed to subtend an angle of 9´½. Take the number answering to 9´ out of the table, namely 382, and subtract from it a proportional part for the half minute, namely 19.1, which subtracted from 382, leaves 362.9. This multiplied by 3, the diameter of the tree, produces 1087.7 feet = the distance from the object end of the telescope.

In this way the distance of a considerably remote object, as a town or building at 10 or 12 miles distant, may be very nearly determined; provided we have the lineal dimensions of a house or other object that stands at right angles to the line of vision. The breadth of a river, of an arm of the sea, or the distance of a light house, whose elevation above the sea or any other point, is known, may likewise in this manner be easily determined.

CHAPTER II.

ON THE EQUATORIAL TELESCOPE, OR PORTABLE OBSERVATORY.

The equatorial instrument is intended to answer a number of useful purposes in Practical Astronomy, independently of any particular observatory. Besides answering the general purpose of a Quadrant, a Transit instrument, a Theodolite, and an Azimuth instrument—it is almost the only instrument adapted for viewing the stars and planets in the day-time, and for following them in their apparent diurnal motions. It may be made use of in any steady room or place, and performs most of the useful problems in astronomical science.

The basis of all equatorial instruments is a revolving axis, placed parallel to the axis of the earth, by which an attached telescope is made to follow a star or other celestial body in the arc of its diurnal revolution, without the trouble of repeated adjustments for changes of elevation, which quadrants and circles with vertical and horizontal axes require. Such an instrument is not only convenient for many useful and interesting purposes in celestial observations, but is essentially requisite in certain cases, particularly in examining and measuring the relative positions of two contiguous bodies, or in determining the diameters of the planets, when the spider’s-line micrometer is used.

Christopher Scheiner is supposed to have been the first astronomer who, in the year 1620, made use of a polar axis, but without any appendage of graduated circles. It was not, however, till the middle of the last century, that any instruments of this description, worthy of the name, were attempted to be constructed. In 1741, Mr. Henry Hindley, a clock-maker in York, added to the polar axis, an equatorial plate, a quadrant of altitude, and declination semicircle; but when this piece of mechanism was sent to London for sale in 1748, it remained unsold for the space of 13 years. Mr. Short, the optician, published in the Philosophical Transactions, for 1750, a ‘description of an equatorial telescope,’ which was of the reflecting kind, and was mounted over a combination of circles and semicircles, which were strong enough to support a tube, and a speculum of the Gregorian construction 18 inches in focal length. This instrument consisted of a somewhat cumbersome and expensive piece of machinery—a representation of which may be seen in volume III of Martin’s ‘Philosophia Britannica, or system of the Newtonian philosophy.’ Various modifications of this instrument have since been made by Nairne, Dollond, Ramsden, Troughton, and other artists; but even at the present period, it has never come into very general use, though it is one of the most pleasant and useful instruments connected with astronomical observations.

As many of these instruments are somewhat complicated, and very expensive, I shall direct the attention of the reader solely to one which I consider as the most simple—which may be purchased at a moderate expence, and is sufficiently accurate for general observations.

This instrument consists of the following parts: A horizontal circle EF (fig. 86.) divided into four quadrants of 90 degrees each. There is a fixed nonius at N; and the circle is capable of being turned round on an axis. In the centre of the horizontal circle is fixed a strong upright pillar, which supports the centre of a vertical semicircle AB, divided into two quadrants of 90 degrees each. This is called the semicircle of altitude, and may, at any time, serve the purpose of a quadrant in measuring either altitudes or depressions. It has a nonius plate at K. At right angles to the plane of this semicircle, the equatorial circle MN is firmly fixed. It represents the equator, and is divided into twice 12 hours, every hour being divided into 12 parts of 5 minutes each. Upon the equatorial circle moves another circle, with a chamfered edge, carrying a nonius by which the divisions on the equatorial may be read off to single minutes; and at right angles to this moveable circle is fixed the semicircle of declination D, divided into two quadrants of 90 degrees each. The telescope PO, is surmounted above this circle, and is fixed to an index moveable on the semicircle of declination, and carries a nonius opposite to Q. The telescope is furnished with 2 or 3 Huygenian eye-pieces, and likewise with a diagonal eye-piece for viewing objects near the zenith. Lastly, there are 2 spirit levels fixed on the horizontal circle, at right angles to each other, by means of which this circle is made perfectly level when observations are to be made.

To adjust the equatorial for observation. Set the instrument on a firm support. Then to adjust the levels and the horizontal circle:—Turn the horizontal circle till the beginning O of the divisions coincides with the middle stroke of the nonius, or near it. In this situation one of the levels will be found to lie either in a right line joining the 2 foot screws which are nearest the nonius, or else parallel to such a right line. By means of the 2 last screws, cause the bubble in the level to become stationary in the middle of the glass; then turn the horizontal circle half round, by bringing the other O to the nonius; and if the bubble remains in the middle, as before, the level is well-adjusted; if it does not, correct the position of the level, by turning one or both of the screws which pass through its ends, till the bubble has moved half the distance it ought to come to reach the middle, and cause it to move the other half by turning the foot-screws already mentioned. Return the horizontal circle to its first position, and if the adjustments have been well made, the bubble will remain in the middle: if otherwise, the process must be repeated till it bears this proof of its accuracy. Then turn the horizontal circle till 90° stands opposite to the nonius; and by the foot-screw,immediately opposite the other 90°, cause the bubble of the same level to stand in the middle of the glass. Lastly, by its own proper screws set the other level so that its bubble may occupy the middle of its glass.

To adjust the line of sight. Set the nonius on the declination semicircle at O, the nonius on the horary circle at VI, and the nonius on the semicircle of altitude at 90. Look through the telescope towards some part of the horizon, where there is a diversity of remote objects. Level the horizontal circle, and then observe what object appears in the centre of the cross-wires, or in the centre of the field of view, if there be no wires. Reverse the semicircle of altitude, so that the other 90° may apply to the nonius; taking care, at the same time, that the other three noniuses continue at the same parts of their respective graduations as before. If the remote object continues to be seen on the centre of the cross-wires, the line of sight is truly adjusted.

