410 Remarks on the Lunar Theory. 



vantage in my favour is as 30 to 23, even admitting that no im« 

 provement was made in the lunar theory from the time of Hip- 

 parchiis to that of Newton! I therefore contend that an entire 

 period is completed within the limits of 760 Chaldean periods. 

 As I before asserted, the difference produced by the ]) 's accel., 

 even if it was completely neglected as far as the period affects 

 the earth, would only amount to about one hour; and as the D 's 

 accel. is proportional to the square of the time, it would in a 

 complete period amount to but little more than four days only. 



I do not contend that the knowledge of these long periods is 

 a matter of any great importance ; but they evidently convey an 

 idea of the sublimity and grandeur of the celestial motions. Mr, 

 Yeates (at p. SS) has given us a statement of the mean synodic 

 revolutions of the ]) as stated by different astronomers: the 

 mean of the last ten of them, or from the time of H'lppurchus^ 

 amounts to 29 days 12 hours 44 minutes 2 seconds 35 thirds, 

 which differs from the respective results of Messrs. Vince, Gre- 

 gory, Woodhouse, Squire, Young, Lalande, Laplace, Delambre, 

 Biot, Burg, and Burckhardt, by less than one-fourth of a second 

 only ! Mr. Yeates on the opposite page has given four results 

 adduced from his own calculations, the mean of which is 29 days 

 12 hours 44 minutes 28 seconds 9 thirds; the extremes of the 

 above are those of Ptolemy and Whiston, 45 thirds in excess, 

 and 2 minutes 35 thirds in deficiency respectively. Mr. Y.'s 

 mean excleeds the mean of the ten results above referred to, by 

 25 seconds 34 thirds: his difference is therefore 34 times greater 

 than that of Ptolemy in excess ; and Whiston 's difference from 

 the mean result is only about one- tenth part in deficiency of 

 what Mr. Yeates's is in excess 1 There must surely be some 

 subtilty, or something superlatively grand and exquisite, in the 

 calculations of Mr. Yeates, as he differs 34 times in excess, from 

 that of any of those above mentioned, all of them most celebrated 

 astronomers which have existed within nearly the last two thou- 

 sand years ! ! This result is indeed very curious. Had Mr. Y. 

 confined himself to giving a list only of the observed eclipses, 

 divested of those which are inserted from calculations, much 

 verbosity would have been spared, and he might have acquitted 

 himself with credit. The inferences to be drawn from what 

 Mr. Yeates has done, will in no wise refute my assertions ; and 

 in respect to the period of 912 years, I defy him to establish it, 

 or to controvert the contents of my former letter. At page 355 

 he says, " I presume, sir, there is no occasion here to introduce 

 anomalistic calculations of the sun and moon : the mass of evi- 

 dence already produced in the corresponding eclipses at 912 

 years distance, and the eclipses recorded to have happened, show 



?nost. 



