15. 



ADDENDUM TO PAPER ON THE SECULAR ACCELERATION OF THE 

 MOON'S MEAN MOTION, No. 4, p. 120. 



[SINCE the sheets of the paper No. 4 were printed off, I have found 

 details of the calculations referred to on p. 127. Start with the equations 



_ ?1 + (<M\ _ I d9 ^\ + I = I m * (i + ? e ' 2 + 3, 



+ - m 2 \ ( 1 - - e'*} cos (20 - 2mt) + -e' cos (20 - 3mt) --e' cos (20 - mt) I , 



2 (\ 2 J Z 2 j 



^dldd = 3 2 f / x _ 5 p/2 \ g . n , 2 ^ _ 2mt . 



at at 2 \\ 2 / ' 



7 1 1 



- e! sin (2^ - 3mt) --e' sin (2^ - mt) V , 



J 



where Z = log(l/r), and for simplicity n has been taken equal to unity, and 

 m = 0'0748013 (1 +/), where f is an undetermined small quantity equal to 

 (lm)8n'/n' of p. 111. We then proceed in the manner of Lecture VII. 

 from an approximate numerical solution. In this way Adams obtained the 

 numbers of p. 127 on Dec. 6, 1859. The work seems to have suggested to 

 him the general method which he outlined in Mon. Not. xxxvin. ; see 

 p. 104; for MSS. of various dates in 1860, 1861, 1863, exist which are 

 preliminary to the developments of p. 108 et seqq. Among them are the 

 numbers below, not included in those developments : ] 



