September 18, 1914] 



SCIENCE 



391 



new mode of finding the moon's motion. 

 Its object was severely practical — to find 

 in the most accurate way and by the short- 

 est path the complete effect of the law of 

 gravitation applied to the moon. It is a 

 development of Hill's classic memoir of 

 1877. Hill in his turn was indebted to 

 some extent to Euler. His indebtedness 

 would have been greater had he been aware 

 of a little-known paper of the latter, ' ' Sur 

 la Variation de la Lune," in which the 

 orbit, now called the variation orbit, is ob- 

 tained, and its advantages set forth in the 

 words : ' ' Quelque chimerique cette question 

 j'ose assurer que, si I'on reussissoit a en 

 trouver une solution parfaite on ne trou- 

 veroit presque plus de difficulte pour deter- 

 miner le vrai mouvement de la Lune reelle. 

 Cette question est done de la derniere im- 

 portance et il sera tou jours bon d'en appro- 

 fondir toutes les difficultes, avant qu'on en 

 puisse esperer une solution complete." 



In the final results of my work the devel- 

 opment aims to include the gravitational 

 action of every particle of matter which 

 can have a sensible effect on the moon's 

 motion, so that any differences which ap- 

 pear between theory and observation may 

 not be set down to want of accuracy in the 

 completeness with which the theory is 

 carried out. Every known force capable 

 of calculation is included. 



So much for the theory. Gravitation, 

 however, is only a law of force: we need 

 the initial position, speed and direction of 

 motion. To get this with sufficient accuracy 

 no single set of observations will serve ; the 

 new theory must be compared with as great 

 a number of these as possible. To do this 

 directly from the theory is far too long a 

 task and, moreover, it is not necessary. In 

 the past every observation has been com- 

 pared with the place shown in the "Nautical 

 Almanac" and the small differences be- 

 tween them have been recorded from day 



to day. By taking many of these differ- 

 ences and reducing them so as to corre- 

 spond with differences at one date, the 

 position of the moon at that date can be 

 found with far greater accuracy than could 

 be obtained through any one observation. 

 At the Greenwich Observatory the moon 

 has been observed and recorded regularly 

 since 1750. With some 120 observations a 

 year, there are about 20,000 available for 

 comparison, quite apart from shorter series 

 at other observatories. Unfortunately 

 these observations are compared with in- 

 correct theories, and, in the early days, the 

 observers were not able to find out, with the 

 accuracy required to-day, the errors of their 

 instruments or the places of the stars with 

 which the moon was compared. But we 

 have means of correcting the observations, 

 so that they can be freed from many of the 

 errors present in the results which were 

 published at the time the observations were 

 made. We can also correct the older 

 theories. They can be compared with the 

 new theory and the differences calculated: 

 these differences need not even be applied 

 to the separate observations, but only to 

 the observations combined into properly 

 chosen groups. Thus the labor involved in 

 making use of the earlier observations is 

 much less than might appear at first sight. 

 For the past eighteen months I have been 

 engaged in this work of finding the differ- 

 ences between the old theories and my own, 

 as well as in correcting those observations 

 which were made at times before the re- 

 sources of the astronomer had reached 

 their present stage of perfection. I have 

 not dealt with the observations from the 

 start: other workers, notably Airy in the 

 last century and Cowell in this, have done 

 the greater part of the labor. My share 

 was mainly to carry theirs a stage further 

 by adopting the latest theory and the best 

 modern practise for the reduction of the 



