precision that we mean by the word parallax. It is convenient to make all our calculations of the moon's place with reference to the centre of the earth. Now, in Figure 40, it will be seen that the moon, if viewed from the centre of the earth, would be seen in the direction EM; but, as viewed from Greenwich, she is seen in the direction GM. The difference between these two directions is the angle GME, and this is called the moon's parallax at Greenwich. In like manner, the angle EMC is the moon's parallax at the Cape of Good Hope; and therefore the angle GMC, which has been found by observations in the way already described, is the sum of the parallaxes of the moon at Greenwich and the Cape of Good Hope.
Now, the method in which the calculation of the moon's distance is actually effected is this. From a knowledge of the earth's dimensions, the length of the line EG is known with considerable accuracy. And though (as I stated in the second lecture) the plumb-line at G is not directed actually to the earth's centre, but in a slightly different direction, H'GE', yet, from knowing the form of the earth, we can calculate accurately how much it is inclined to the line HGE, which is directed to the earth's centre. Thus, we know the angle H'GH, and we have observed the angle H'GM with the mural circle, and the difference is the angle HGM, which therefore is known. Then we assume, for trial, a value of the distance EM. With the length EM, the length EG, and the angle HGM, it is easy to calculate the angle GME. The same process is used to calculate the angle CME. We then add these two calculated angles together, and find whether their sum is equal to the angle GMC, which we have found from observation. If the sum is not equal to that quantity found from observation,
