we must try another assumption for the length of EM, and go through the calculation again. And this we must do over and over again, till the numbers agree.
It has been supposed that the observations are made at the same instant at Greenwich and the Cape of Good Hope. This is not strictly correct; but the difference of time is known, and the moon's motion is well enough known to enable us to compute how much the angle P'CM changes in that time; and thus we can find what would have been the direction of CM, if the observation had been made at exactly the same instant as the observation at G.
After having got this notion of the value of the moon's distance, and knowing the method of computing the parallax, it is necessary to apply that computed parallax to every observation made, in order to find the position of the moon as seen from the centre of the earth. Now, if we have made a considerable series of observations of the position of the moon as viewed from the Observatory, and then, by calculating every parallax, if we have got the corresponding places of the moon as viewed from the centre of the earth, we find this, that the same law holds in the motion of the moon round the earth as in the motion of the earth and planets round the sun; that is, that the moon moves in an ellipse which is in a plane passing through the earth's centre.
When we consider it sufficiently established that the moon does revolve in a plane passing through the earth's centre, we can take that assumption as the basis of calculation to be compared with observations; and we can find what the moon's distance is, from observations at a single Observatory. The effect of parallax is always to make the object appear lower. If the moon were viewed from the centre of the earth,
