146 SECULAR VARIATIONS OF THE ELEMENTS OF 



For the root */= 2".925086, we get, 



0.3697416 



0.3561999 



v/.<^~ . "> TIT/F. 



6=H inTo " ' 9V- K) 10 



588.7466 



ITZ 



IV, . 



10 10 



Whence &=133 55' 52".8 ; and log. JV/ r =6.9405338. 



N 6 =+0.0030841, W T =+0.00087204, 



N t ' =+0.0017851, N, T =+0.00071215, 



JV 6 " =+0.0015998, JV 6 " =-0.0176594, 



^'"=+0.0011424, ^"=+0.0018922. 



For the root </ 7 = 26".117473, we get, 



3026288 , r/r , 0.2224873^ _60.04189 



SBl= ~TO To 7 ; y "~ 10 10 10 10 



Whence /? 7 =306 19' 21".6; and log. iV/ r =7.7962857. 



N, =-0.0002635, ^'" = =+0.00625584, 



JV 7 ' =0.0003035, ^7" : -0.0157362, 



^ 7 " =-0.0027085, NS' =,+0.00068567, 



# 7 "=-0.0092412, W =+0.000076911. 



22. For an increment of + 4 ij7/i 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 i u r =+ ir ; or for ??i r =l-^3416.195. 



^1=^+38.078720.^ +181.976176; 

 4'=0 2 +23.1907166.<H- 98.4490593; 

 ^"=^+18.7198881.^+ 72.8857520; 

 4 1 =/+18.6278118.#+ 61.6540448; 

 J 2 =0 2 +13.3828119.+ 9.178963; 



10:089397. 



(491) 



D =0 2 +44.5181269.#+588.346190 ; 

 D = y 2 +52.0193531.^+605.574324 ; 



D 1=i / 2 +44.4628062^+176.258864 ; 

 /) 2= ^^_47.1787023^+ 33.673551 ; 

 Z> 3 =i/ 2 + 3.4692S99.-7+ 1.72977087. 



(492) 



=^+32.45831 



6; 1 

 . j 



C = j^+22.263602| [9.4381189J6'; 

 C'=- 1<7+17.6256851 1 [9.1138076J&'; 

 C"'=+[0.3976676]6'; 

 C"*=+[0.4411620]&'. 



(493) 



(494) 



