16 



SECULAR VARIATIONS OF THE ELEMENTS OF 



_ { ezw jM±Df" 



inn] E3 



e= Pa/,-Bdi/* 

 1 n3 ei] 



1M HZ] 



N' = 

 N" = 

 N'"= 



AN+f . 



!E3-EI]^ 3 

 lES-ES^"' 



• \ezi cm] i . 



' I EH] E3J 



, jEZ] EZU_fl^ 



• IE3 E3l 



• IEZ1 EZ]J 



_ { ^]_E3 1 ^ 



■ =(Z4>Z5 5 Z6 ) %7);( 56 ) 





N" = 

 N'"= 



A'N+f" . 



JES-EZ]^'" 

 ?EZ]-[E3!£" 



(57) 

 (58) 

 (59) 



EZE^/'-tZIJEZJA/^lIZlEZlffr -EZEA/" 

 EZl EZ1 AD '— H3 EUD ^'^ E3 E3 ^"^"— EH] E3 ^° 



"" E3EZ]AT-En]EZ]A/" r 



"EZJEZ]^ ' — h 2 !! - 1 !^"^" 



(60) 



2T = 



A^ /r +/i 



N VII = 



iezkezua 



A^ F +/s 



~?E3-[I3!A : 



{EZH-EUIA 



N TI =-, 



A 2 N 2y +A 



IEZH-ESIA 



"{E3-M-7EIA 



HEZREZHA' 



(61) 

 (62) 

 (63) 



ri3mi]A/2 - EZEA/i ^ E3EZ3A/4 -EZEA/3 

 -E73EZ1AA-E3E3AA EZ1EZ1AA-E3EZ1AA 



fjZmiJA/o-EIIlCI^A/a 

 -E3EZ]^iA-EZ]E3-4A 



(64) 



11. Equations (53) to (64) are entirely rigorous. They are, moreover, under a 

 very simple and convenient form for the computation of N', N", N"\ &c. ; and, as 

 there are duplicate and independent formula? for all these quantities, any error that 

 may accidentally creep into the computation of one formida is at once detected by 

 computation of the other. They have also this additional advantage: sometimes 

 one of the formula? for N, N', N", &c, gives value for these quantities of the form 