To find the correction to be applied to observations by the semicircle of altitude. Set the nonius on the declination-semicircle to 0, and the nonius on the horary circle to XII; direct the telescope to any fixed and distant object, by moving the horizontal circle and semicircle of altitude, and nothing else; note the degree and minute of altitude or depression; reverse the declination-semicircle, by directing the nonius on the horary circle to the opposite XII; direct the telescope again to the same object, by means of the horizontal circle and semicircle of altitude, as before. If its altitude or depression be the same as was observed in the other position, no correction will be required; but, if otherwise, half the difference of the two angles is the correction to be added to all observations made with that quadrant, or half of the semicircle which shows the least angle, or to be subtracted from all the observations made with the other quadrant, or half of the semicircle. When the levels and other adjustments are once truly made, they will be preserved in order for a length of time, if not deranged by violence; and the correction to be applied to the semicircle of altitude is a constant quantity.

Description of the nonius. The nonius—sometimes called the vernier—is a name given to a device for subdividing the arcs of quadrants and other astronomical instruments. It depends on the simple circumstance, that if any line be divided into equal parts, the length of each part will be greater, the fewer the divisions; and contrariwise, it will be less in proportion as those divisions are more numerous. Thus, in the equatorial now described, the distance between the two extreme strokes on the nonius is exactly equal to 11 degrees on the limb, but that it is divided into 12 equal parts. Each of these last parts will therefore be shorter than the degree on the limb in the proportion of 11 to 12, that is to say, it will be ¹/₁₂th part, or 5 minutes shorter. Consequently, if the middle stroke be set precisely opposite to any degree, the relative positions of the nonius and the limb must be altered 5 minutes of a degree, before either of the two adjacent strokes next the middle on the nonius, can be brought to coincide with the nearest stroke of a degree; and so likewise the second stroke on the nonius will require a change of 10 minutes, the third of 15, and so on to 30, when the middle line of the nonius will be seen to be equi-distant between 2 of the strokes on the limb; after which the lines on the opposite side of the nonius will coincide in succession with the strokes on the limb. It is clear from this, that whenever the middle stroke of the nonius does not stand precisely opposite to any degree, the odd minutes—or distance between it and the degree immediately preceding—may be known by the number of the stroke marked on the nonius, which coincides with any of the strokes on the limb.38 In some instruments the nonius-plate has its divisions fewer than the number of parts on the limb to which it is equal; but when once a clear idea of the principle of any nonius is obtained, it will be easy to transfer it to any other mode in which this instrument is contrived.

To find by this equatorial the MERIDIAN LINE, and the time, FROM ONE OBSERVATION OF THE SUN. In order to this it is requisite that the sun’s declination, and the latitude of the place be known. The declination of the sun may be found, for every day, in the Nautical Almanack, or any other astronomical Ephemeris; and the latitude of the place may be found by means of the semicircle of altitude, when the telescope is directed to the sun or a known fixed star. It is likewise requisite to make the observation when the azimuth and altitude of the sun alter quickly; and this is generally the case, the farther that luminary is from the meridian:—Therefore, at the distance of 3 or 4 hours, either before or after noon, (in summer) adjust the horizontal circle; set the semicircle of altitude, so that its nonius may stand at the co-latitude of the place; lay the plane of the last-mentioned semicircle in the meridian, by estimation, its 0 being directed towards the depressed pole; place the nonius of the declination semicircle to the declination, whether north or south. Then direct the telescope towards the sun, partly by moving the declination semicircle on the axis of the equatorial circle, and partly by moving the horizontal circle on its own axis. There is but one position of these which will admit of the sun being seen exactly in the middle of the field of view. When this position is obtained, the nonius on the equatorial circle shows the apparent time, and the circle of altitude is in the plane of the meridian. When this position is ascertained, the meridian may be settled by a land-mark at a distance.

With an equatorial instrument, nearly similar to that now described, I formerly made a series of ‘day observations on the celestial bodies,’ which were originally published in vol. 36 of ‘Nicholson’s Journal of Natural Philosophy,’ and which occupy twenty pages of that journal. Some of these observations I shall lay before the reader, after having explained the manner in which they are made.

The instrument was made by Messrs. W. and S. Jones, opticians, Holborn, London. The telescope which originally accompanied the instrument was an achromatic refractor, its object-glass being 8½ inches focal distance, and one inch diameter. This telescope, not admitting sufficiently high magnifying powers for the observations intended, was afterwards thrown aside for another telescope, having an object-glass 20 inches focal length, and 1¾ inch diameter, which was attached to the equatorial machinery in place of the small telescope. It was furnished with magnifying powers of 15, 30, 45, 60, and 100 times. The instrument was placed on a firm pedestal about three feet high. The feet of this pedestal had short iron pikes, which slipped into corresponding holes in the floor of the apartment adjacent to a south window, so that when the direction of the meridian was found, and the circles properly adjusted, the instrument was in no danger of being shifted from this position. Though this instrument generally stood fronting the southern part of the heavens, yet the equatorial part, along with the telescope, could occasionally be removed to another position fronting the north and north-west, for observing the stars in those quarters.

Manner of observing stars and planets in the day-time by the equatorial. Before such observations can be made, the semicircle of altitude must be placed in the meridian, and the degree and minute pointed out by the nonius on the horizontal circle, when in this position, noted down in a book, so that it may be placed again in the same position, should any derangement afterwards happen. The semicircle of altitude must be set to the co-latitude of the place; that is, to what the latitude wants of 90°. Suppose the latitude of the place of observation be 52° 30´ north, this latitude subtracted from 90°, leaves 37° 30´ for the co-latitude; and therefore, the semicircle of altitude—on which the equatorial circle is fixed—must be elevated to 37° 30´, and then the equatorial circle on the instrument coincides with the equator in the heavens. Lastly, the telescope must be adjusted on the declination semicircle, so as exactly to correspond with the declination of the heavenly body to be viewed. If the body is in the equator, the telescope is set by the index at 0 on the semicircle of declination, or at the middle point between the two quadrants, and then when the telescope, along with the semicircle of declination, is moved from right to left, or the contrary, it describes an arc of the equator. If the declination of the body be north, the telescope is elevated to the northern division of the semicircle; if south, to the southern part of it.

