W. B. Taylor — Crumpling of the Earth's Crust. 255 



mean motion," pointed out an incompleteness in Laplace's inves- 

 tigation by the neglect of a certain series of terms ; and he 

 showed that the effect of this series would be to reduce the 

 actual acceleration due to the diminution of eccentricity in the 

 earth's orbit to about 6" ; leaving the residual discrepancy of 

 4" or 5" of acceleration (as compared with the positions indi- 

 cated from the ancient eclipses), to be still accounted for.* 



Herman Helmholtz, in a lecture on the " Interaction of 

 Natural Forces," delivered at Konigsberg, Feb. 7, 1854 (with- 

 out knowledge of Adams' work), pointed out to his hearers 

 that " The motions of the tides, however, produce friction ; all 

 friction destroys vis viva, and the loss in this case can only 

 affect the vis viva of the planetary system. We come thereby 

 to the unavoidable conclusion that every tide — although with 

 indefinite slowness, still with certainty — diminishes the store of 

 mechanical force of the system ; and as a consequence of this 

 the rotation of the planets around their axes must become more 

 slow."f 



Charles Delaunay, who with fine analytic skill had for several 

 years been engaged on the theory of the moon, in 1859 under- 

 took a careful examination of the results obtained by Mr. 

 Adams, which impeached the accuracy of his great country- 

 man, Laplace ; and in a memoir " On the secular acceleration 

 of the mean movement of the Moon," presented to the French 

 Academy, he fully confirmed the bold criticism of Mr. Adams.:}: 

 And he affirmed that the necessary elongation of the day by 

 tidal retardation is quite competent to account for the apparent 

 residual acceleration of the moon. 



In 1862 the eminent mathematician, Arthur Cayley, inde- 

 pendently investigated the problem ; and in a paper " On the 

 secular acceleration of the Moon's mean motion," he also cor- 

 roborated the correctness of Mr. Adams' great discovery.§ 



In 1864, eleven years after his first suggestive memoir, 

 Mr. Ferrel returned to the subject of the elongation of our 

 day. In a "Note on the influence of the Tides in causing an 

 apparent secular Acceleration of the Moon's mean motion," he 

 remarks: "At the time of the original publication of Mayer's 

 paper, and also at the time of my own, Laplace's result of 



* Phil. Trans. Roy. Soc, June 16, 1853, vol. cxliii, pp. 397-406. Also Monthly 

 Notices, Roy. Astr. Soc, 1853, vol. xiv, pp. 59-62. And Reply to Objections, 

 M. N., 1860, vol. xx, pp. 225-240, and 279-280. 



f L. E. D. Phil. Mag., June, 1856, vol. xi, p. 513. Also Am. Jour. Sci., 1857, 

 vol. xxiv, p. 212. 



\ Comptes Rendus Acad. Sci., Jan. 17 and April 25, 1859, vol. xlviii, pp. 137, 

 138, and 817-827. Also numerous papers on the subject in succeeding volumes. 

 Especially a paper " On the apparent acceleration of the mean motion of the 

 Moon, due to the actions of the Sun and Moon on the waters of the sea." — 

 Comptes Rendus, 1866, vol. xlii, pp. 197-200, 575-579, 704-707, etc. 



§ Monthly Notices, Roy. Astr. Soc, 1862, vol. xxii, pp. 171-230. 



