DISTANCE, SIZE, AND MASS.

9

affect more or less seriously the estimate of eitherA C or B C. And a very brief consideration of thematter will show that the greater is the distance of Cas compared with the base-line A B,—in other words,the smaller the angle 0,—the more serious will be theeffect of any error in the observation of the angles Aand B.

Now, the difficulty experienced by the astronomerin the application of this direct method to the deter-mination of the distances of celestial objects, consistschiefly in this : that his base-line must always beexceedingly small compared with the distance whichhe wishes to determine. It is, indeed, only in thecase of the moon that the astronomer can apply thismethod with the least chance of success ; and even inher case the problem is by no means an easy one.We shall see presently that the distance of the moonexceeds the earth’s diameter in round numbers somethirty times. If the reader draw a figure, as in fig. 1,but so that each of the lines A 0 and B 0 is aboutsixty times as long as A B, he will see that the angleat C is exceedingly minute, insomuch that a veryslight error in the determination of either of the baseangles at A and B would lead to a serious error in theestimate of the distance of C, even supposing a fulldiameter of the earth could be taken as the base-line.

Now, when we remember that the ancient astrono-mers were unable to undertake long voyages for thepurpose of determining the moon’s distance, andthat, even though they could have set observers at