These adjustments being made, take the difference between the Right Ascension of the sun and the body to be observed; and if the Right Ascension of the body be greater than that of the sun, subtract the difference from the time of observation; if not, add to the time of observation.39 The remainder in one case, or the sum in the other, will be the hour and minute to which the nonius on the equatorial circle is to be set; which being done, the telescope will point to the star or planet to whose declination the instrument is adjusted. When the heavenly body is thus found, it may be followed, in its diurnal course, for hours, or as long as it remains above the horizon. For as the diurnal motion of a star is parallel to the equator, the motion of the telescope on the equatorial circle, will always be in the star’s diurnal arc; and should it have left the field of the telescope for any considerable time, it may be again recovered, by moving the telescope onward according to the time which elapsed since it was visible in the field of view. We may illustrate what has been now stated by an example or two. Suppose on the 30th April, 1841, at 1 o’clock, P.M. we wished to see the star Aldebaran. The Right Ascension of this star is 4^h 27^m; and the sun’s Right Ascension for that day at noon, as found in ‘White’s Ephemeris,’ or the ‘Nautical Almanack,’ is 2^h 30^m. Subtract this last number from 4^h 27^m, and the remainder 1^h 57^m, shows that the star comes to the meridian on that day at 57 minutes past 1 o’clock, P.M. And as the time of observation is 1 P.M., the nonius which moves on the equatorial circle must be set to 3 minutes past XI, as the star is at that hour 57 minutes from the meridian. The declination of Aldebaran is 16° 11´ north, to which point on the semicircle of declination, the telescope must be adjusted, and then the star will be visible in the field of view. Again, suppose we wished to observe the planet Venus on the 1st January, 1842, at 12 o’clock noon. The sun’s Right Ascension on that day is 18^h 46^m, and that of Venus 17^h 41^m, from which the sun’s Right Ascension being subtracted, the remainder is 22^h 55^m, or 55 minutes past 10, A.M. Here, as the Right Ascension of Venus is too small to have the sun’s Right Ascension taken from it, we borrow 24 hours, and reckon the remainder from XII at noon. As the planet at 12 noon, is 1 hour 5 minutes past the meridian, the nonius on the equatorial circle must be set to that point, and the telescope adjusted to 23° 6´ of south declination, which is the declination of Venus for that day, when this planet will appear in the field of view.

Observations on the fixed stars and planets, made in the day-time by the Equatorial.

For the purpose of illustrating the descriptions now given, and for affording some information respecting celestial day observations, I shall select a few of the observations above alluded to, which I formerly published in Nicholson’s Journal, along with a few others which have been since made. These observations were made with a view to determine the following particulars:—1. What stars and planets may be conveniently seen in the day-time, when the sun is above the horizon? 2. What degrees of magnifying power are requisite for distinguishing them? 3. How near their conjunction with the sun they may be seen? and 4. Whether the diminution of the aperture of the object-glass of the telescope, or the increase of magnifying power, conduces most to render a star or a planet visible in day-light. Having never seen such observations recorded in books of astronomy or in scientific journals, I was induced to continue them, almost every clear day for nearly a year, in order to determine the points now specified. Some of the results are stated in the following pages.

Observations on fixed stars of the first magnitude. April 23, 1813, at 10^h 15^m, A.M., the sun being 5½ hours above the horizon. Saw the star Vega, or a LyrÆ, very distinctly with a power of 30 times. Having contracted the aperture of the object-glass to ⁹/₁₀ of an inch, saw it on a darker ground, but not more plainly than before. Having contracted the aperture still farther, to half an inch, I perceived the star, but not so distinctly as before. The sky being very clear, and the star in a quarter of the heavens nearly opposite to the sun, I diminished the magnifying power to 15, and could still perceive the star, but indistinctly; it was just perceptible. August 23, at 0^h 12^m, P.M., saw the star Capella, or a AurigÆ, with a power of 60, and immediately afterwards with a power of 30; the aperture undiminished. With this last power it appeared extremely distinct, but not so brilliant and splendid as with the former power. Having diminished the aperture to ⁹/₁₀ of an inch, it appeared on a darker ground, though in the former case, it was equally perceptible. A few minutes afterwards, could distinguish it with a power of 15, the aperture being contracted to half an inch. It appeared very small; it was with difficulty the eye could fix upon it in the field of the telescope; but when it was once perceived, its motion across the field of view could be readily followed. It could not be perceived, when the diminished aperture was removed. The sun was then shining in meridian splendour.

August 10th, 9^h 30^m, A.M. Saw the star Sirius with a power of 60, the aperture contracted to ⁹/₁₀ inch. Saw it likewise when the aperture was diminished to half an inch, but not so distinctly as through the aperture of inch. Having put on a power of 30, could distinguish it distinctly enough through each of the former apertures, and likewise when they were removed; but somewhat more distinctly with the apertures of nine-tenths and half an inch than without them. At this time the star was 2^h 42^m in time of Right Ascension west of the sun, having an elevation above the horizon of about 17° 10’; the sun shining bright, and the sky very much enlightened in that quarter of the heavens where the star appeared. There was also a considerable undulation of the air, which is generally the case in the hot mornings of summer—which renders a star more difficult to be perceived than in the afternoon, especially when it is viewed at a low altitude. June 4th, 1^h 30^m, P.M., saw Sirius with a power of 30 with great distinctness, the aperture not contracted. The star was then within 1^h 50^m, in time of Right Ascension east from the sun. August 24th, 9^h 5^m, A.M., saw the star Procyon, or a Canis-Minoris distinctly with a power of 60, the aperture not contracted. When diminished to ⁹/₁₀ inch, it appeared rather more distinct, as the ground on which it was seen was darker. With a power of 30, and the aperture contracted to ⁹/₁₀ inch, could perceive it, but somewhat indistinctly. When the equatorial motion was performed, in order to keep it in the field of view, it was sometime before the eye could again fix upon it. When the aperture was diminished to half an inch, it could not be perceived. Saw it when both the apertures were removed, but rather more distinctly with the aperture of ⁹/₁₀ inch. The difference in the result of this observation, from that of Capella, above stated, was owing to the star’s proximity to the sun, and the consequent illumination of the sky in that quarter where it appeared. Its difference in Right Ascension from that of the sun was then about 2^h 5^m of time, and its difference of declination about 4° 50´.40 This star may be considered as one of those which rank between the first and second magnitudes.

