ON THE MAGNITUDE OF THE SOLAR SYSTEM. 95 



ing around it. Like all the world's greatest sages, lie seems to have 

 taught ouly orally. A century elapsed before his doctrines were reduced 

 to writing by Philolaus of Crotona, and it was still later before they 

 were taught in public for the first time by Ilicetas, or as he is sometimes 

 called Nicetas, of Syracuse. Then the familiar cry of impiety was 

 raised, and the Pythagorean system was eventually suppressed by that 

 now called the Ptolemaic, which held the field until it was overthrown 

 by Copernicus almost two thousand years later. Pliny tells us that 

 Pythagoras believed the distances to the sun and moon to be, res])ec- 

 tively, 252,000 and 12,600 stadia, or, taking the stadium at 025 feet, 

 29,837 and 1,492 English miles; but there is no record of the method 

 by which these numbers were ascertained. 



After the relative distances of the various planets are known, it only 

 remains to determine the scale of the system, for which purpose the 

 distance between any two planets sufiQces. We know little about the 

 early history of the subject, but it is clear that the primitive astrono- 

 mers must have found the quantities to be measured too small for 

 detection with their instruments, and even in modern times the prob- 

 lem has proved to be an extremely difticult one. Aristarchus, of 

 Samos, who flourished about 270 B. C, seems to have been the first to 

 attack it in a scientific manner. Stated in modem language, his rea- 

 soning was that when the moon is exa(;tly half full the earth and 

 sun, as seen from its center, must make a right angle with each other, 

 and by measuring the angle between the sun and moon, as seen from 

 the earth at that instant, all the angles of the triangle joining the 

 earth, sun, and moon would become known, and thus the ratio of the 

 distance of the sun to the distance of the moon would be determined. 

 Although perfectly correct in theory, the difticulty of deciding visually 

 upon the exact instance when the moon is half full is so great that it 

 can not be accurately done, even with the most powerful telescoijes. 

 Of course Aristarchus had no telescope, and he does not explain how 

 he ett'ected the observation, but his conclusion was that at the instant 

 in question the distance between the centers of the sun and moon as 

 seen from the earth is less than a right angle by one-thirtieth irM't 

 of the same. We should now express this by saying that the angle is 

 87°, but Aristarchus knew nothing of trigonometry, and in order to 

 solve his triangle he had recourse to an ingenious, but long and cum- 

 bersome, geometrical process, which has come down to us, and afibrds 

 conclusive proof of the condition of Greek mathematics at that time. 

 His conclusion was that the sun is nineteen times farther fr<mi the earth 

 than the moon, and if we combine that result with the modern value of 

 the moon's parallax, viz, 3,122.38", we obtain for the solar parallax 

 180", which is more than twenty times too great. 



The only other method of determining the solar parallax known to 

 the ancients was that devised by Hipparchus about 150 B. C. It was 

 based on measuring the rate of decrease of the diameter of the earth's 



