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Evidence for the apparent Rotation of the Heavens round the Earth.—The Equatoreal.—Refraction.—The Transit Instrument.—The Mural Circle.—Mode of Observing.

BEFORE entering upon the subject of my proposed course of Lectures,^[1] it may perhaps be desirable that I should state, in as brief terms as possible, the views which have induced me to deliver them to the members of this Institution. When it was intimated to me that the offer of the course would be desirable, and when I felt that my compliance would show my good will to the Museum, I could not help thinking in the first place, that I should be in some slight degree departing from the intentions and objects of the Institution, though in the next place, I was certainly inclined to the opinion that such departure would be more imaginary than real. I thought that lectures on Natural Philosophy would seem to be hardly proper in an Institution intended for Natural History; but still I was convinced that their subjects were so closely connected, that the habits of thought which they induced, and the mode of treating them, were so similar in many respects, that what applied to the ​one would in a great degree apply to the other. Indeed, I felt that most persons would be better prepared for the study of Natural History generally, by the study of Natural Philosophy in its various Branches, than if they were in ignorance of the latter, but there were other considerations connected with the desire I have entertained to deliver these Lectures, not so much allied to the subject of Astronomy as matters of private feeling. I have been personally long connected, not with the town of Ipswich precisely, but with the neighbourhood. I remember, with gratitude, that the first time I was shown an astronomical object of any great interest, it was exhibited to me by the founder of the mechanical and manufacturing Institution which has now risen to such great importance in the town of Ipswich. It was by the elder Mr. Ransome that I was first shown the planet Saturn, with a telescope manufactured by his own hands. And I may add, that the first Nautical Almanac I possessed, was received as a present from a gentleman then residing in Ipswich, who has now risen to great eminence in the Metropolis as an engineer. From these and other circumstances I was desirous, when the opportunity should occur, of offering to the members of the Museum, or to any other similar body in the town of Ipswich, a course of Lectures on Astronomy.

In offering them to the authorities of the Museum, I made but one remark—that I understood it would be perfectly agreeable to the members of the Institution, and that if such were the case, it would be also exceedingly agreeable to myself, that the regulations for the attendance upon the Lectures should be framed in such a way as to give facilities of introduction to persons concerned in the mechanical operations of ​the town. And here I must beg to say, that the alliance between astronomers and mechanics is much closer than it may seem to be at the first view of the matter. Astronomers have to rely very closely upon mechanics for every part of the apparatus connected with their operations. Possibly mechanics have derived something from their connection with astronomers; but at all events, I am certain the debt is on the other side. I may adduce, as a practical instance, that the last instrument erected at the Royal Observatory, Greenwich, and to which I attach great importance, was constructed by the mechanics of Ipswich; whilst I am at the present time in negotiation with one of the mechanical establishments in the town, for another instrument of considerable importance in astronomical observations. To this I may add, that the whole of Astronomy is geometrical in its character, and that a great part of it is mechanical. I mention these things to show that the alliance between astronomers and mechanics is very close indeed; and this being the fact, I shall endeavour to do for the mechanics the best in my power. What I offer on this occasion will be offered with hearty good will, and if the Lectures be not successful, I hope the failure will have arisen from no fault of my own.

Perhaps I may be allowed to make another remark. I should wish to invite especially the attention of those who are commonly called working-men, to the few Lectures I propose to deliver. The subjects upon which I have to treat are commonly regarded as rather beyond their reach; I take this opportunity of saying that the subjects of the Lectures will not be beyond any working-man's comprehension. Everybody who has examined the history of persons ​concerned in the various branches of science, has been enabled to learn that, whereas on the one hand those who are commonly called philosophers may be as narrow-minded as any other class, and as little informed; so on the other hand, those who have to gain their daily livelihood by handicraft, may associate their trades or businesses, whatever they may be, with accomplishments of the most perfect and the most elevated kind. I think, then, it is right I should repeat, that these Lectures will be directed in some measure with the object of being perfectly comprehended, by that class of people. It is not my object, however, to deal with what may be called the picturesque in Astronomy. I have proposed it to myself as a special object, to show what may be comprehended, by persons possessing common understandings and ordinary education, in the more elevated operations of astronomical science. The Lectures will be, therefore, of what I may call a mathematical kind. But in speaking of this, I beg that the ladies present will not be startled. I do not mean to use algebra or any other science, such as must be commonly of an unintelligible character to a mixed meeting. When I used the word mathematical, I mean that it will be my object, to show how the measure of great things may be referred to the measure of smaller things; or to sum up in few words, it will be my object in an intelligible way, to show the great leading steps of the process by which the distance of the sun and the stars is ascertained by a yard measure—the process by which the weight of the sun and the planets is measured by the pound weight avoirdupois. Occasionally I shall be prepared to go into details; but my principal business will be to show the great steps upon which those who wish to ​study Astronomy may enter, and by which they may attain a general comprehension of the rules which will lead them from one step to another.

I shall now proceed with my subject.

