36 



By integration, 



t ="— ^ (v — 2e sin (►— t)) which requires no correction, as the 



origin of t is arbitrary. 



The above is relative to the moon about the earth ; but if we 



suppose f and a to be the same quantities relative to the earth 

 about the sun, or rather the sun about the earth as v and a are 

 relative to the moon about the earth. 



.=4 



supposing the earth's orbit without excentricity and S (the mass 

 of the sun) very great in comparison of M. 



3 3 



Hence ^ {» — 2e sin (c— t)) = -^ 



, . a" S' Perindic lime moon , / 1 r>\ 



or makmg; m — — — - — ^ ," -r— — -n nearly (19) 



o I ,,i Furwdic time earth ■' ^ ' 



D = m V — 2 em sin (v— t) 



Having thus obtained approximate values of u and " in terms 

 of y, we proceed to find the approximate values of P and R 

 for substitution in the equation (c) 



In the preceding figure E, P and S represent the places of the 

 earth, moon and sun. 



SE = a; EP =la:i SEP = >-^ 



u 



The attraction between S and E will be represented by ^y-^, the 



mass of the earth being neglected in comparison of that of the 

 sun. 