Similar observations to the above were made and frequently repeated on the stars Rigel, Aldebaran, Betelguese Cor-Leonis and other stars of the first magnitude, which gave nearly the same results. The stars Altares and Fomalhaut are not so easily distinguished, on account of their great southern declination, and consequent low elevation above the horizon. The following observation on Arcturus may be added. June 3rd, observed Arcturus very distinctly, a little before 7 in the evening, the sun being about 1^h 40^m above the horizon, and shining bright—with a power of 15; the aperture not contracted. It appeared very small but distinct. This star is easily distinguishable at any time of the day with a power of 30.

Observations on stars of the second magnitude. May 5, 1813, at 6^h, P.M.; the sun being an hour and three quarters above the horizon. Saw Alphard, or a HydrÆ, a star of the second magnitude, with a power of 60; the aperture diminished to ⁹/₁₀ inch. A few minutes afterwards could perceive it, but indistinctly, with a power of 30, the aperture contracted as above. It could not be seen very distinctly with this power, till about half an hour before sun-set. It was then seen rather more distinctly when the aperture was contracted than without the contraction. May 7th. Saw the star Deneb, or Leonis, distinctly with a power of 60, about an hour and a half before sun-set. August 20th. Saw Ras Alkague, or a Ophiuchi, at 4^h 40^m, P.M., with a power of 100, the sun being nearly 3 hours above the horizon, and shining bright. Perceived it about an hour afterwards, with a power of 60—with the aperture contracted to ⁹/₁₀ inch, and also when this contraction was removed. The star was seen nearly as distinctly in the last case as in the first. August 27, 5^h, P.M., the same star appeared quite distinct with a power of 60, the aperture not contracted. It did not appear more distinct when the aperture was contracted to ⁹/₁₀ inch. The sun was then more than 2 hours above the horizon. August 28th. Saw the star Pollux, or Gemini, 2 hours after sun-rise with a power of 60, aperture undiminished. November 12th, 1_h 30´, P.M. Saw the star Altair, or a AquilÆ, with an 8½ inch telescope, 1 inch aperture, carrying a power of 45, the aperture not contracted. Having contracted the aperture a little, it appeared somewhat less distinct. This star is reckoned by some to belong to the class of stars of the first magnitude; but in White’s ‘Ephemeris’ and other Almanacks, it is generally marked as being of the second magnitude. It forms a kind of medium between stars of the 1st and of the 2nd magnitude.

Similar observations, giving the same results, were made on the stars Bellatrix, Orion’s Girdle, a AndromedÆ, a Pegasi, Alioth, Benetnasch, North Crown, or a CoronÆ Borealis, and various other stars of the same magnitude.

From the above and several hundreds of similar observations, the following conclusions are deduced.

1. That a magnifying power of 30 times is sufficient for distinguishing a fixed star of the first magnitude, even at noon-day, at any season of the year; provided it have a moderate degree of elevation above the horizon, and be not within 30° or 40° of the sun’s body. Also, that, by a magnifying power of 15, a star of this class may be distinguished, when the sun is not above an hour and a half above the horizon. But, in every case, higher powers are to be preferred. Powers of 45 or 60, particularly the last, were found to answer best in most cases, as with such powers the eye could fix on the star with ease, as soon as it entered the field of the telescope.

2. That most of the stars of the 2nd magnitude may be seen with a power of 60, when the sun is not much more than 2 hours above the horizon; and, at any time of the day, the brightest stars of this class may be seen with a power of 100, when the sky is serene, and the star not too near the quarter in which the sun appears.

3. That, in every instance, an increase of magnifying power has the principal effect in rendering a star easily perceptible. That diminution of aperture, in most cases, produces a very slight effect; in some cases, none at all; and, when the aperture is contracted beyond a certain limit, it produces a hurtful effect. The cases in which a moderate contraction is useful, are the two following:—1. When the star appears in a bright part of the sky, not far from that quarter in which the sun appears. 2. When an object-glass of a large aperture, and a small degree of magnifying power, is used. In almost every instance the contraction of the object-glass of the 8½-inch telescope with a power of 45, had a hurtful effect. But when the 20-inch telescope carried a power of only 15, the contraction served to render the object more perceptible.

Observations on the Planets made in the day-time.

Some of the planets are not so easily distinguished in the day-time as the fixed stars of the first magnitude. The one which is most easily distinguished at all times, is the planet Venus.

1. Observations on Venus. My observations on this planet commenced about the end of August, 1812, about three or four weeks after its inferior conjunction. About that period, between ten and eleven in the forenoon, with a power of 45, it appeared as a beautiful crescent, quite distinct and well-defined, with a lustre similar to that of the moon about sun-set, but of a whiter colour. The view of its surface and phase was fully more distinct and satisfactory than what is obtained in the evening after sun-set; for, being at a high elevation, the undulation near the horizon did not affect the distinctness of vision. The planet was then very distinctly seen with a power of 7 times, when it appeared like a star of the first or second magnitude. I traced the variation of its phases, almost every clear day, till the month of May, 1813. As at that time, it was not far from its superior conjunction with the sun, I wished to ascertain how near its conjunction with that luminary it might be seen; and particularly whether it might not be possible, in certain cases, to see it at the moment of its conjunction.

The expressions of all astronomical writers previous to this period, when describing the phases of Venus, either directly assert, or, at least imply, that it is impossible to see that planet, in any instance, at the time of its superior conjunction. This is the language of Dr. Long, Dr. Gregory, Dr. Brewster, Ferguson, Adams, B. Martin, and most other writers on the science of astronomy. How far such language is correct will appear from the following observations and remarks.

