perpendicular to the surface, and therefore, if we suppose the earth to be fluid, the plumb-line will be always perpendicular to its surface. If, then, we plant the Zenith Sector at A, Figure 18 or 20, the plumb-line will hang in a direction perpendicular to the surface at A. But if at B, the plumb-line must hang in the direction perpendicular to the surface at B: therefore if at A we observe a star nearly overhead, then the plumb-line will fall over the point G of the arc; but if we carry the Zenith Sector to B, and turn the telescope to the same star, the plumb-line will fall on the point g of the arc. Inasmuch, therefore, as the telescope, from being directed to the same star, which is excessively distant, takes the same direction in different places; and, inasmuch as the plumb-line takes different directions in different places; by means of these we get the variable positions of the plumb-line referred to the invariable position of the telescope. I then called your attention to Figures 20 and 21, and said, if we suppose the vertical lines at A and B to be carried down till they meet at H, the angle made by these two verticals, or by the two plumb-lines, would be the difference of the Zenith-distances of the star as observed at A and B; that is to say, the difference of the two angles made by the telescope with the plumb-line, first at A, and secondly at B. Having got the angle of these two lines, AH and BH, and the length of the line AB which connects their ends, we are enabled to calculate the length AH or BH, or the number of miles of distance of their intersection H. This is, in point of fact, the semi-diameter which must be taken in order to sweep the curvature of the arc AB; or, if you please, we may put the result in this shape: we may say that, having travelled 830 miles, we find the inclination of
