more than 180 degrees, for the measure at Greenwich being 108 degrees, and that at the Cape of Good Hope being 7312 degrees, the sum of these is 18112 degrees. How are these 7312 degrees to be accounted for? This angle of 112 degrees is the angle made by the two lines GM, CM. I have arrived thus at the conclusion: that at the distance of the moon, the angle between the two lines, of which one is directed to the Greenwich Observatory, and the other to the Observatory at the Cape of Good Hope, is 112 degrees. Having the position of Greenwich and the Cape of Good Hope, knowing the angle is 112 degrees, and knowing the directions of the lines from the two Observatories, I can compute the distance of the moon at once.
Here we must remark, that the observations of which I have spoken would be of no use, if we had not got the measure of the earth. That measure, however, as I explained in a former lecture, has been obtained by the aid of our yard measure; and it is worth while to recall the principal steps of the process. By means of the yard measure we measured a base line—in a survey by means of the base line, with triangulation, we obtained the length of some very long lines upon the earth's surface; and by the use of the Zenith Sector at different parts of the earth, in combination with the measures of these long lines, we got the general dimensions of the earth as expressed in yards; then, knowing the position of the Observatory at Greenwich, and knowing the position of the Observatory at the Cape of Good Hope, we have the means of getting from these general dimensions of the earth, the length of the line GC in yards, and its position in regard to the other lines; we know also that the angle GMC is 112