April 24, 1813, 10^h 50´ A.M. Observed Venus with a power of 30, the aperture not contracted. She was then about 31 minutes, in time, of right ascension, distant from the sun. Their difference of declination 3° 59´. She appeared distinct and well-defined. With a power of 100, could distinguish her gibbous phase. May 1st, 10^h 20^m, A.M. Viewed this planet with a power of 60; the aperture not contracted. It appeared distinct. Saw it about the same time with a power of 15, the aperture being contracted to ⁹/₁₀ inch. Having contracted the aperture to ½ inch, saw it more distinctly. When the contracted apertures were removed, the planet could with difficulty be distinguished, on account of the direct rays of the sun striking on the inside of the tube of the telescope. The sun was shining bright, and the planet about 25´ of time in R.A. west of his centre, their difference of declination being 3° 7´. May 7th, 10^h, A.M. Saw Venus distinctly with a power of 60, the sun shining bright. It was then about 19´ in time of R.A. and 4° 27´ in longitude west of the sun; their difference of declination being 2° 18´. I found a diminution of aperture particularly useful when viewing the planet at this time, even when the higher powers were applied. This was the last observation I had an opportunity of making prior to the conjunction of Venus with the sun, which happened on May 25th, at 9^h 30^m, A.M. Its geocentric latitude at that time being about 16´ south, the planet must have passed almost close by the sun’s southern limb. Cloudy weather for nearly a month after the last observation, prevented any further views of the planet, when it was in that part of the heavens which was within the range of the instrument. The first day that proved favourable after it had passed the superior conjunction, was June 5th. The following is the memorandum of the observation then taken.

June 5th, 9^h, A.M. Adjusted the Equatorial Telescope for viewing the planet Venus, but it could not be perceived, on account of the direct rays of the sun entering the tube of the telescope. I contrived an apparatus for screening his rays, but could not get it conveniently to move along with the telescope; and therefore determined to wait till past eleven, when the top of the window of the place of observation would intercept the solar rays. At 11^h 20^m, A.M., just as the sun had passed the line of sight from the eye to the top of the window, and his body was eclipsed by it, I was gratified with a tolerably distinct view of the planet, with a power of 60. The aperture being contracted to ⁹/₁₀ inch. The distinctness increased as the sun retired, till, in two or three minutes, the planet appeared perfectly well-defined. Saw it immediately afterwards, with a power of 30, the aperture contracted as before. Saw it also quite distinctly with a power of 15; but it could not be distinguished with this power, when the contracted aperture was removed. At this time Venus was just 3° in longitude, or about 13´ in time of R.A. east of the sun’s centre, and of course only about 2¾ degrees from his eastern limb; the difference of their declination being 27´, and the planet’s latitude 11´ north.

Several years afterwards, I obtained views of this planet, when considerably nearer the sun’s margin than as stated in the above observation, particularly on the 16th October, 1819, when Venus was seen when only 6 days and 19 hours past the time of the superior conjunction. At that time its distance from the sun’s eastern limb was only 1° 28´ 42´´. A subsequent observation proved that Venus can be seen when only 1° 27´, from the sun’s margin—which I consider as approximating to the nearest distance from the sun at which this planet is distinctly visible.—I shall only state farther the two or three following observations.

June 7th, 1813, 10^h, A.M. Saw Venus with a power of 60, the aperture being contracted to ⁹/₁₀ inch—the direct rays of the sun not being intercepted by the top of the window. The aperture having being further contracted to ½ inch, could perceive her, but not quite so distinctly. When the contractions were removed, she could scarcely be seen. She was then 3° 33´ in longitude, and nearly 15 minutes in time of R.A. distant from the sun’s centre. Some fleeces of clouds having moved across the field of view, she was seen remarkably distinct in the interstices—the sun at the same time, being partly obscured by them.—August 19th, 1^h 10´, P.M. Viewed Venus with a magnifying power of 100. Could perceive her surface and gibbous phase almost as distinctly as when the sun is below the horizon. She appeared bright, steady in her light, and well defined, without that glare and tremulous appearance she exhibits in the evening when near the horizon. She was then nearly on the meridian. On the whole, such a view of this planet is as satisfactory, if not preferable, to those views we obtain with an ordinary telescope in the evening, when it is visible to the naked eye.

All the particulars above stated have been confirmed by many subsequent observations continued throughout a series of years. I shall state only two recent observations which show that Venus may be seen somewhat nearer the sun than what is deduced from the preceding observations, and at the point of its superior conjunction. March 10th, 1842, observed the planet Venus, then very near the sun, at 19 minutes past 11, A.M. It had passed the point of its superior conjunction with the sun, on the 5th March, at 1^h 19^m, P.M. The difference of right ascension between the sun and the planet was then about 6½ minutes of time, or about 1° 37½´, and it was only about 1° 21´ distant from the sun’s eastern limb. It appeared quite distinct and well-defined, and might perhaps have been seen on the preceding day, had the observation been then made.—The following observation shows that Venus may be seen still nearer the sun than in the preceding observations, and even at the moment of its superior conjunction. On the 2nd of October, 1843, this planet passed the point of its superior conjunction with the sun, at 4^h 15^m, P.M. At two o’clock, P.M.—only two hours before the conjunction, I perceived the planet distinctly, and kept it in view for nearly ten minutes, till some dense clouds intercepted the view. It appeared tolerably distinct and well-defined, though not brilliant, and with a round full face, and its apparent path was distinctly traced several times across the field of view of the telescope. I perceived it afterwards, about half past four, P.M., only a few minutes after it had passed the point of conjunction, on which occasion it appeared less distinct than in the preceding observation, owing to the low altitude of the planet, being then only a few degrees above the horizon. The observations, in this instance, were made not with an equatorial instrument, which I generally use in such observations, but with a good achromatic telescope 44½ inches focal distance, mounted on a common tripod, with a terrestrial power of 95 times. A conical tube about ten inches long was fixed on the object-end of the telescope, at the extremity of which an aperture, 1½ inch diameter was placed, so as to intercept, as much as possible, the direct ingress of the solar rays. The top of the upper sash of the window of the place of observation was likewise so adjusted as to intercept the greater part of the sun’s rays from entering the tube of the telescope. The sun’s declination at that time was 3° 26´ south, and that of Venus 2° 12´ south; consequently, the difference of declination was 1° 14´ = the distance of Venus from the sun’s centre; and as the sun’s diameter was about 16´, Venus was then only 58´ from the sun’s northern limb, or 6´ less than two diameters of the sun.

