8 



SECULAR VARIATIONS OF THE ELEMENTS OF 



7. We must now substitute the values of b% and the corresponding values of a, 

 in equation (24) ; and change m', successively into m", in'", m ir , &c, and we shall 

 obtain the values of (o,i), (0,2), (0,3), &c, or the coefficient of the action of each 

 of the planets on Mercury. The characters 0, 1, 2, 3, 4, 5, 6, 7, refer respectively 

 to Mercury, Venus, the Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Then 

 changing n into n', and m', into m", ni", &c, we shall obtain the values of (1,2), 

 (1,3), &c, or the action of each outer planet on Venus. And in like manner we 

 shall obtain (2,3), (2,4), (2,5), &c; (3,4), (3,5), &c, or the action of each outer planet 

 on each inner one. We shall then obtain (1,0), (2,0), (2,1), &c, or the action of an 

 inner planet on an outer one by means of the equations (6), (7), (10), &c. 

 In this maimer we have obtained the following results : — 



(o,i) = (l-{y ). 2".9986729 log. 0.4769291 : 



(0,2) = (l+fi" ). 0.8617070 



(o,3) = (l4-/a"'). 0.0279815 



(o,4) = (l+^ jr ). 1.6028375 



(o >5 ) = (l+^). 0.0772642 



(o,e) = (1+^). 0.0013324 



(0,7) = (l-hO. 0.0004603 



log, 

 log 



9.9353596 

 8.4468702 

 log. 0.2048895 

 log. 8.8879781 

 log. 7.1246469 

 log. 6.6629969. 



0.0 



(1+p ). 0". 1758273 

 (l_|y ). 6 .6305873 

 = (l-iv). 0.1020355 

 :(1+/ F ). 4.2028443 

 (l+(i r ). 0.1988873 

 :(l+p w ). 0.0034100 

 ■. (l-\-fi yn ). 0.0011765 



log. 9.2450862 

 log. 0.8215520 

 log. 9.0087513 

 log. 0.6235433 

 log. 9.2986071 

 log. 7.5327484 

 log. 7.0706089 



(2,0): 



0.0 = 



(2,3): 



(».*) = 



(2,6): 



(2,6) 



(2.0 



(1+ff )• 

 (1+^). 



:(l+f. F ). 



: (1+^ J )- 

 :(l+ ( 0. 



0".0406239 

 5 .3310972 

 .2982001 

 7 .0682646 

 .3265163 

 .0055565 

 .0019144 



log. 8.6087813 

 log. 0.7268166 

 log. 9.4745078 

 log. 0.8493128 

 log. 9.5139049 

 log. 7.7447989 

 log. 7.2820328 



( 3 ,o) = (l-hu ). (T.0077700 



( 3 ,i) = (L4y ). 0.4832186 



(8,.) = (l+tf ). 1.7564488 

 (3,4) = (l+ fi IV ).14 .6598964 



(.,.) = (l+f* r - ). 0.6313987 



(3,e) = (l+ 1 a F/ )- 0.0105215 



(a,») = (l+pf). 0.0036105 



log. 7.8904196 

 log. 9.6841436 

 log. 0.2446355 

 log. 1.1661309 

 log. 9.8003037 

 log. 8.0220791 

 log. 7.5575701 



