27] OF THE MOON'S MEAN MOTION, ETC. 223 



- mV cos (20 - 3n't) + ~ mV cos (20 - n't) 



425 , . de' 



- - m 2 e' j- sin (20-2n't) 



24 ndt 



and therefore 



\ndt = + 3me' sin n't-~m? ( 1 -- e' 2 ) sin (20-2n't) 



J \ 2 / 



- mV sin (25 - 3n') + iV sin (25 - n't) 



+ 3 cos n't + mV ~ cos (20 - 2') - m* cos (20 - 3n't) 



ndt 24 ndt ' 48 wrf ' 



Hence ^ differs from lwc/< by periodic terms only, which proves the 

 proposition. 



CtTi 



The value of j- above found agrees with that found in my paper 

 published in the Philosophical Transactions for 1853. 



