DISTANCE AND GRANDEUR OF THE SUN 93 



The theorem of Hipparchus gave not merely the relative 

 but also the absolute measures of the solar and lunar distances, 

 hence a direct measure of their size. Cleomedes l tells us that 

 Hipparchus computed the sun's bulk at 150 times that of the 

 earth ; Ptolemy made it 170 times. But Aristarchus, by what 

 method he does not state, figured the diameter of the sun at 

 between six and seven times that of the earth, hence about 

 three hundred times its bulk. He sets the moon's diameter 

 at one-third that of the earth an error of but one-twelfth ; 

 admirable, if yet imperfect approximations. The march of 

 the mind had begun! 



Yet was this the nearest approach which the ancients made 

 to the truth ? There is, in an oddly- jumbled work, Opinions 

 of Philosophers, attributed, with slight probability, to familiar 

 old Plutarch, a paragraph which says that Eratosthenes had 

 engaged the same problem. True to his love of concrete 

 measures, he gives the distance of the moon at 780,000 stadia, 

 of the sun at 804,000,000 stadia. Marvellous prevision of the 

 truth ! For though he makes the distance of the moon only 

 about twenty earth radii too small by two-thirds of the reality 

 his figure makes the sun distant 20,000 radii, which, as nearly 

 as we may estimate the stadium, was practically the distance 

 that, after three centuries of patient investigation with micro- 

 meters and heliometers, is set down as the reality. What was 

 his device ? how did he guess so wonderfully ? We have no 

 mortal idea. Perchance in some buried villa at Herculaneum, 

 or elsewhere, a papyrus may exist which may one day tell us. 

 Until then we have not so much as a conjecture. 



The estimates of Eratosthenes are somewhat vitiated by 

 a remark we find in Macrobius, 2 that he gave the diameter of 

 the sun at about twenty-seven times that of our earth. His 

 great predecessor, Aristarchus, had already fixed the visual 

 diameter of the sun at half a degree, which required that its 

 diameter should be about yx^th of its distance ; this, on the 

 figures of Eratosthenes would have made the sun at least 

 ninety times the earth's diameter, or 700,000 times its bulk. 

 But Macrobius came in the fifth century A.D., and it may be 

 that his remark is an error. True, the figures of Eratosthenes 



1 De Mundo, Lib. I. chap. i. 



2 Somnium Scipionis, Lib. I. chap. xx. 



