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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]

Popular astronomy airy(1881) page 17.png

      ​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

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      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

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      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

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