DISTANCE AND GRANDEUR OF THE SUN 89 



So much was self-evident ; was there any way to make an 

 actual measure ? The first we know of to attack the problem 

 was the predecessor of Eratosthenes in the school of Alexandria, 

 a contemporary and possibly the teacher of Archimedes, when 

 the young Sicilian went from Syracuse to Alexandria to school. 

 This was that Aristarchus who, to Laplace, " paroit etre dans 

 1'antiquite celui qui eut les plus justes notions de la grandeur de 

 1'univers." He was, as we shall see, the forerunner of Copper- 

 nicus ; if grandeur of conceptions be a measure of the brain, 

 or ingenuity of its powers, then we must rank Aristarchus with 

 Democritus and Archimedes as one of the three or four most 

 acute intellects of the ancient world. 



The eccentric actions of the moon, the varying shadow it 

 casts, or receives, its so-called inequalities, were then among 

 the principal problems of the heavens ; and over them the 

 Alexandrian astronomer must have puzzled with the rest. 



Pondering over the various " phases " which the moon 

 presents, it presently came to him that the extent of the moon's 

 surface visible to" us depends on the direction of the source of 

 illumination that is, the sun. So, as the moon swings in its 

 circle, it will reach its first " quarter " in a little shorter time 

 than it passes from this to the second " quarter," or full moon. 

 This is clear from a moment's consideration ; since the moon 

 shines by the light of the sun, then when its disk is, to our eyes, 

 just cut in two, it is at right angles to an observer on the earth, 

 as the figure describes : 



FIG. 8. 



Now, unless the sun be at an infinite distance from both the 

 earth and the moon, it is clear that the time of passage from a 

 new moon at N to its first " quarter " at D must be a little less 

 than through a full quarter of its orbit, i.e. to H ; so the time 

 from the first quarter will be a little longer to a full moon at F 

 by the length of the arc H D. It is perfectly easy to time the 



