68 FROM NEBULA TO NEBULA 



and the centripetal attraction of the earth, there is a con- 

 stant equality. We have hitched two horses together of 

 equal strength and pace, to team the moon and the planets 

 around their several courses. 



There is, however, a slight modification of this prin- 

 ciple that must be taken into account; slight in amount, 

 but vitally important theoretically. It is this: The 

 Prime Resultant, being gravitational in character, such 

 movement as it gives rise to is a falling movement, conse- 

 quently accelerating. The moon, therefore, should 

 logically be revolving around the earth faster and faster 

 in accordance with the well-known law that the advance 

 of a falling body increases with the square of the time. 

 Harken now to this passage from Young (Gen'l Astr. p. 

 301), and note the italicized words; the italics being his 

 own: 



There remains one lunar irregularity among the multitude of 

 lesser ones, which is of great interest theoretically, and is still a 

 bone of contention among mathematical astronomers, namely, the 

 secular acceleration of the moon's mean motion. It was found 

 by Halley, early in the last century, by a comparison of ancient 

 with modern eclipses, that the month is certainly shorter than it 

 was in the days of Ptolemy, and that the shortening has been pro- 

 gressive, apparently going on continuously In 100 

 years the moon, according to the results of Laplace, gets in ad- 

 vance of its mean place about 10" , and the advance increases 

 with the square of the time! 



This vexed question of the acceleration of the moon 

 has, since the time of Newton, commanded the life efforts 

 of some of the best mathematicians the world has pro- 

 duced, always with one goal in mind, namely, TO SMOOTH 

 IT OUT AND CAUSE IT TO DISAPPEAR. It seems never to have 

 occurred to any of them, any more than to the Ptolemaists 

 struggling with their seventieth refractory epicycle, that 



ITS VERY REFUSAL TO IRON OUT IS A SIGNIFICANT FACT DIRECT- 

 ING ATTENTION TO SOME FUNDAMENTAL ERROR. An idea of 



the enormous amount of labor involved in this mathe- 

 matical problem, known among astronomers as "the 

 theory of the moon ' ', may be gained from this statement 

 of Professor Ernest W. Brown, the latest, and now rec- 



