on stone piers, if the instrument is of a large size, or upon metal piers, if the instrument is of a smaller size; the telescope so adjusted, and turning in this manner, moves only in the meridian. And here it is important to remark that in all standard observations in Astronomy, the instrument is not turned to stars in any part of the heavens, but we have to wait until the stars come upon the meridian. We must so manage as not to be too late, or we lose our observation. The transit instrument must be adjusted in reference to our notion of what we want to observe. The object of all this is to define the places of the stars, in relation one to another; the places of the planets, the sun, the comets, the moon, in relation to the stars, and so on: in fact the use of all observing instruments of this class is to define the place of one object in relation to some one or other fixed objects. I then endeavoured to explain that for exact definition of the place of an object, it is necessary to use a system of what, in mathematics, are called co-ordinates; and that, when the object is or appears to be upon a surface, two co-ordinates are necessary. By this term, I mean two measures of some kind or other; as distances from two fixed lines, or distances from two fixed points, or length of the line from one point and inclination of that line to the horizon. Thus, for determining the position of the stars in reference one to another, it is a matter of importance to choose the most convenient co-ordinates. Considering the stars as they are represented on the celestial globe, if we wish to define the place of any star, the most convenient co-ordinates we can use are these: in the first place, to see how far the globe must have turned from a certain position before the star passes under the brass meridian; and in the next place to see
