Determination of the Sun's Distance. 125 



triangle which will be right angled at the moon. The angle 

 also by which the sun and moon was separated could be 

 observed at the same instant, and hence the three angles of 

 a triangle obtained. Aristarchus took for his unit of measure 

 the distance of the earth from the moon, and arrived at the 

 result that the sun was nineteen times as far from the earth 

 as the moon ; we now know it to be nearly four hundred times. 

 The method of Aristarchus, however, did not admit of a 

 precise practical application, inasmuch as the exact instant 

 of dichotomy, or half moon, could not be well determined, 

 and the slightest error in that respect would be fatal to 

 accuracy. 



This distance of the sun, namely, nineteen times the 

 moon's distance, was accepted for nearly two thousand years 

 subsequent to its determination. Ptolemy so far accepted it 

 as to combine it with his determination of the moon's 

 distance from the earth, making the sun's distance five 

 millions of miles. 



It was not until Kepler's time, in the seventeenth century, 

 that this amount was discovered to be far too small, when 

 that celebrated astronomer arbitrarily multiplied it by three, 

 making it fifteen millions of miles. Notwithstanding this 

 somewhat unscientific and summary proceeding on so grave 

 a matter, astronomy owes to this celebrated astronomer the 

 honour of making the first real step towards the solution of 

 the great problem, by the enunciation of his three great 

 laws of planetary motions, the substantial truth of which the 

 illustrious Newton subsequently demonstrated. 



Kepler's third law shows that the squares of the periodic 

 times of the revolutions of the planets around the sun are to 

 each other as the cubes of their mean distances ; therefore, if 

 the periods in which the planets perform their orbits around 

 the sun can be ascertained, the relative distances of the 

 planets from the sun and from each other are determinate. 

 These periods have been observed by most of the ancient 

 astronomers, and indeed in Kepler's time they may be con- 

 sidered to have been almost as well known as at the present 

 day ; although the question of whether the sun's distance 

 was ten, or a hundred millions of miles, was still 

 unsolved, Kepler's law made known the proportional 

 distances of the bodies of our solar system with an accuracy 

 very little behind our knowledge of the present day. 



It will be borne in mind, that no absolute distances have 

 yet been spoken of, but from what has been said of Kepler's 



