358 Prof. G. H. Darwin. On an Apparatus for [Dec. 15, 



it follows that 



P = 0-01564, Q = 0-00114, R == 0-00147, S = O'OlGll. 



Then, when the substitution of the values of If W T) is carried 

 out, we find 



By the definition of 0< T > it appears that 0< T > is the increment 

 of twice the mean moon's hour angle during the time from O d O b of 

 month up to O d O h of month T, that is to say 0W = 2 (7 <r) t for the 

 time specified. The following table gives the values of 0( T > and of its 

 cosine and sine for each month : 



11 335 7T+67 49 -0-378 -0-926 



If cos 6( r \ sin 0< T ) are regarded as quantities having annual and semi- 

 annual inequalities, we may write 



cos 0W = oo + i cos 307 + fa sin 30r + 02 cos 60T + fa sin 60T + . . . . 

 sin 0W = 70 + 71 cos 30r + ^ sin 30r + 72 cos 60T + d z sin 60r + . . . . 



On analysing the numerical values of cos 0W, sin 0W by the ordinary 

 processes, I find, 



o= -0-165, 7o = +0-273, 



1= +0-626, 7l = -0-500, 



fa= +0-756, 1= +0-642, 



2 = +0-159, 7 2 = -0-046, 



fa= +0-199, ? _ +0-166. 



But in 2 the harmonic constituents of g a when analysed for 



