418 



MEMOIRS OP THE AMERICAN ACADEMY 



If we put y 



2p' 



J* 



P 



or in Laplace's notation 



2n' 



n 



n 



, and recollect that 



Wt' 



need the formula) only for the case of an inferior perturbed by a superior 



planet; and moreover make 



7 



jw> 



H, and 7 £ (2) 



I& and G m being Laplace's symbols ; we shall have 



// 



t 



2/(7 



1 



/ 



I 



y 



&.e+i 



Hy + 8/ 



(2) 



2 



a 



7 



da 



+ 



1 



4 .(2) 



a o 



r * 



y 



<2) 



j 



2<l-/>{ (3 





4 



8 



J 



/ 



a) 



a> 

 1 d*b. 



l a dJ h 



3 



If, in the next place, K and ft are derived from the equations 



K cos (j8 

 K sin (0 



^Tsin <p — t/sin qo' cos (jt' 



«7*sin cp' sin (V 





the inequality in longitude we are computing is 



m 



Xsin [L — 2 £' + /?] 



5" and J may be regarded as functions of a, and are positive between the limits 



iponding to ^ = 550" and p 



650 



The common logarithms of these quan 



tities are here tabulated for every 0.001 of a between the limits above mentioned ; 

 the values of b k and b h and their differentials were obtained from Eunkle's Tables 

 of the Coefficients of the Perturbative Function. 



0.595 

 .596 

 .597 

 .598 

 .599 



log 77. 

 0.3153369 

 .3165277 

 .3177113 



.3188875 



.3200561 



log/. 

 9.871828 

 .873131 

 .874420 

 .875695 



.876956 



0.605 

 .606 

 .607 

 .608 

 .609 



log//. 

 0.3269054 



.3280187 



.3291236 



.3302199 



.3313075 



log J. 



9.884214 



.885370 

 .886511 

 .887636 

 .8887*5 



.600 

 .601 



.602 



.603 



0.604 



. .3212173 

 .3223707 

 .8235163 

 .3246540 



0.3257838 



.878202 

 .879434 

 .880652 

 .881855 

 9.883043 



.610 

 .611 

 .612 

 .613 

 0.614 



.3323864 

 .3334562 

 .3345169 

 .3355683 

 0.3366103 



.889836 

 .890910 

 .891967 

 .893007 

 9.894030 