We will consider what are the general phenomena of the motion of the stars which are to be observed on any fine night. I must observe in the first place, that I shall use the term east to denote the whole of the horizon extending from the north point, through the east point, to the south point; the term west to denote the whole of the horizon extending from the south point, through the west point, to the north. Now, if we look out on any fine night, the first general fact that we observe is this—by watching that eastern horizon from time to time, through the whole extent from north to south, we see stars are rising; and by watching that western horizon from time to time, through the whole extent from north to south, we see that stars are setting. By looking out at different times in the course of an evening, you will see these things as I have pointed out. The next general fact which you will observe is this—that the stars do not rise perpendicularly. They rise obliquely; and those which rise near to the south or near to the north rise very slantingly indeed. Those nearest to the east rise at a certain slope, which is different for every different place upon the earth. Those which set near to the north or near to the south set very slopingly; those which set nearest to the west set with a sharp incline. This is the case so far as regards merely the rising and setting of the stars. But if you trace the whole path of any one of these stars, it describes such a course as the following. It rises somewhere in the east, in the sloping direction I have described; it continues to rise with a ​path, becoming more and more horizontal, till it reaches a certain height in the south, where its course is exactly horizontal; and then it declines by similar degrees, and sets at a place in the west, just as far from the north point as the place where it rose in the east, If you select a star that has risen near to the north, it takes a long time in rising to its greatest height, it rises to a higher place in the south, and sets by the same degrees. Lastly, if you look to the north, and give your attention to those stars which are fairly above the horizon, you find the stars going round and describing a complete circle: these stars are called circumpolar.

Here I would remind my auditors that it is necessary, in order to understand a Lecture upon Astronomy, that they should have a little previous knowledge of the science that they should know the names and situations of some of the more conspicuous stars, otherwise it will be impossible for them to proceed. I therefore assume that a portion of my audience possess this requisite knowledge. I presume you know which is the Polar Star; I presume also that you know which is the Great Bear. Now, these are objects of such importance, that nobody ought to think of entering an astronomical lecture-room who is not acquainted with them. There is another star remarkable for its brilliancy, which is in this country circumpolar, called Capella; and there is another star, which is also nearly circumpolar, it is the bright star in the constellation Lyra.

Now I will call your attention to each of these in succession, The Polar Star is one which, roughly speaking, does not change its place during the whole night. Whenever you look out you find it in the same place. But speaking a little more accurately, ​it does change its place and move in a small circle. If you examine the stars of the Great Bear, you will observe that they turn in a circle considerably larger than that of the Polar Star, but they are still visible in the whole extent of the circle, and they turn completely round in it, without descending below the horizon. If you examine the next bright star Capella, which you will find on the globe in the constellation Auriga, you will find it describes a circle also, of which the Pole Star is apparently the centre. It goes very near the horizon when lowest in the north, and almost over our heads when highest in the south. If you examine the movement of the last of the stars I have mentioned, namely, the bright star in the constellation Lyra, you will find it moves in such a circle that it as nearly as possible touches the horizon. In the south of England it just descends below the north horizon; here (at Ipswich) it does not, but it passes so near the horizon that it can rarely be seen in the north.

Thus, if we fix a straight rod in a certain standard direction, pointing nearly, but not exactly, to the Polar Star, we find that the stars which are close in the direction of this rod, as seen by viewing along it, describe a very small circle; the stars further from it describe a larger circle; others just touch the northern horizon; whilst, in regard to others, if they do describe a whole circle at all, part of that circle is below the horizon; they are seen to come up in the east, to pass the south, and to go down in the west, and they are lost below the horizon from that place till they rise again in the east. These are the fundamental phenomena of the stars. It is important that any person, who wishes to understand Astronomy, should look into the matter, and see with his ​own eyes that the. stars really do partake of these motions; that the Polar Star does nearly stand still; that the stars at various distances from the Polar Star, do move round in the way I say, one in a circle of one size, and another in a circle of another size: that others do move round in circles still larger, so that at their lowest points they just touch the north horizon; that others move round in circles so large that the lower part of these circles is lost, whilst the higher part rises above the horizon. It is of importance that anybody, who wishes to understand Astronomy thoroughly, should look out, and see for himself, that these things do happen in the way I have attempted to describe; by the observations so made, he will acquire a conviction of the truth far deeper and more lasting than from anything that can be pointed out in a course of Lectures.

From observing the way in which these motions take place, that we may assume one point of the sky as a centre, and that the movements of the stars are of such a nature that they will appear to turn round that one centre; the first idea that naturally occurs is, that the starry heavens, as we see them (I do not affix any precise meaning to that term), or a shell in which the stars seem to be fixed, do turn round an axis. It is necessary to show that this is supported by accurate means of observation. Now there is one instrument in use in the best Astronomical Observatories, which is specially intended for the elucidation of this phenomenon—it is the instrument called the Equatoreal. I should be glad if some of the wealthy manufacturers in this town would set up an Equatoreal instrument. The Equatoreal is an instrument, which, in one form, is represented in Figure 1. It turns round an axis ​AB, and the axis is placed in that direction which

leads to the point of the sky around which the stars ​appear to turn, and which is not far from the Polar Star. The axis being adjusted with great accuracy in that direction, the instrument turns round that axis, and it carries the telescope CD, which, of course, so long as you give it no other motion, retains the same inclination to that axis; but to which you may give another motion, so as to place it in different positions, as C'D' or C"D", directed to stars in different parts of the heavens. The instrument, then, is employed for the purpose of giving evidence as to the motions of the stars. It is used in this manner. The telescope is directed to any one star, and then by turning the instrument round the axis, it is found, that without any alteration in the position of the telescope in relation to the axis, the telescope will follow the star from its rising to its setting. And it is the same wherever the star may be, whether near the Pole, (in which case the telescope is in such a position as C'D', very little inclined to the axis,) or far from the Pole, (in which case the telescope would be much inclined to the axis, as in the position of C"D",) upon turning the instrument round its axis, the telescope still follows the star. This is a fact of accurate observation, for the confirmation of which this kind of astronomical instrument is peculiarly adapted. In this way it is established as a general fact, that all the stars move accurately in circles round one centre.

