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SCIENCE 



[N. S. Vol. XL. No. 1029 



also to the student of geodesy and, if I may 

 coin a word, of selenodesy, some results 

 which can be deduced more accurately from 

 a study of the moon's motion than in any 

 other way. A long-continued exploration 

 with few companions which ultimately leads 

 to territories where other workers have 

 already blamed paths gives the impression 

 of having emerged from the thick jungle 

 into open country. The explorer can once 

 more join forces with his brother astron- 

 omers. He can judge his own results more 

 justly and have them judged by others. 

 If, then, an excuse be needed for over- 

 stepping the limits which seem, by silent 

 consent, to have been imposed on those who 

 devote themselves to lunar problems, it con- 

 sists in a desire to show that these limits 

 are not necessary and that a study of the 

 motion of the moon can be of value and can 

 contribute its share to the common funds 

 of astronomy. 



The history of the motion of the moon 

 has been for more than two centuries a 

 struggle between the theorists and the ob- 

 servers. Ever since the publication of the 

 "Principia" and the enunciation of the 

 law of gravitation by Isaac Newton, a con- 

 stant effort has been maintained to prove 

 that the moon, like the other bodies of the 

 solar system, obeyed this law to its farthest 

 consequences. While the theory was being 

 advanced, the observers were continually 

 improving their instruments and their 

 methods of observing, with the additional 

 advantage that their efforts had a cumula- 

 tive effect: the longer the time covered by 

 their observations, the more exact was the 

 knowledge obtained. The theorist lacked 

 the latter advantage : if he started anew he 

 could only use the better instruments for 

 analysis provided by the mathematician. 

 He was always trying to forge a plate of 

 armor which the observer with a gun whose 

 power was increasing with the time could 



not penetrate. In the struggle the victory 

 rarely failed to rest with the observer. 

 Within the last decade we theorists have 

 made another attempt to forge a new plate 

 out of the old materials; whether we have 

 substantially gained the victory must rest 

 partly on the evidence I have to place be- 

 fore you to-day and partly on what the ob- 

 server can produce in the near future. 



There are three well-defined periods in 

 the history of the subject as far as a com- 

 plete development of the moon's motion is 

 concerned. From the publication of the 

 "Principia" in 1687, when Newton laid 

 down the broad outlines, until the middle 

 of the eighteenth century, but little prog- 

 ress was made. It seems to have required 

 over half a century for analysis by symbols 

 to advance sufficiently far for extensive 

 applications to the problems of celestial 

 mechanics. Clairaut and d'Alembert both 

 succeeded in rescuing the problem from the 

 geometrical form into which Newton had 

 cast it and in reducing it to analysis by the 

 methods of the calculus. They were fol- 

 lowed by Leonard Euler, who in my opinion 

 is the greatest of aU the successors of Isaac 

 Newton as a lunar theorist. He initiated 

 practically every method which has been 

 used since his time, and his criticisms show 

 that he had a good insight into their rela- 

 tive advantages. A long roll of names fol- 

 lows in this period. It was closed by the 

 publication of the theories of Delaunay and 

 Hansen and the tables of the latter, shortly 

 after the middle of the nineteenth century. 

 From then to the end of the century the 

 published memoirs deal with special parts 

 of the theory or with its more general 

 aspects, but no complete development ap- 

 peared which could supersede the results 

 of Hansen. 



My own theory, which was completed a 

 few years ago, is rather the fulfilment to 

 the utmost of the ideas of others than a 