This is the nearest approximation to the sun at which I have ever beheld this planet, and it demonstrates that Venus may be seen even when within a degree of the sun’s margin; and it is perhaps the nearest position to that luminary in which this planet can be distinctly perceived. It shows that the light reflected from the surface of Venus is far more brilliant than that reflected from the surface of our moon; for no trace of this nocturnal luminary can be perceived, even when at a much greater distance from the sun, nor is there any other celestial body that can be seen within the limit now stated. This is the first observation, so far as my information extends, of Venus having been seen at the time of her superior conjunction.41

The practical conclusion from this observation is, that, at the superior conjunction of this planet, when its distance from the sun’s margin is not less than 58´, its polar and equatorial diameter may be measured by a micrometer, when it will be determined whether or not Venus be of a spheroidal figure. The Earth, Mars, Jupiter and Saturn are found to be not spheres but spheroids, having their polar shorter than their equatorial diameters. But the true figure of Venus has never yet been ascertained, because it is only at the superior conjunction that she presents a full enlightened hemisphere, and when both diameters can be measured, except at the time when she transits the sun’s disk, which happens only twice in the course of 120 years.42

The following conclusions are deduced from the observations made on Venus.

1. That this planet may be seen distinctly, with a moderate degree of magnifying power, at the moment of its superior conjunction with the sun, when its geocentric latitude, either north or south, at the time of conjunction, is not less than 1° 14´, or, when the planet is about 58´ from the sun’s limb. This conclusion is deduced from the observation of Oct. 2, 1843,45 stated above.

2. Another conclusion is—that during the space of 583 days, or about 19 months—the time this planet takes in moving from one conjunction with the sun to a like conjunction again—when its latitude at the time of its superior conjunction exceeds 1° 14´, it may be seen with an equatorial telescope every clear day without interruption, except about the period of its inferior conjunction, when its dark hemisphere is turned towards the earth, and a short time before and after it. When its geocentric latitude is less than 1° 14´, it will be hid only about four days before, and the same time after its superior conjunction. During the same period it will be invisible to the naked eye, and consequently no observations can be made upon it with a common telescope, for nearly six months, and sometimes more, according as its declination is north or south, namely about two or three months before, and the same time after its superior conjunction, except where there is a very free and unconfined horizon. In regard to the time in which this planet can be hid about the period of its inferior conjunction, I have ascertained from observation, that it can never be hid longer than during a space of 2 days 22 hours; having seen Venus, about noon, like a fine slender crescent, only 35 hours after she had passed the point of her inferior conjunction; and in a late instance she was seen when little more than a day from the period of conjunction. The longest time, therefore, that this planet can be hid from view during a period of 583 days, is only about 10 days; and when its latitude at the time of the superior conjunction, equals or exceeds 1° 14´, it can be hid little more than two days. This is a circumstance which cannot be affirmed of any other celestial body, the sun only excepted.

3. That every variation of the phases of this planet—from a slender crescent to a full enlightened hemisphere—may, on every clear day, be conveniently exhibited by means of the equatorial telescope. This circumstance renders this instrument peculiarly useful in the instruction of the young in the principles of astronomy. For, if the phase which Venus should exhibit at any particular time be known, the equatorial telescope may be directed to the planet, and its actual phase in the heavens be immediately exhibited to the astronomical pupil.

4. Since it is only at the period of the superior conjunction that this planet presents a full enlightened hemisphere, and since it is only when this phase is presented that both its diameters can be measured—it is of some importance that observations be made on it at the moment of conjunction, by means of powerful telescopes furnished with micrometers, so as to determine the difference (if any) between its polar and equatorial diameters.

5. Another conclusion from the observations on Venus, is, that a moderate diminution of the aperture of the object-glass of the telescope is useful, and even necessary in viewing this planet when near the sun. Its effect is owing in part to the direct solar rays being thereby more effectually excluded; for when these rays enter directly into the tube of the telescope, it is very difficult, and almost impossible to perceive this planet, or any other celestial body when in the vicinity of the sun.

Observations on Jupiter and other planets.

This planet is very easily distinguished in the day-time with a very moderate magnifying power, when it is not within 30° or 35° of the sun. The following extract from my memorandums may serve as a specimen. May 12, 1813, 1^h 40^m, P.M. Saw Jupiter with a power of 15 times, the aperture not contracted. The planet appeared so distinct with this power, that I have reason to believe, it would have been perceived with a power of 6 or 7 times. When the aperture was contracted ⁹/₁₀ inch, and afterwards to half an inch, there was little perceptible difference in its appearance. It was then about 58° in longitude, east of the sun.