But there is another important thing to discover—with what rapidity do the stars turn? Do some travel quicker than others? Do some go quickly in one part, and slowly in another? Now, we have most accurate means of determining whether the speed be irregular or uniform, as regards the speed of any one star in any part of its motion—whether the ​speed be irregular or uniform, in comparing the speed of one star with the speed of another star. I think that the best criterion which I can give is by a piece of mechanism which has been contrived, and applied to this purpose. (See Figure 2.) The best Equatoreals are furnished with a racked wheel attached to the axis, in which works an endless screw or worm, as at E, Figure 1. By turning it, the whole instrument is made to revolve. This worm, or screw, is turned by an apparatus which is constructed expressly for uniform movement. Various contrivances have been used for making this motion as uniform as possible. The one usually adopted, with some modifications (as represented in Figure 2), depends on the use of centrifugal balls AB, similar to those which are used to regulate the motions of steam engines. Everybody knows well that whirling these balls round by the rotation of the axis CD, to which they are attached, causes them to spread out. When the speed has reached a certain limit, the spreading out of these brings the moving parts, as at E and F, into contact with the fixed parts GH, and produces a degree of friction which prevents further acceleration; and thus a uniform speed is produced, with very great nicety. This contrivance is in constant use on my Equatoreal at the present time. You will observe it is essential to have a machine moving uniformly. In the motion of a common clock, though the movement from day to day, from hour to hour, and from minute to minute, is uniform, yet it is not so with the smaller divisions of seconds: the clock works with jerks, and does not go uniformly. Now the machine here is going on without any jerks with a smoothness and uniformity scarcely to be obtained by any other apparatus. In all the best Observatories ​in Greenwich, Berlin, Paris, and all others of any importance, this apparatus is used; in fact, it is used also in all the leading private Observatories, and the clock work which I now exhibit is borrowed from a private Observatory—from the Observatory of Dr. Lee. A spindle KL from this apparatus is attached to the worm which carries the Equatoreal. It makes the telescope of the Equatoreal revolve round the axis uniformly, and it thus gives us the means of ascertaining, with the utmost exactness, whether it be true, or whether it be not true, that all the stars do move with equal angular speed around one imaginary axis. When this machinery is in play, the telescope is adjusted, and pointed to the star. Whether it be turned to a star near the Pole, or to a star at a distance from the Pole, the effect is this—that the star is constantly seen in the field of view of the telescope—the telescope turns just as fast as the star moves.

Observe now the results obtained from these things. The first thing I mentioned was, if the telescope be directed to a star, and the instrument be turned it follows the star in the whole of its course. The next result, which is particularly connected with the use of this machine, is, that the same uniform motion round the axis follows any of the stars, wherever you select them. This is the same as saying that the stars move, as it were, all in a piece; and when you come to examine how it bears on Astronomy, you cannot attach too great an importance to these results. It is indeed the great and fundamental principle of Astronomy, that the stars do move as if they were attached to a shell, or in other words, that they move all in a piece. As to the explanation of that, I shall not trouble you at present. I simply call attention ​to the fact, that the stars move all in a piece—either that they are connected with some one thing turning upon an axis, or that they stand still while the earth turns round an axis of its own; one or other of these things is certain.

Having now come to that result, as one which is generally established, I shall just mention a slight departure from it. Perhaps you may be surprised to hear me say the rule is established as true, and yet there is a departure from it. This is the way we go on in science, as in everything else; we have to make out that something is true; then we find out under certain circumstances that it is not quite true and then we have to consider and find out how the departure can be explained. Now this is the fact. When we have a telescope of considerable power attached to the Equatoreal, so that we can see a small departure from the centre of the telescope in the position of the star we are looking at, and when we trace the course of that star down to the horizon, we find this as the universal fact that though the instrument be set up as carefully as possible, yet the star is not quite so near the horizon as we are led to expect. What can the cause be? There is a consideration that explains it perfectly—it is what is called refraction.

In order to see what refraction is, we may advantageously examine refraction on a larger scale. In a room generally darkened, let a lamp be introduced, as at A, Figure 3, and let it shine through a hole B in a screen CD, so as to produce a spot of light E on the wall. Place in the course of that ray of light a trough F, whose sides are pieces of plate glass. Now pour some water into the trough, and see what effect it produces. You will observe that the light is ​immediately thrown to the top of the wall, as at G. If the hole in the screen be so large that it is not

Fig. 3.

entirely covered by the trough, there will still remain a little light on the wall below, which shows the original direction. You will now see how much the direction of the light has been diverted by the action of the water in the trough. That effect is produced by the refraction of the water. It did not exist before the water was there, but it does exist now that the water is in the trough. I will now show the bearing of this matter on the subject of the disturbance in the position of stars. Figure 4 represents the prism of water we have been looking at.

Fig. 4.

