90 THE WORLD MACHINE 



moon's revolution and its phases. Aristarchus did this and 

 believed that he found the first quarter twelve hours shorter 

 than the second. To satisfy this result it was a simple matter 

 to'compute that the line from E to S that is, from the earth 

 to the sun must be about eighteen or twenty times the length 

 of the line from the earth to the moon. 



Here, then, was a measure of the distance of the sun ! But 

 was there any certainty that it was right ? Was there any 

 way to check it, to confirm it ? 



It is not very difficult to see that if, at its first " quarter," 

 the face of the moon appears to us just cut in two, the moon 

 forms with the earth and the sun a right-angled triangle, such 

 as S D E in the figure. It is then only needful to measure the 

 angle at E that is, the angle subtended by the moon and sun 

 to be able to draw this triangle in the right proportions. This 

 would give the distance of the sun in terms of the distance of 

 the moon. 



All this seems simple enough on paper ; but of an afternoon 

 when the sun is setting and the moon is in the sky, it is worth 

 a moment's thinking over as to whether such an idea would 

 ever have come to you. Note, too, that the angle between the 

 moon and the sun : is very nearly a right angle, so that the 

 smallest error will have enormous consequences. Consider how 

 difficult it is to tell just when we see exactly half the moon. 

 One will think less then that Aristarchus failed than of the 

 noble mind which could work out such an idea. 



The Alexandrian's measure of the angle was nearly three 

 degrees too small ; his reckoning was put by the yl^th part 

 of a circle. It is only fair to add this has been computed from 

 other data ; the angle is almost as difficult to measure in our 

 day as in his. So the line opposite this angle was about twenty 

 times too short. It is evident that his error lay in fixing the 

 moment when the moon was at right angles ; for the time of 

 passage to the first and second quarter was wrong in exactly 

 the same proportion. Aristarchus reckoned this difference at 

 twelve hours ; in reality it is on the average only thirty-six 

 minutes. He was right in his theory ; his errors lay beyond 

 his powers to control. With his resources we could do no 

 better now. 



But attend to the curious consequences. Involved in the 

 same initial mistake, the impossibility of fixing the exact moment 



