OF ARTS AND SCIENCES : DECEMBER 13, 1864. 381 



accelerated that amount in a century. But as the observed secular 

 acceleration of the moon as determined from the records of ancient 

 eclipses, is only about 11" per century, and this amount of acceleration 

 seemed, at that time, to be almost exactly accounted for by the real 

 acceleration caused by the secular change in the eccentricity of the 

 earth's orbit, as determined by Laplace, so that he inferred that the 

 length of the day had not changed j^^ of a centesimal second since 

 the time of Hipparchus, it was inferred in that paper that, if tidal ac- 

 tion had any sensible effect, it must be counteracted by a correspond- 

 ing contraction of the earth's volume from a gradual loss of heat. 



IMayer, in his interesting paper on Celestial Dynamics, has also 

 shown that the attraction of the moon upon the tides retai'ded by fric- 

 tion, tends to increase the length of the day. He has not, however, 

 attempted to determine the amount of effect produced from any as- 

 sumed form and position of the tidal wave or aqueous spheroid, but 

 assumes that the retarding pressure must be at least one thousand mil- 

 lions of kilogrammes, and upon this hypothesis he determines that the 

 length of the day would have increased -^^ of a second in the last 

 twenty-five hundred years, if the volume of the earth had not changed, 

 and that, if the length of the day has not changed, the radius of the 

 earth must have diminished Aj metres in the same time. Although 

 Mayer's paper was originally published several years before mine, yet 

 as it has only quite recently been brought before English readers by 

 means of a translation published in the London, Edinburgh, and Dub- 

 lin Philosophical Magazine, and also in Silliman's Journal, it was en- 

 tirely unknown to me at the time of the publication of my paper. 



At the time of the original publication of Mayer's paper, and also 

 at the time of the publication of my own, Laplace's result of about 

 11" per century, for the amount of acceleration of the moon's mean 

 motion arising from a secular change of the eccentricity of the earth's 

 orbit, was supposed to be correct, but since that time, it is known, De- 

 launay and Adams, and also quite recently, Mr. Cayley, by separate 

 and independent investigations, have all obtained less than 6" for the 

 amount of secular accelex-ation per century, and it is with reference to 

 its bearing upon this new determination that I especially desired to 

 bring forward the subject at this time. This determination, compared 

 with the most reliable determination of the acceleration deduced from 

 the discussion of the recorded observations of ancient eclipses, leaves 

 about 6" to be accounted for by tidal action, or some other unknown 



VOL. VI. 41 