The effect of it is this—a beam of light, coming in the direction of the line AB, does not pursue its original direction, but when it is received by the ​prism of water, it is turned in the direction CD. If you examine the prism, (as it is usually called in Optics, meaning the same form as that of a trough), you find that when the point of it is downwards, the effect of it is that the beam of light which comes in this direction AB, is turned in the direction CD, or more upwards. There is a rule on this matter, which is thus expressed—that the course of the light is always turned to the thicker part of the prism. Or if you observe what is the bending of the light at the two surfaces of the prism, this is the way in which it may be expressed when the light comes from the air into the water, its direction is bent more nearly towards the direction of the line which is perpendicular to the surface—when it goes from the water to the air, it is bent further from the perpendicular.^[2] In the particular use of the prism, with its point downwards, these two things are combined in such a manner, that at each of these surfaces the direction of the beam of light is bent upwards. Of course you will infer that if the prism were turned in the opposite

Fig. 5.

way as at Figure 5, so that its point was upwards, ​then the course of the light would be bent downwards.

Now, as regards astronomical observations, we have no water or glass concerned; but we have a thing which produces refraction, and that is atmospheric air. The common air produces refraction. The visible exhibition of this refraction is one of those nice experiments which I cannot attempt to exhibit to an audience like this. But it may be shown in various ways; as, for instance, by forming a prism of glass, and compressing more air into it; or again, by exhausting the air from it. It is shown that the effect of air is precisely the same in kind as the effect of water, though much less in degree. It may be stated as a general law, that where light enters from external space into air, or into water, or glass, or diamond, if you please, or any other transparent substance—where light enters from external space into any one of these substances, its course is bent in such a direction that it is more nearly perpendicular to the dividing surface than it was before. Now, having laid that down as a general law, let us see what its application will be to atmospheric air. In making astronomical observations,

Fig. 6.

let us assume that Figure 6 represents a part of the ​earth, covered by atmosphere—the black part being the earth, the dusky part the atmosphere. Suppose a beam of light is coming in the direction AB from a star, and suppose that at B it comes on the atmosphere it is coming then here exactly under the same circumstances in which in Figure 5 the beam of light comes upon the surface of the prism. According to the law which I have just mentioned, it will be bent in such a manner that its direction after it has entered the atmosphere is more nearly perpendicular to the bounding surface than before. Therefore, in conformity to that law, it is bent in the direction BC, and it reaches the eye of the observer at C, in the direction BC. If you observe the relation which the second line BC has to the first AB, you will see it is more nearly perpendicular to the horizon; or, standing at C on the surface of the earth, you have to look a little higher to see the star than if you were on the outside of the atmosphere, at B; or the star, in consequence of the action of the atmosphere, appears higher. Now this I have mentioned would be the case if the atmosphere had a definite boundary, and were uniform throughout its extent; but the same thing takes place if the atmosphere has not a definite boundary, and varies in density from stratum to stratum the same effect takes place from one stratum of the atmosphere to the next.^[3]

​In this manner we find there is a rational explanation of this too great elevation of the stars. Taking as foundation the established law of optics, determined by experiments on glass and water, and computing from this what ought to be the deflection of light, and what ought to be the elevation of the star produced by the refraction of light by the atmosphere, and applying that as a correction to the observations made by the Equatoreal Instrument, of which I have spoken, it is proved that the whole thing comes quite right—that the stars move exactly in circles, not approximately, but (as far as the human eye and instruments can discover) exactly as if they turned uniformly round one imaginary axis. This is the grand fact which must be regarded as the foundation of Astronomy.

I shall now mention, in as few words as I can, how observations of all kinds are made, and how upon these observations the most accurate astronomical determinations are based. In the first place we will show the use of the telescope, and how it is used with wires in the field of view. The instrument thus fitted up is not used for mere gazing, but for accurate observation. If you go into an observatory, and look into any of the telescopes, you will see a set of bars. It will be perhaps beyond your comprehension what these bars are, and what they are for. Stars are seen to pass these ​as if the stars and the bars were at the same distance from the eye. These bars are in reality fine cobweb threads, or something of the kind, fixed in the telescope very near to the eye. Perhaps Figure 7

Fig. 7.

may serve to illustrate the construction of the telescope. There is no tube, but that is immaterial. At A is what we call a lens, that is to say, a piece of glass convex on both sides, and therefore thickest in the middle. It is here supposed to be fixed in a hole in a wooden screen MN. The property of this lens of glass is, if there be a luminous object in the distance, it collects all the light from that object; and instead of suffering it to go out in a broad sheet of light, it makes it contract so that the light from each point in the object is collected at a corresponding point on the screen; and therefore all the corresponding points of light on the screen, which belong to the original points of light in the original luminous appearance, when put together, form an image which is exactly similar to the original object. The image, however, is turned upside down, because the light which comes from the upper part of the luminous object and goes through the lens, passes downwards towards the lower part of the screen KL. ​These properties of a lens can easily be proved by experiments with a common burning glass, or a reading glass, or spectacle glass, such as is used by elderly people.

