106 



SECULAR VARIATIONS OF THE ELEMENTS OF 



—(2,2)= — #—13.072173 

 (o,2)(2,i)-^-(o,i)=— 1.531958 

 Sum =— { (/+14.604131 } 

 log. { (o,i)-Ks,i) j = [0.7927855] 

 ThereforeJ w =— jflr+14.604131} X 

 [0.7927855J6'". 



_(i,0=— £— 11.3147682 

 (o,i)(i,»)h-(o,«)= —23.0739263 

 Sum =— { ^+34.3886945 } 

 log. |(o,2)-^-(3,2) | = [9.6907241] 

 Therefore F"'=— \ £+34.3886945 £ X 

 [9.6907241]6'". 



— (6,6)=— £+ 2.7662522 



( 4 ,eX«,B)-K*,«)= + 0.0142946 

 Sum =— | £+2.7805468 J 



log. 1(4,8)^.(7, 5 )| =[1.5514854] 

 Therefore F 3 =— { £+2.7805468 { X 

 [1.5514854]6 4 . 



— (o , 5)=_ £—18.5962129 

 ( 4 , 5 )(o,6)-K4,6)= —27.1673827 

 Sum =—{£+45.7635956} 

 log. {(*,6)h-(7,6)| [9.4626364] 

 Therefore .F 4 =— |45.7635956+£| X 

 [9.4626364]& 4 . 



=_ 0.0350059.y 2 - 

 = _ 0.0002174.£ 2 - 



Computation of the Equations of the fourth degree. 



=— 35.3483155.£ 2 — 817.363351.£— 3456. 



=— 0.5237732.£ 2 — 8.843924.£— 33. 



=— 0.5272484./— 16.147000.£— 120. 



=— 0.0493054.£ 2 — 0.919173.£— 3. 



- 1.010537.£— 6. 



- 0.005302.£— 0, 



- 1.910880.0— 10. 



- 1.615446.£— 28. 



- 0.004755.£— 0. 



- 0.003993.£— 0, 

 + 0. 

 + 0. 

 + 0, 



— 



— 0. 



— 0, 

 Sum of preceding terms =— 36.4838658.£ 2 — 847.824361.£— 3659. 



Add (0,0)(l,l)(2,2)( 3 ,3) = 



£ 4 +47.5100615.£ 3 +809.5847278.£ 2 +5804.515976.£+14461. 

 Sum is the value of equation (53). 

 Whence we get 



£ 4 +47.5100615.£ 3 +773.1008620yi 

 +4956.69l615.£ +10801.93370 j 

 In like manner we get 



- ( 2 



00.«)( 



0,o)(3,3) 



- (3 



.)(.,.)( 



o,o)(i ,1) 



- 



o)(o,i)( 



2,2)(3,3) 



- ( 3 



*)(}•')( 



0,o)(2,2) 



- ( 2 



o)(o, 2)( 



1 ,l)(3,3) 



- ( 3 



o) (0,3)1 



i.0(«.») 



+2(3 



2 )( 2 .\)( 



1,3) (0,0) 



+2( 2 



o)(o,i)( 



1 , 2)(3 , 3) 



+2(3 



00.°)( 



0,3) (2, 2) 



+ 2(3 



o)(0,2)( 



2,3)(l,l) 



+ 



o)(o,i)( 



3,2)(2,3) 



+ ( 2 



0M< 



3,o)(o,3) 



+ ( 2 



o)(o ,2)1 



3,l)(l ,3) 



— 2(3 



o)(o,i)( 



1 , 2) (2 , 3) 



—2(3 



00.°)( 



0,2)(2,3) 



— 2(3 



0)(0,2)| 

 prprhn 



2,l)(l,3) 

 T tpi'lTlK 



144265 



01142 



97930 



59019 



95240 



03216 



64409 



35570 



06216 



04518 



27616 



00768 



00173 



09214 



04366 



00728 



67438 



60808 



<Z'Zn Z*> Z>)- ( 369 ) 



( s 



4)(4 



5 )( 6,6 )( 7 ' 7 ) 



(c 



•)(« 



6 )( 4 ' 4 )( 7 ' 7 ) 



(7 



0(« 



7)(4, 0(5,0 



( G 



4)(4 



6)(5,5)(7,7) 



(7 



00 



7 )( 4 ' 4 )( 6 ' 6 ) 



(7 



0(4 



7 )( a ' 5 )( 6 ' 6 ) 



=—134.9642669.£ 2 —460.796228.£— 241.911599 

 = _ 0.3883479./— 3.169047.£— 1.890359 

 =— 0.1131268./— 2.953581.£— 15.804014 

 =_&. 0.0710140,v 2 — 1.366608.£— 0.855687 

 = + 0.0142805..7 2 — 0.146774.£— 0.296764 

 = _ 0.0043007.£ 2 — 0.091874.£— 0.221237 



