136 



SECULAR VARIATIONS OF THE ELEMENTS OF 



For the root 6 = 2".9160771, we get, 



, 0.3678168 0.3545173 

 x '= + - Tmo . 2/6= 



581.0884 



Whence #,=133 56' 42".7 ; log. N 6 ir =96.9440543. 



#.=+0.0030457; N 6 ' r =+0.0008812 ; 



JN,' =+0.0017834 ; N r =+0.00071774 ; 



JV 8 "=+0.0016079; JV 6 r/ = 0.0176842; 



^'"=+0.0011581; 

 For the root 7 = 25".9350099, we get, 



85,= 



0.2996051 



7=+ 



0.2202944 



NJ"= 0.0018963. 



59.02778 



1Q10 y I 1010 JQ10 



Whence /3 T =306 19' 35".l ; log. JV/ r =97. 7993434. 



NI =0.0002735; N 7 ' r =+0.0063000; 



JV/ =0.0001463 ; N 7 r =0.0156907 ; 



N 7 "= 0.0027849 ; JV/' =+0.0006888 ; 



JV T W = 0.0093834 ; JV 7 "'=+0.00007719. 



18. If we now suppose the mass of Mars to be doubled, we shall have the pre- 

 liminary computations by making all the coefficients of equations (269-274) posi- 

 tive. We shall then obtain the following 



Fundamental Equations for /'=+!; or for m"'=l-=-1340318.5 



^=^+38.394808.^ +184.259392; 

 A=f+ 23.2280108.^+ 98.9712014; 

 ^"=^+18.8430013^+ 73.7719022; 

 A=^+18.41 11446.0+ 60.3416523; 

 ^ 2 =(f +13.1958172.0+ 8.983726; 

 A,=0 2 +26.3853904.0+ 9.939432. 



(467) 



D =0 2 +44.9052274.0+596.989960 ; 

 D =0 2 +52. 1576683.0+608.070284; 

 J D"=0 2 +32.4642145.0+260.9092264 ; 

 D 1 =0 2 +43.8990384.0+172. 465387 ; 

 Z) 2 =0 2 +46.4946594.0+ 32.948855 ; 

 Z>,=0 2 + 3.4292114.0+ 1.69255259. 



B= \ .7+32.74835 1 b ; B= ^+17.6069231 \ b 



(4GS) 



C = 10+22.553639| [9.4381 189]6'; 

 C'= 10+17.6669357|[9.1138076]6'; 

 C"=+[6.3976676]6'; 

 C rw =+[0.4411620]i'. 



(469) 



(470) 