Suppose, now, that the stand GH is placed on the south side of A, and that a lamp is slid along it successively from B to C, D, E, and F. This movement exactly imitates the apparent movement of the stars as they pass across the south, travelling from the east to the west. The effect of it is, that if the screens are placed at proper distances, a spot of light is seen on the screen KL, moving in the opposite direction, as from b, successively to c, d, e, and f. Now, if there are traced upon KL a set of bars or dark wires, the spot of light passes over them in succession, first over one and then over another. Now this is truly and veritably an astronomical telescope. At A is the lens forming the image of the star on KL is the set of wires in the field of view if you placed an eye-glass on the other side of KL, and viewed the wires with it, you would have a complete astronomical telescope. This is the arrangement by which astronomical observations are really and truly made. Every astronomical telescope intended for accurate observations is fitted up with wires of this kind.

On looking to the south with the naked eye, the star travels from left to right. But on looking into the telescope with an eye-glass, as on the other side of KL, the image of the star is seen travelling from right to left; and its speed is so much magnified by the magnifying power of the telescope, that the motion is sensible and even rapid. It goes over the bars in succession, and one of the duties of the observer is to note the time at which it pssses over every one of ​these, and to take the mean or average of all, so as to diminish the error of a single observation. Having shown the way in which the transit of the star is observed over a series of bars, I proceed to point out the way in which it is made useful for the determination of some of the most important points in Astronomy.

First of all, I wish to point out what is the thing we want to do in representing the position of the stars, and what are the general principles of fixing that position. There is a term we use in mathematics—co-ordinates; it is a word not used in common language, and I would avoid it if possible; but it is necessary to use some word which will convey the idea; and its meaning will be perfectly intelligible if you consider how you are to represent the position of anything whatever. Suppose that we have before us a celestial globe, with stars and other objects upon it. How are we to define the positions of those? The thing to which I desire to call your attention is this—that where we have anything of a surface, real or imaginary, we must have two elements of some kind to define the position of any point upon it. In Figure 8, suppose that AB represents a wall; D a

Fig. 8.

speck of dirt upon it. I want to define the position of that speck of dirt. What could I do? I could ​measure the distance AC horizontally from one end of the wall, and CD vertically from the floor. That would define it accurately, and I could write down the measures in figures, so that a person at any distance could make a speck in a position exactly similar on another wall. I might do it in other ways. I might measure the distance AD from the corner A, and the distance ED from the corner E, and describing circles with these sweeps in my compasses from each corner in succession, I should be able to find exactly the position of that speck of dirt. I might do it in another way, too. I might say, if I go from the corner A to that speck of dirt D, the distance is so many feet, and the inclination of the line AD to the horizon is such an inclination as I can represent. That would do. But, in whatever way I do it, I must take two measures; there is no way in which it is possible, in the nature of things, that the position of that speck of dirt on the wall, or the position of a star in the sky, can be represented, except by two elements.

Now the question presents itself. What are the two elements most convenient for representing the position of a star in the heavens? There are two elements which, ever since accurate astronomical observations began, have been fixed on by all astronomers as the most advantageous. One is thus described: supposing we can fix on the imaginary pole or place of rotation of the stars, then one element is the distance of the star, as measured from that pole in degrees. I will speak in a short time of what is really meant by a degree. The other is, supposing the celestial globe, or the sphere of the heavens, to turn round an axis, as we have shown it does; then the question is, how far has it to turn from a certain ​position before that star, whatever it is, comes under the meridian. If we can write down in figures (for these are the things by which alone we can preserve a satisfactory record)—if we can write down in figures how far the globe has to turn from a certain position, till any one star comes under the meridian of the globe, or under the imaginary meridian which passes over our heads; and if at the same time we can tell how far the star is from this pole, round which the whole of the sphere turns, we can fix the place of the star. These are the two co-ordinates. I pray your attention to these things, which are necessary for determining the position of a star—one, how far the globe must turn before the star is on the meridian; the other, what is the measure of the distance from the pole of the heavens to the star at the time when it does come on the meridian, or, indeed, at any other time, as that distance does not sensibly change in a day.

The thing to which I would first direct your attention is, the way in which we ascertain how far the globe must turn before the star comes into the meridian. Figure 9 represents what is called the Transit Instrument. It is an instrument in perpetual use in every observatory. You see the instrument is not adapted to gaze at all points of the heavens; in ordinary use it can be turned round the axis AB, and has no other motion whatever. Now, what we want to do with this transit instrument is, to supply the place of the brass meridian of a common celestial globe. We cannot put a brass meridian over the heavens, or over our heads; but we want to make a telescope move in such a manner that the line CDE passing along the telescope, and prolonged to the starry heavens, shall exactly describe a curve resembling ​the brass meridian. Consider, now, the various conditions necessary. First, every person who is

Fig. 9.

