21] ON THE SECULAR VARIATION OF THE MOON'S MEAN MOTION. 147 



95 95 



or 3 30 = m 







= .'. a 16 = 3m 3 



21 

 14m 2 3^33 m 2 = 0, 



o 



133 133 



or 3a st = -m 3 .\ a 33 = -> 



19 19 



or 30* = m- .'. a^=-m\ 



11. In order to obtain the relation between a and a t , we must sub- 

 stitute the value just found for aSu, in the same equation, and equate to 

 zero the non-periodic part, observing that the terms 



12 I dv \ ( 1 - - e"> } sin (2v - 2mv) +-e' sin (2v - 2mv - c'mv) 

 a , J l\ 2 / 



- e' sin (2v 2mv + c'mv) Y a 8 



give 



12m 2 fj n J95 ^ e'de' _ 93^ ^ e'de' _ 19 ^ eW\ 



96 m ndt] 



u 



285 m 4 f T e'cfe' 

 = -- In at j- nearly, 



4 a, J Ticfc 



285m 4 , , . . ,. 



= -- -- e as their non-periodic part. 

 8 a 



Also the terms 



15m" f , e'de'ndt /r> . 21m 2 (, de' ndt , , , 



M" TT -j-cos(2i/-2mi')-- cZv r: -j- cos (2i/-2mv-c'mj/) 



2 a, J ncft S/ 7 4 a, J a dv 



m 2 f , rfe' ncZ< /r> , x 



.!!L\dv r -r- cos (2v - 2mv + c'mv) 

 a, J ndt dv 



+! 



192 



