DISTANCE AND GRANDEUR OF THE SUN 91 



of the dichotomy of the moon, the one result was confirmed 

 by the other, though the two seemed reached by wholly inde- 

 pendent means. By yet more singular mischance, a third 

 method came to the support of the other two. 



This third means lay in a consideration of the size of the 

 conical shadow cast by the earth and the time it takes for the 

 moon to pass through it during an eclipse. Whether this 

 idea was present to the same amazing brain from which had 

 sprung the others, we do not know. It must have been very 

 early perceived that in this shadow cone was some sort of a 

 clue ; Aristotle had studied it with attention, and he was not 

 eminent either as an astronomer or a mathematician. Aris- 

 tarchus had certainly given it a great deal of thought, for he 

 had made a measure of it and set its diameter, which is not 

 very far from the truth. It is certain that he had some method 

 by which he estimated the relative diameter of the sun and 

 earth, as we shall see ; and the problem could have been worked 

 out in this rough way : 



Knowing the size of the earth, and the size and distance 

 of the moon, we may note, during the total occultations of the 

 moon, the maximum time elapsed from the moment the edge 

 of the moon touches the earth's shadow to the moment it begins 

 to emerge. This will enable us to construct a figure showing 

 the slant of the conical shadow of the earth, thus : 



FIG. 9. 



On the other hand, during an eclipse of the sun, the moon 

 on the average just about covers the sun's disk. That is, to 

 an observer on the earth at a, the sun and moon during a total 

 eclipse of the sun subtend, on the average, one and the same 

 angle, B a C or D a F. So, one has merely to prolong the lines 