acquainted with the celestial globe, knows that the brass meridian ought to be perpendicular to the horizon; for securing that condition in the curve described by the transit instrument, the two points AB must be exactly level. In the next place, the brass meridian of a common globe is not what is called a small circle, but it divides the globe into two equal parts. For that purpose it is necessary that ​the telescope CD should be square to its axis AB. The astronomer ascertains whether it be truly square or not, by looking at a distant mark, first with the pivots A,B, of the instrument resting on the piers a,b, and then with the axis turned over, so that the pivots A,B, rest on the piers b,a. If the telescope points equally well to the mark in both positions of the axis, the telescope is truly square to its axis. The third condition is, that when the axis is level, and the telescope is square to its axis—on turning the instrument round its axis, the line CDE shall pass through the pole of motion of the celestial sphere. Now, the way of obtaining this condition is as follows:—We take advantage of that admirable Polar Star, which is a blessing to astronomers of the northern hemisphere. The Polar Star, as I have said, turns round like the rest, although in a small circle. Let FGHIKL represent the circle in the sky in which the Polar Star turns round in the order FGHIKLF. Suppose that in turning the transit instrument round its axis AB, the line CDE prolonged will trace on the sky the line GI or FK, as the case may be. The Polar Star in its revolution passes that line twice. Now, what we want is, that that line CDE, carried on to the sky, should be so directed, that in the motion of the telescope it should pass exactly through the centre of the circle which the Polar Star describes, and therefore that it should divide into two equal halves the circle which the Polar Star describes. We ascertain it in this manner. We can measure the description of the parts of the circle of the Polar Star by time. One of the most important parts of the apparatus by which that astronomical observation is made, is a clock. The clock should go well, and should beat loudly and distinctly. The astronomer ​observes the Polar Star when it passes the transit instrument at its upper passage, as at K, and also when it passes its lower passage, as at F. If these are twelve hours apart, we know that the transit instrument is in its proper position. For as the star describes the whole circle, in twenty-four hours, if the times of passing at F and K are twelve hours apart, there must be exactly half the circle between them, and therefore the line FK must pass through the centre of the circle, or through the Pole of the heavens. But supposing the transit instrument were a little out of position, so that the line described by CDE prolonged would be GI, then the star would require more than twelve hours to pass from its visible upper passage at I, through KLF, to its visible lower passage at G, and fewer than twelve hours to pass from its visible lower passage at G, through H, to its visible upper passage at I. In this manner we are enabled to adjust this transit instrument to its position with the utmost accuracy.

Having explained the manner in which the transit instrument is placed accurately in its proper position, I will now explain its use, I will assume you are looking to the south. The observer stations himself at his transit instrument, not looking at all parts of the sky, but waiting to observe the stars as they pass the meridian. The clock is going all the time. A star is seen to be approaching the meridian: the observer directs the telescope so as to observe the star when it actually crosses the meridian, and then looks into the telescope. In the telescope he sees the wires, and sees the image of the star travelling along, and he observes the passage of the star over every wire. Just before the star begins to pass, he looks to the clock face for the hours and minutes, ​and he then listens to the clock, which beats seconds—in that manner he gets the hour, the minute, the second, and the fraction of a second, at which that bright star passes every wire, and by taking the mean or average of these, he finds the time at which the star passes the meridian. He looks again, and he sees a planet coming into the field of view. He directs his telescope to that planet, and in like manner he gets the time by the clock at which that planet passes the meridian—the hour, the minute, the second, and the fraction of a second. He sees another star. The telescope is moved to the proper position he notes the time in the same manner, and he finds the hour, the minute, the second, and the fraction of a second, as before. Another star comes in the same way. Such is the duty which a transit-observer has to perform—the watching of objects which are passing the meridian in endless succession. He has this instrument, which is confined in its motions to the meridian, and which admits of no other motion; and the clock, by which he notes the hour, the minute, the second, and the fraction of a second; by the use of the various wires, he observes the time at which the object passes each wire; and by taking the mean of all, he finds very accurately the time at which the object passes the meridian: such are the duties of the transit-observer.

The next thing is to ascertain the elevation of the object when it passes the meridian. Now before we enter upon the use of the Mural Circle, I must offer a word or two upon Geometry. I dare say everybody here, like myself, has in his time, studied books containing measures—so many barleycorns make an inch, so many inches make a foot, so many feet make a yard, etc., as well as so many yards make a mile, ​and so many miles make a degree. But the publication in a book of measures of such an expression as "69 miles make a degree" is in the highest degree reprehensible, as giving false ideas on one of the most important expressions in science. No schoolmaster ought to introduce books into his school, teaching that 69 miles make a degree. What do we mean by a degree? The use of the word degree is to define inclination, and it ought to be looked upon as defining a measure of inclination only, and not as defining a measure of length. If I had to describe the position of two arms of a pair of compasses, I should say they were inclined; but the notion of their inclination is entirely different from the notion of a measure of length. But we want some means for describing how much these two arms are inclined. Now the method of describing how much these two arms are inclined, is got at in this way: we use the word degree for a certain small inclination, such that if we first give one arm an inclination of one degree to the other, then incline it one degree further, then one degree in addition, and so on to 360 degrees, the arm will have gone through the whole circle of inclination, and will have returned back again to its first position. But these degrees, as you will perceive, have nothing to do with lineal measures; they are inclinations, and nothing else; they have nothing more to do with lineal measures than they have to do with pounds weight, or pounds sterling. We do, however, find it necessary to use the word degree in determining what might at first sight appear to be linear measures. For instance, if a star be seen at the point A, Figure 10, and if another star be seen at the point B, and if I want to measure the distance between them, I say they are so many degrees apart; but yet I do not ​mean any number of miles, or any lineal measure. If I apply the hinge C of a pair of compasses to my

Figs. 10 & 11.

eye, and direct one arm CD to the star A, and the other arm CE to the star B, and then if I observe the inclinations of these arms; if the arms are square, one arm has made one fourth of the complete turn round from the other; and as we call the whole circle 360 degrees, one fourth of the turn round when the compasses are square is 90 degrees, and we say that the stars are 90 degrees apart. If instead of that, I have to put the arms of the compasses in a less inclined position, as in Figure 11, the distance of the stars may be 50 degrees, or 30 degrees, or some smaller number of degrees. This must be fully understood before we can enter upon the explanation of the Mural Circle.