Though Jupiter when at a considerable distance from the sun, and near his opposition, appears to the naked eye with a brilliancy nearly equal to that of Venus, yet there is a very striking difference between them, in respect of lustre, when viewed in day-light. Jupiter, when viewed with a high magnifying power, in the day-time, always exhibits a very dull cloudy appearance; whereas Venus appears with a moderate degree of splendour. About the end of June 1813, between 5 and 6 in the evening, having viewed the planet Venus, then within 20° of the sun, and which appeared with a moderate degree of lustre, I directed the telescope to Jupiter, at that time more than 32° from the sun, when the contrast between the two planets was very striking, Jupiter appearing so faint as to be just discernible, though his apparent magnitude was nearly double that of Venus. In this observation a power of 65 was used. In his approach towards the sun, about the end of July, I could not perceive him when he was within 16° or 17° of his conjunction with that luminary.—These circumstances furnish a sensible and popular proof, independently of astronomical calculations, that the planet Jupiter is placed at a much greater distance from the sun than Venus; since its light is so faint as to be scarcely perceptible when more than 20 degrees from the sun, while that of Venus is distinctly seen amidst the full splendour of the solar rays, when only about a degree from the margin of that luminary. With a power of 65 I have been enabled to distinguish the belts of Jupiter before sun-set, but could never perceive any of his satellites till the sun was below the horizon. There are no observations which so sensibly and strikingly indicate the different degrees of light emitted by the different planets as those which are made in the day-time. To a common observer, during night, Jupiter and Venus appear, in a clear sky, nearly with equal brilliancy, and even Mars, when about the point of his opposition to the sun, appears with a lustre somewhat similar, though tinged with a ruddy hue; but when seen in day-light their aspect is very dissimilar. This circumstance evidently indicates, 1. that these planets are placed at different distances from the sun, and consequently are furnished with different degrees of light proportional to the square of their distances from that luminary;—and 2. that there are certain circumstances connected with the surfaces and atmospheres of the planetary bodies, which render the light they emit more or less intense, independently of their different distances from the central luminary. For Mars, though much nearer to the sun than Jupiter, is not so easily distinguished in the day-time, and, even in the night-time, appears with a less degree of lustre.

My observations on Saturn in day-light, have not been so frequent as those on Jupiter. I have been enabled to distinguish his ring several times before sun-set, with a power of 65; but his great southern declination, and consequent low altitude, at the periods when these observations were made, were unfavourable for determining the degree of his visibility in day-light; for a planet or a star is always more distinctly perceptible in a high than in a low altitude, on account of the superior purity of the atmosphere through which a celestial object is seen when at a high elevation above the horizon. This planet, however, is not nearly so distinctly visible in day-light as Jupiter, and I have chiefly seen it, when the sun was not more than an hour or two above the horizon, but never at noon-day; although it is probable that with powerful instruments it may be seen even at that period of the day. The planet Mars is seldom distinctly visible in the day-time, except when at no great distance from its opposition to the sun. The following is a memorandum of an observation on Mars, when in a favourable position. October 24, 1836. Saw the planet Mars distinctly with a power of about 60, at 40 minutes past 9 A.M., the sun having been above the horizon nearly three hours. It appeared tolerably distinct, but scarcely so brilliant as a fixed star of the first magnitude, but with apparently as much light as Jupiter generally exhibits when viewed in day-light. It could not be traced longer at the time, so as to ascertain if it could be seen at mid-day; on account of the interposition of the western side of the window of the place of observation. The ruddy aspect of this planet—doubtless caused by a dense atmosphere with which it is environed—is one of the causes which prevents its appearing with brilliancy in the day-time. With respect to the planet Mercury, I have had opportunities of observing it several times after sun-rise, and before sun-set, about 10 or 12 days before and after its greatest elongation from the sun, with a power of 45. I have several times searched for this planet about noon, but could not perceive it. The air, however, at the times alluded to, was not very clear, and I was not certain that it was within the field of the telescope; and therefore, I am not convinced but that, with a moderately high power, it may be seen even at noon-day.

Such are some specimens of the observations I have made on the heavenly bodies in the day-time, and the conclusions which may be deduced from them. I have been induced to communicate them, from the consideration, that the most minute facts, in relation to any science, are worthy of being known, and may possibly be useful. They may at least gratify the astronomical tyro with some information which he will not find in the common treatises on astronomy, and may perhaps excite him to prosecute a train of similar observations for confirming or correcting those which have been noted above.

Besides the deductions already stated, the following general conclusions may be noted.—1. That a celestial body may be as easily distinguished at noon-day, as at any time between the hours of nine in the morning and three in the afternoon, except during the short days in winter. 2. They are more easily distinguished at a high than at a low altitude—in the afternoon than in the morning, especially if their altitudes be low—and in the northern region of the heavens than in the southern. The difficulty of perceiving them at a low altitude is obviously owing to the thick vapours near the horizon. Their being less easily distinguished in the morning than in the afternoon is owing to the undulations of the atmosphere, which are generally greater in the morning than in the afternoon. This may be evidently perceived by looking at distant land-objects at those times, in a hot day, through a telescope which magnifies about 40 or 50 times, when they will be found to appear tremulous and distorted in consequence of these undulations, especially if the sun be shining bright. In consequence of this circumstance, we can seldom use a high terrestrial power with effect on land objects, except early in the morning, and a short time before sun-set. Their being more easily distinguished in the northern region of the heavens is owing to that part of the sky being of a deeper azure, on account of its being less enlightened than the southern with the splendour of the solar rays.

Utility of Celestial Day Observations.

The observations on the heavenly bodies in the day-time, to which I have now directed the attention of the reader, are not to be considered as merely gratifications of a rational curiosity, but may be rendered subservient to the promotion of astronomical science. As to the planet Venus—when I consider the degree of brilliancy it exhibits, even in day-light, I am convinced that useful observations might frequently be made on its surface in the day-time, to determine some of its physical peculiarities and phenomena. Such observations might set at rest any disputes which may still exist respecting the period of rotation of this planet. Cassini, from observations on a bright spot, which advanced 20° in 24^h 34^m determined the time of its rotation to be 23 hours, 20 minutes. On the other hand, Bianchini, from similar observations, concluded that its diurnal period was 24 days and 8 hours. The difficulty of deciding between these two opinions, arises from the short time in which observations can be made on this planet, either before sun-rise, or after sun-set, which prevents us from tracing, with accuracy, the progressive motion of its spots for a sufficient length of time. And, although an observer should mark the motion of the spots at the same hour, on two succeeding evenings, and find they had moved forward about 15° in 24 hours, he would still be at a loss to determine, whether they had moved only 15°, in all, since the preceding observation, or had finished a revolution and 15° more. If, therefore, any spots could be perceived on the surface of Venus in the day-time, their motion might be traced, when she is in north declination, for 12 hours or more, which would completely settle the period of rotation. That it is not improbable that spots, fitted for this purpose, may be discovered on her disk in the day-time, appears from some of the observations of Cassini, who saw one of her spots when the sun was more than eight degrees above the horizon.46 The most distinct and satisfactory views I have ever had of this planet were those which I obtained in the day-time, in summer, when it was viewed at a high altitude, with a 44½ inch achromatic telescope, carrying a power of 150. I have at such times distinctly perceived the distinction between the shade and colour of its margin, and the superior lustre of its central parts, and some spots have occasionally been seen, though not so distinctly marked as to determine its rotation. Such distinct views are seldom to be obtained in the evening after sun-set, on account of the undulations of the atmosphere, and the dense mass of vapours through which the celestial bodies are viewed when near the horizon.

