the direction of the side of the triangle FE ; I turn it then to the same distant signal G. Therefore, by these observations, I have really and truly got, by the theodolite, the measure of the two angles of the triangle at E and F. Now, that is sufficient. Every person who has a knowledge of trigonometry, knows that if we have got the measures of the side EF, and of these two angles, we are able, either to construct the triangle on paper, or to determine, by calculation, the whole of its parts. Or, without pretending to understand or to have heard of such a word as trigonometry, any person can see, that by observing how much I turn the telescope at E, for instance, I can make the same turn of a line on paper; that I can make the two directions of the line incline to each other by that angle. Knowing how much this telescope has been turned from one object to the other, I can make the same angle on paper here; I can do the same for the other end of the base, and then, prolonging these lines until they meet, I get the distance of the distant signal. This is sufficient. But, to make assurance doubly sure, it is usual to place a third theodolite at G, and then to observe the signals at E and F. And the reason is this: we know by geometry that if we take the measures of the three angles at A, at B, and at C, in degrees, minutes, and seconds, and add them together, the sum will be 180 degrees; so that the observation of the angle at G, is a verification of the measures of the two angles at E and F.
Now, then, we have made the first step in triangulation. Having measured the base line EF, by means of a yard measure, as represented by some of our standard rods, and having measured the angles,
