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Rh 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



speck of dirt upon it. I want to define the position of that speck of dirt. What could I do? I could