8 



SECULAR VARIATIONS OF THE ELEMENTS OP 



7. We must now substitute the values of #,', and the corresponding values of a, 

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

 obtain the values of (o,i)> (. 2 ), (' 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 ri, and m', into m", m'", &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 manner we have obtained the following results : 



(0,1) = 



(0,7) = 



(2,0) = 

 (2.1)= 



(')= 

 (2,6)= 



(3,0) = 



). 2".9986729 



). 0.8617070 



). 0.0279815 



'). 1.6028375 



). 0.0772642 



r ). 0.0013324 



r O. 0.0004603 



). 0". 1758273 



). 6.6305873 



). 0.1020355 



r ). 4.2028443 



). 0.1988873 



r ). 0.0034100 



r/ ). 0.0011765 



). 0".0406239 



). 5.3310972 



). 0.2982001 



'). 7.0682646 



). 0.3265163 



'). 0.0055565 



r O. 0.0019144 



). (T.0077700 

 ). 0.4832186 

 ). 1 .7564488 

 (,,4) = (1-fy ).14 .6598964 

 (i,. ) = (!+!'' ). 0.6313987 

 (i, e) = (!-{-/'). 0.0105215 

 (3, 7) = (1-|-/"). 0.0036105 



log. 0.4769291; 

 log. 9.9353596 ; 

 log. 8.4468702; 

 log. 0.2048895; 

 log. 8.8879781 ; 

 log. 7.1246469; 

 log. 6.6629969. 



log. 9 

 log. 

 log. 9 

 log. 

 log. 9 

 log. 7 

 log. 7. 



log. 8. 

 log. 0. 

 log. 9. 

 log. 0. 

 log. 9. 

 log. 7. 

 log. 7. 



2450862; 

 8215520; 

 0087513; 

 6235433; 

 2986071; 

 5327484; 

 0706089. 



6087813; 

 7268166; 

 4745078 ; 

 8493128; 

 5139049; 

 7447989 ; 

 2820328. 



log. 7.8904196 ; 

 log. 9.6841436; 

 log. 0.2446355 ; 

 log. 1.1661309; 

 log. 9.8003037; 

 log. 8.0220791 ; 

 log. 7.5575701. 



