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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

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      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.

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      Fig. 4.

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      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,

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      Fig. 6.

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