This Mural Circle is an instrument very much varied in form. Figure 12 represents the instruments in use at the Royal Observatory, Greenwich, at Edinburgh, and Cambridge. A is a stone pier which supports the axis of the instrument, and to which ​microscopes a, b, c, d, e, f, are attached. The face of the pier which carries the microscopes, fronts either

FIG. 12.

the east or the west. The construction of the instrument is this: there is a circle BC, which turns round an axis DE, (not visible in the view) that passes through the pier A. The circle BC has the telescope FG attached. This circle is graduated into degrees and minutes and other sub-divisions on its outside, containing 360 degrees in its whole circumference. Its position would be sufficiently observed for ordinary purposes if there were a pointer fixed to the pier at one part, but there are reasons (depending on the liability of the axis to be disturbed in its bearing, and on the tendency of the circle to bend under its own ​weight) which make it desirable that there should be pointers at several parts of it. In the instruments at Cambridge and Greenwich, and other places, there are six pointers; they are not ordinary pointers, but microscopes, by means of which the spaces between the divisions can be sub-divided with greater accuracy than they could be by other means. Therefore you will perceive very easily, that by the use of these microscopes, viewing the circumference of this circle, it is possible to determine and register the position of this circle, (and consequently the position of the telescope which is fastened to it,) with very great accuracy indeed.

In all measures, however, we want a starting-point. What we want to ascertain with the circle is, how far the telescope is pointed above the horizon. It is therefore a very important thing to ascertain what is the reading of the circle when the telescope points horizontally. There is a contrivance used in most modern observatories for this purpose which is worthy of attention—it is the use of observations by reflection. Suppose that a star is seen by the observer to be approaching the meridian, he places a trough of quicksilver in such a direction that the star can be seen by reflection in the quicksilver. When the telescope is pointed towards the reflection in the quicksilver, then we know that the telescope is pointed below the horizon, just as much as it is pointed above the horizon to see the star by direct vision. This results from the optical law of reflection. For in Figure 13, if EG be the position of the telescope placed to receive the light which comes from the star in the direction SG, and if F′G′ be the position of the telescope placed to receive the light which comes from the star to the quicksilver in the direction ​S′O, and is thus reflected in the direction OG′, then by the law of reflection, S′O and G′O make

Fig. 13.

equal angles with the surface of the quicksilver. But as the quicksilver is perfectly fluid, its surface is exactly horizontal. So that G′O and S′O make equal angles with the horizon; and therefore F′G′O points as much below the horizon as OS′ or FGS points above it. The observer therefore looks at the star by reflection in the quicksilver; he takes the reading of the microscopes; he then turns the instrument so as to see the star by direct vision in the telescope, and then he takes the reading of the microscopes; then by taking the mean between the reading of the circle corresponding to these two observations, it is certain that we have got the reading corresponding to the horizontal position of the telescope. That gives us a starting-point; and having got that, whenever we ​observe a star in any position whatever on the meridian, inasmuch as we have got the reading of the circle when the telescope is directed to that star, and as we know the reading of the circle which corresponds to the horizontal position of the telescope—then by taking the difference between these readings, we know in degrees and minutes the inclination of the telescope, or the degrees and minutes by which the star is elevated above the horizon. The method of observation which I have described is going on at an Observatory every day. It is necessary, however, to remark that (as has been already said) every star appears too high, in consequence of refraction; a correction must therefore be subtracted from the elevation thus found, in order to discover at what elevation it would have been seen, if there had been no atmosphere about us.

Now, suppose that we observe the Polar Star. This star, though very near the Pole, describes a small circle round the Pole, and therefore goes as much above the Pole at one time when it is highest, as it does below the Pole at another time when it is lowest. Therefore, by taking the angular elevation above the horizon, in degrees, minutes, and seconds, of the Polar star when at the highest point above the Pole, and applying the proper correction for refraction; and taking its angular elevation in degrees, minutes, and seconds, when at the lowest point below the Pole, and applying the proper correction to this for refraction; and taking the mean between the two elevations so corrected; we get the true angular elevation of the celestial Pole. In that manner we have got the accurate calculation of the angular elevation of that Pole in the north, round which the heavens appear to turn.

​Now, allow me to point out what we have obtained with regard to these celestial objects.