Nor do I consider it altogether improbable that its satellite (if it have one, as some have supposed) may be detected in the day time, when this planet is in a favourable position for such an observation; particularly when a pretty large portion of its enlightened surface is turned towards the earth, and when its satellite, of course, must present a similar phase. About the period of its greatest elongation from the sun, and soon after it assumes a crescent phase, in its approach to the inferior conjunction, may be considered as the most eligible times for prosecuting such observations. If this supposed satellite be about one third or one fourth of the diameter of its Primary, as Cassini, Short, Baudouin, Montbarron, Montaigne, and other astronomers supposed, it must be nearly as large as Mercury, which has been frequently seen in day-light. If such a satellite have a real existence, and yet undistinguishable in day-light, its surface must be of a very different quality for reflecting the rays of light from that of its primary; for it is obvious to every one who has seen Venus with a high power, in the day-time, that a body of equal brilliancy—though four times less in diameter—would be quite perceptible, and exhibit a visible disk. Such observations, however, would be made, with a much greater effect in Italy and other Southern countries, and particularly in Tropical climates, such as the southern parts of Asia and America, and in the West India Islands, where the sky is more clear and serene, and where the planet may be viewed at higher altitudes, and for a greater length of time, without the interruption of clouds, than in our island.

Again, the apparent magnitudes of the fixed stars—the quantity of light they respectively emit—and the precise class of magnitude which should be assigned to them—might be more accurately determined by day observations, than by their appearance in the nocturnal sky. All the stars which are reckoned to belong to the first magnitude are not equally distinguishable in day-light. For example, the stars Aldebaran and Procyon are not so easily distinguished, nor do they appear with the same degree of lustre by day, as the stars a LyrÆ and Capella. In like manner the stars Altair, Alphard, Deneb Ras Alkague, considered as belonging to the second magnitude, are not equally distinguishable by the same aperture and magnifying power—which seems to indicate, that a different quantity of light is emitted by these stars, arising from a difference either in their magnitude, their distance, or the quality of the light with which they are irradiated.

The following are likewise practical purposes to which celestial day observations may be applied. In accurately adjusting Circular and Transit instruments, it is useful, and even necessary, for determining the exact position of the meridian, to take observations of certain stars, which differ greatly in zenith distance, and which transit the meridian nearly at the same time. But as the stars best situated for this purpose, cannot, at every season, be seen in the evenings, we must, in certain cases, wait for several months till such observations can be made, unless we make them in the day-time, which can very easily be done, if the instrument have a telescope adapted to it, furnished with such powers as those above stated, or higher powers if required. I have likewise made use of observations on the stars in the day time for adjusting a clock or watch to meantime, when the sun was in a situation beyond the range of the instrument, or obscured by clouds, and when I did not choose to wait till the evening. This may, at first view, appear to some as paradoxical; since the finding of a star in day-light depends on our knowing its right Ascension from the sun, and this last circumstance depends, in some measure, on our knowing the true time. But if a watch or clock is known not to have varied above seven or eight minutes from the time, a star of the first magnitude may easily be found, by moving the telescope a little backwards or forwards, till the star appear; and when it is once found, the exact variation of the movement is then ascertained, by comparing the calculations which were previously necessary, with the time pointed out by the nonius on the Equatorial circle—or, in other words, by ascertaining the difference between the time assumed, and the time indicated by the instrument, when the star appears in the centre of the field of view. All this may be accomplished in five or six minutes.

Besides the practical purposes now stated, the Equatorial telescope is perhaps the best instrument for instructing a learner in the various operations of practical astronomy, and particularly for enabling him to distinguish the names and positions of the principal stars. For, when the right Ascension and Declination of any star is known, from astronomical tables, the telescope may be immediately adjusted to point to it, which will infallibly prevent his mistaking one star for another. In this way, likewise, the precise position of the planet Mercury, Uranus, Vesta, Juno, Ceres, Pallas—a small comet, a nebula, a double star, or any other celestial body not easily distinguishable by the naked eye, may be readily pointed out, when its right Ascension and Declination are known to a near approximation.

In conclusion, I cannot but express my surprise, that the Equatorial telescope is so little known, even by many of the lovers of astronomical science. In several respectable academies in this part of Britain, and, if I am not misinformed, in most of our universities, this instrument is entirely unknown. This is the more unaccountable, as a small equatorial may be purchased for a moderate sum; and as there is no single instrument so well adapted for illustrating all the operations of Practical Astronomy. Where very great accuracy is not required, it may occasionally be made to serve the general purposes of a transit instrument for observing the passages of the sun and stars across the meridian. It may likewise be made to serve as a theodolite for surveying land and taking horizontal angles—as a Quadrant for taking angles of altitude—as a level—as an equal altitude instrument—an azimuth instrument for ascertaining the sun’s distance from the north or south points of the horizon—and as an accurate Universal Sun Dial, for finding the exact mean or true time, on any occasion when the sun is visible. The manner of applying it to these different purposes will be obvious to every one who is in the least acquainted with the nature and construction of this instrument.

The price of a small Equatorial instrument, such as that described p. 454, is about 16 guineas, exclusive of some of the eye-pieces, which were afterwards added for the purpose of making particular observations. Instruments of a larger size, and with more complicated machinery, sell from 50 to 100 guineas and upwards. Messrs. W. and S. Jones, Holborn, London, construct such instruments.

ON THE QUADRANT.

figure 87.