verify the observations in case of suspicion of error. Now, having the base of the triangle, and the two angles next that base, there is then no difficulty in laying them down on paper, or in calculating the other sides of the triangle. Then we may use one of these computed sides as a measured base, and if from its two ends we can see some other signal, we can observe it with our theodolites, and compute its distance in the same manner: and in this way the triangulation goes on. Thus, in Figure 17, a series of triangles was formed, extending from Shanklin Down, in the Isle of Wight, to Clifton, in the South of Yorkshire.
I called your attention particularly to the remark, that this is the first instance in which we use the yard measure, which is done by actual application in measuring the length of the base, and by computation from this in measuring the length of every one of the sides of the triangles; and thus we do really get the different distances in the triangulation, by the use of a yard measure.
I then mentioned to you that, supposing we had extended the survey over a very long distance, the next thing was to make use of the Zenith Sector, Figure 19, which consists in its important feature, of a telescope with a graduated arc CE attached to it, turning on two pivots AB, and with a plumb-line suspended from, or passing over, one pivot B, and crossing the graduated arc. (The Mural Circle may be used for the same purpose, but the Zenith Sector is rather more convenient.) We have then to consider that, whatever the form of the earth may be, using the expression as applying to the fluid part of the earth, we must suppose also from the nature of a fluid, that the direction of a plumb-line is
