8

THE MOON :

We have, however, no record of the results actuallyobtained by Hipparchus , and we must turn to thepages of the great work, the Almagest , written byPtolemy about two centuries and a half later, for thefirst exact statement respecting the moon’s distance,and tho means used for determining it by the astrono-mers of old times.

The fundamental principle on which the measure-ment of the distance of any inaccessible object de-pends, is a very simple one. If a base-line (A B,fig. 1, Plate I.) be measured, and the bearing of the in-accessible object C from A and B (that is, the directionof the lines A C, B C, as compared with the line A B)be carefully estimated, then the distances A C and B 0can, under ordinary circumstances, be determined.For, in the triangle ABC, we know the base-lineA B, and the two base angles at A and B; so thatthe triangle itself is completely determined. Therefore,the ordinary formulae of trigonometrical calculation,—or even a careful construction,—will give us the sidesA C and B C.

If in all such cases we could determine A B and thebase angles at A and B exactly, we should know theexact lengths of A C and B C. But even in ordinarycases, each observation must be to some extent,greater or less, inexact. Accordingly, the estimateddistance of the object must be regarded as only anapproximation to the truth. Setting aside mistakesin the measurement of the base-line, mistakes indetermining the angles at A and B will obviously