4] THE SECULAR ACCELERATION OF THE MOON'S MEAN MOTION. 127 



.(- ,2348,30) 





M O = 1-00280,21804 ^ = -'00008,57021 



w a = <?'(- -02000,72) #, = /(- '00057,37) 



.,= "02159,9810 p 5 = '00839,2060 q 



M 8 = e'(-09111,95) p s = e' ('03096,86) 



Ui = ef (--01360,74) p s = e' (- '00579,81) 



' (- '00004,59) 

 '00839,1893 

 e' ('03096,70) 

 e'(- '00579,85). 



in -~ , &c. may be derived 



[The MS. in which these numbers were derived has not been found ; 

 the Variation terms will be found to agree closely with the more accurate 

 values of p. 106 ; the coefficient />, is comparable directly ; a and 5 may 

 be found by forming log l/r ; u a and u t shew that /u, is taken equal to 

 unity ; the errors are in the eighth place of decimals. The terms in e' 

 may have been found by the method of Lecture X. ; they are somewhat 

 more correct than the values there given ; the terms in e'- would result 

 from a second application of that method ; they appear to be far more 

 correct than can be found by transformation of e.g. Delaunay's expression 



for the longitude. The coefficients of j 

 from the results of p. 113; e.g. we have 



d r = -OL (0'00157,0744) = ! (0'00157,0744) 

 dt n'dt ^ lm mat ^ 



= -^(0-00169,7737).] 



We now observe that the coefficients given by the non-periodic term 

 and the coefficients of cos 2^, sin 2f involve e' 2 as the lowest order, while 

 all the rest involve e' in the first power and after that the cube and 

 other odd powers. Clearly we may omit from our equations all terms 

 except those of lowest order. 



