84 



SCIENCE. 



[N. S. Vol. XI. No. 264. 



half century, contributions alike formid- 

 able by reason of their bulk and by reason 

 of the complexity of their mathematical 

 details. An account of the theory of the 

 perturbative function, or of the theory of 

 the moon, for example, would alone require 

 space little short of a volume.* To men- 

 tion only the most conspicuous names, 

 there is the pioneer and essentiallj^ pre- 

 requisite work of the illustrious Gauss and 

 the incomparable Bessel. There is the re- 

 mai'kable work of the brilliant Leverrier 

 (1811-1877), and the not less brilliant 

 Adams (1819-1892), f well known to popu- 

 lar fame by reason of what may be called 

 their mathematical discovery of the planet 

 Ifeptune. Then came the monumental 

 ' Tables de la Lune ' J from the arithmetical 

 laboratory of the indefatigable Hansen ; 

 and this marvellous production was quickly 

 followed (1860) by the equally ponder- 

 ous, and mathematically more important, 

 ' Theorie du Mouvement de la Lune '§ from 

 the pen of the admirably fertile and indus- 

 trious Delaunay. And finally, there is the 

 still more elaborate work, bringing this 

 great problem of the solar system well-nigh 

 to completeness of solution, which, by 

 common consent, is credited to the two pre- 

 ceding presidents of the American Math- 

 ematical Society. || Probably no mathe- 



*A good account of the progress in dynamical 

 astronomy from 1842 to 1867 is given by Delaunay in 

 ' Eapport sur les Progrfes de I'Astronoraie,' Paris, 

 1867. 



t The papers of Adams have been edited by Pro- 

 fessor W. G. Adams and supplied with a biographical 

 memoir by Professor J. W. L. Glaisher, under the 

 title ' Scientific Papers of .John Coueh'Adams,' Cam- 

 bridge, at the University Press, Vol. I., 1896. 



X Published by the British government in 1857. 



^ Memoires de V Academie des Sciences de I'Institut Im- 

 perial de France, Tovaes, XXVIII., XXIX. 



II For an account of the more recent work of Gyld^n 

 and Poincar^, reference is made to the presidential ad- 

 dress of Dr. G. W. Hill, "Remarks on the progress 

 of celestial mechanics since the middle of the oeu- 

 ■ tury " ; Bullelin American Matliemaiical Society, 2d 

 series. Vol. II., No. 5, p. 125. 



matico-physical undertakings of the century 

 have yielded so many definite, quantitative 

 results to the permanent stock of knowl- 

 edge as the researches in dynamical as- 

 tronomy. 



But notwithstanding the astonishing de- 

 gree of perfection to which this science has 

 been brought, there are still some outstand- 

 ing discrepancies which indicate that the 

 end of investigation is yet a long way off. 

 The moon, which has given astronomers as 

 well as other people, more trouble than any 

 other member of the solar system, is still 

 devious to the extent of a few seconds in a 

 century. The earth, also, it is suspected, 

 is irregular as a time-keeper by a minute 

 but sensible amount ;* while it has been 

 proved recently by the exquisite precision 

 of modern observations, that the earth's 

 axis of rotation wanders in a complex way 

 through small but troublesome angles from 

 its mean position, thus causing variations 

 in the astronomical latitude of a place. f 



* The effect of tidal friction on the speed of rotation 

 of the earth appears to have been first explained by 

 Ferrel in a ' Note on the influence of the tides in 

 causing an apparent acceleration of the moon's mean 

 position. ' This paper was read before the American 

 Academy of Arts and Sciences, in December, 1864, 

 only a few weeks before Delaunay read a similar paper 

 before the French Academy. See Ferrel's autobiog- 

 raphy cited above. See also Delaunay's account of 

 his own work in 'Rapport sur les progres de P astron- 

 omie,' Paris, 1867. 



t The cause of such variations is found in the rela- 

 tive mobility of the parts of the earth, especially in 

 the mobility of the oceans and atmosphere. Three 

 types of variation may occur, namely : lat, that due 

 to sudden changes in the relative positions of the parts 

 of the earth's mass ; 2d, that due to secular changes 

 in position of those parts ; and 3d, that due to periodic 

 shiftings of those parts. Of these the most important 

 appears to be the periodic type. A surprising, and as 

 yet not fully explained, discrepancy brought to light 

 by the discovery of latitude variations is the fact that 

 the instantaneous axis of rotation of the earth makes a 

 complete circuit around the axis of figure in about 

 428 days, instead of in about 305 days as has been 

 supposed from the time of Euler down to the present 

 decade. The discovery of this discrepancy is due to 



