146 SECULAR VARIATIONS OF THE ELEMENTS OF 



For the root g 6 =— 2".925086, we get, 



0.3697416 



N 6 IV ; y,=- 



0.3561999 



N ir - z 



588.7466 



N> 



1Q10 ^'6 > oe — 1010 — « ' ~» 10 10 



Whence #,=133° 55' 52".8; and log. iV/ r =6.9405338. 



N 6 =+0.0030841, jV/ r =+0.00087204, 



W =+0.0017851, N 6 7 =+0.00071215, 



N e " =+0.0015998, N™ =-0.0176594, 



^'"=+0.0011424, JV™=+0.0018922. 



For the root g,=— 26". 11 7473, we get, 



0.3026288 A7Jr , 0.2224873 „ m _ 60.04189 



«H== W o & n 2/r=H io 55 7 ' 7_ 10 10 7 * 



Whence /3 7 =306° 19' 21".6 ; and log. JV/ r =7. 7962857. 



N 7 =-0.0002635, iV/ r =+0.00625584, 



JV"/ =-0.0003035, N/ =-0.0157362, 



JV 7 " =-0.0027085, # 7 W =+0.00068567, 



JV 7 "'=-0.0092412, JV™=+0.000076911. 



22. For an increment of -\-fr>m r , to the assumed mass of Saturn, we shall obtain 

 the preliminary computations by merely making all the coefficients positive in 

 equations (307-312). We shall then obtain the following 



Fundamental Equations for p 



-+JL; or for m r =l-^-3416.195. 

 "^40 J 



^=^+38.078720.^ +181.976176; 

 ^'=^+23.1907166.(7+ 98.4490593 

 ^"=# 2 +18.7198881.0+ 72.8857520 

 ^=^+18.6278118.^+ 61.6540448 

 ^ 2 =0 2 +13.3828119.#+ 9.178963; 

 ^3=^+26.5724027.^+ 10:089397. 



D =^+44.5181269.^+588.346190 ; 

 D =y 2 +52.0193531.^+605.574324 ; 

 D"=0 2 +32.1854533.#+256.3822746; 



^=^+44.4628062.^+176.258864 ; 

 Z> 2 =< 7 2 +47.1787023.#+ 33.673551 ; 

 i> 3 =(/ 2 + 3.4692599.^+ 1.72977087. 



(491) 



(492) 



5=^+32.45831 } b; £' = f#+17.5956788}&; 1 (493) 



S» = {o+13. 143888 16. i 



\9+ 



C =_|^+22.263602^ [9.4381189]6'; 

 C =_ {0+17.6256851 } [9.1 138076]Z>'; 

 <7"=+[0.3976676]&'; 

 C"'=+[0.4411620]6'. 



(494) 



