on Misterton Carr, connected with, the triangulation, by which the distance from A (Shanklin Down, in the Isle of Wight) to D, (a place called Clifton, in Yorkshire,) was measured.
The next thing to be done, having measured the length of the line EF, Figure 15, is to measure the distance of the signal G. It is, perhaps, on a mountain, perhaps with sea between it and EF. The object is to get the signal as far off as it can be seen. These signals have been observed at the distance of 110 miles. Signals in Ireland, on the Wicklow Mountains, and on Slieve Donard, have been observed from Ben Lomond, in Scotland; from Precelly and Snowdon, in Wales; and from Scaw Fell, in Cumberland. Having, then, measured EF, I wish to ascertain the distance of G. For that purpose I take away the signal at E, and plant a theodolite in its place. The theodolite is adjusted on the point E with the utmost care. Now, by means of this theodolite, making use of it in the usual manner, first of all I observe the signal F at the end of the base, and then turning it until I observe the signal G on the distant hill, I obtain the angle of an imaginary triangle GEF, if you may so call it The triangle is, in fact, formed by the rays of light which come from the signal at one station, to the eye, or instrument, at the other; when I turn the telescope of the theodolite at E towards F, it is in the direction of one side, EF, of the triangle; and when I turn it so as to view the distant signal G, it is in the position of the other side of the triangle; and therefore the angle, by which the theodolite turns, is the measure of that angle FEG of the triangle. I then plant the theodolite at F; I direct it in like manner to the end of the base E, and then the light it receives is in
