W. Ilarkness — Magnitude of the Solar System. 233 



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 tri- 

 angle 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 difficulty of deciding visually upon the exact instant 

 when the moon is half full is so great that it cannot be accurately 

 done even with the most powerful telescopes. Of course Aris- 

 tarcus had no telescope, and he does not explain how he effected 

 the observation, but his conclusion was that at the instant in ques- 

 tion the distance between the centers of the sun and moon, as 

 seen from the earth, is less than a right angle by -^ part of the 

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

 87 degrees, but Aristarcus knew nothing of trigonometry, and 

 in order to solve his triangle, he had recourse to an ingenious, but 

 long and cumbersome geometrical process which has come 

 down to us, and affords conclusive proof of the condition of 

 Greek mathematics at that time. His conclusion was that the 

 sun is nineteen times further from the earth than the moon, 

 and if we combine that result with the modern value of the 

 moon's parallax, viz : 3422'38 seconds, we obtain for the solar 

 parallax 180 seconds, 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 shadow cone by noting the duration 

 of lunar eclipses, and as the result deduced from it happened to 

 be nearly the same as that found by Aristarcus, substantially 

 his value of the parallax remained in vogue for nearly two 

 thousand years, and the discovery of the telescope was required 

 to reveal its erroneous character. Doubtless this persistency 

 was due to the extreme minuteness of the true parallax, which 

 we now know is far too small to have been visible upon the 

 ancient instruments, and thus the supposed measures of it were 

 really nothing but measures of their inaccuracy. 



The telescope was first pointed to the heavens by Galileo in 

 1609, but it needed a micrometer to convert it into an accurate 

 measuring instrument, and that did not come into being until 

 1639 when it was invented by Wm. Gascoigne. After his 

 death in 1644, his original instrument passed to Richard Town- 

 ley who attached it to a fourteen foot telescope at his resi- 

 dence in Townley, Lancashire, England, where it was used by 

 Flamsteed in observing the diurnal parallax of Mars during its 

 opposition in 1672. A description of Gascoigne's micrometer 

 was published in the Philosophical Transactions in 1667, and 