By the use of the transit instrument, when properly adjusted, and the clock, we observe the time of transit of a principal star, and we observe the time of transit of any other objects, smaller stars, planets, or whatever else they may be. By means of these observations, we have a difference of times of transit. We can place no reliance upon the clock, except this, that it gives us the difference of time between the passage of principal stars, and that of other objects. Suppose that our clock is so adjusted, that if we observe the time of that principal star passing the instrument to-day, and again observe the time at which it passes the instrument to-morrow, the clock describes accurately twenty-four hours. If it does not describe accurately twenty-four hours, we know how great its error is in twenty-four hours, and we can apply a proportionate part of the error to every interval of time; so that it is in every respect as serviceable as if it were accurately adjusted. Supposing, then, that our clock was adjusted in such a manner that it indicated twenty-four hours, from the time of a principal star passing to the time at which the same object passed again—this amounts to saying, that it indicates twenty-four hours in the time in which the whole heavens turn round. Assuming, then, that the planet which we have observed, passes the telescope one hour after the principal star passes, then we must conclude that the heavens have turned for one hour; or have performed one twenty-fourth part of their whole revolution, before that part of the heavens in which the planet is seen, passes our meridian. And this is precisely one of the co-ordinates which, as I said, serves to determine the position of ​the stars, or the planets, in reference one to another. What we want to know is, the interval of the successive times at which they pass the meridian. Assuming that the starry heavens turn uniformly, this interval (which in the instance above we have supposed to be one hour), enables us, if we wish, for instance, to register the planet's place on a globe, to turn the globe one hour, or one twenty-fourth part of a revolution, from the position in which the principal star was under the meridian, and then we know that the planet which we have observed, will be somewhere under the meridian, in that new position of the globe. That is the result of the observations with the transit instrument.

The next thing is, by means of the observation of the Polar Star with the Mural Circle, and by determining how high any other object appears when it passes the meridian, to determine the angular distance of any object from the Pole. These two observations amount to this:—the first gives the angular distance of the Pole from the north horizon. It is, however, rather more convenient to refer the position of the Pole to the point which is exactly upwards usually called the Zenith. The change is very easily made; for as the angular distance from the Zenith to the horizon is ninety degrees,^[4] we have only to subtract the elevation of the Pole (or of any other object) from ninety degrees, in order to obtain its zenithal ​distance on the north side of the Zenith. Thus we find that between the Zenith and the Pole there are so many degrees, and minutes, and seconds, of angular distance. That is obtained from the observations with the Mural Circle, directed to the Polar Star. By using the same instrument in the same manner, but directed to a planet or other object, we find the angular distance from the Zenith to the planet on the south side of the Zenith. We have then, got these two things: we have got the angular distance of the Polar Star from the Zenith on one side, and the angular distance of the planet from the Zenith on the other side. By adding these together, we have the angular distance of the planet from the North Pole. This is the other co-ordinate necessary to define the planet's place.

As I said before, by the transit instrument we have found what is the proportion of a revolution through which the celestial globe must be turned in respect to a certain fixed star, in order that we may fix the position of the globe when the body passes the meridian; and by the observations with the Mural Circle, we have fixed the distance of the object from the Pole, when that object passes the meridian. These are the two co-ordinates which completely define the planet's place. If we had a globe we could mark down the place of the object at once. Or, instead of this, the result of the two kinds of observation may be registered in figures.

I have referred the times of transit of planets and small stars to one principal star, supposing it taken as a point of departure. This method was adopted by my predecessor, Dr. Maskelyne, and by several of the best astronomers. Dr. Maskelyne adopted the bright star of Aquila, as his fundamental star; others, ​however, have used several bright stars, whose relative positions have been well ascertained; and this is now the more usual course.

The methods of which I have spoken, give us the means of recording, with the greatest accuracy, the position of any object as viewed from any point of the earth, and we come to the same conclusions, as to the relative positions of the stars, wherever we may be placed. Thus, at the Cape of Good Hope, where there is an Observatory in the highest order, the relative positions of the stars are seen to be precisely the same as when they are viewed from the European Observatories. If you observe how many hours, minutes, and seconds, one star is before the other when it passes the meridian, and how many degrees, minutes, and seconds, one star is higher than the other when it passes the meridian—whether it it is observed here or at the Cape of Good Hope, it amounts to precisely the same thing there is not the slightest difference. From this we must draw one of two conclusions: either that the stars are, as it were, stuck in a shell of a very great size; or else, that the distance between the North of Europe and the Cape of Good Hope is unmeasureably small, compared with the distances of the stars; or that the distance of the stars is unmeasurebly great as compared with the distance from the North of Europe to the Cape of Good Hope.

I shall now conclude this lecture. In the next lecture I shall treat of the figure and dimensions and rotation of the earth; of the movements of the Sun amongst the stars; and of the motions of the planets.

1 ↑ The circumstances under which these Lectures were originally delivered are explained in the preface.

2 ↑ The reader is particularly desired to remark that the word perpendicular does not mean perpendicular to the horizon, or vertical, unless it is so expressed. When the expression perpendicular to the surface of the glass is used, it means what a workman would probably call square to the surface of the glass. The vertical direction at any place is that of a plumbline hanging there, or perpendicular to the surface of still water.

3 ↑ Thus, if we suppose the atmosphere to consist of a series of parallel beds or strata, Bc, cd, de, &c. each of which is of uniform density throughout, the ray AB falling on the boundary BD of the uppermost stratum will be bent in the direction Bc, so as to be more nearly perpendicular to BD. Again, when it reaches cE, the boundary of the next stratum, it will in like manner be bent in the direction cd. The same thing will happen every time it comes to the boundary of a new stratum; and at last, when it reaches the earth's surface at C, its direction will be Cg. The star, instead of appearing to the observer at A, will consequently be seen at I, in the direction of Cg.

4 ↑ The reader will easily understand this, if he remarks that upon opening a pair of compasses so that one leg points exactly upwards and the other leg points to the horizon; the two legs are then exactly square to each other, and therefore one leg has been turned away from the other by one-fourth part of the movement which would bring it round to the other again, or by one-fourth part of 360 degrees.