THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



For the root g,= 2".9160954, we get, 



0.3679185 0.3544211 



x o -J~ 10 , ^Vo ; y t - 1() 



y^~ ihio -tv a 



581.1008 



Whence $,=133 55' 46".2; and log. ^'==6.9440507. 



JV; =+0.0030592, JV7" =+0.00087912, 



W =+0.00 17767, JV/ =+0.00071774, 



N: =+0.0015913, JV a w =-0.01 76843, 



.^=4*0.0011505, _# 6 rj/ =+0.00190064. 



For the root g-= 25".936797, we get, 



0.2995996 vrlr , 0.2201126 



/V . . - /\/ * r - 



7 ~ "To 1 " ^ 7 



' TVT_^. 7 T =+- 



59.01481 

 10' 



Whence /3 7 =306 18' 15".6 ; and log. ^/ F =7.7993080. 



N, =0.0002579, N 7 ir =+0.00629953, 



Nj' =0.00030335, N 7 T =0.0156858, 



JV 7 "= 0.00256615, N," =+0.00068848, 



#/"= 0.0092794. ^ ra 



D =^ 3 +44.6 177028.^7+590.564857 ; 

 17=, 7 2 +52.1872233. i 7+610.731488 ; 

 J D"=/+32.3787870.( 7 +259.4006143; 

 Z) 1 =^ 2 +44.0905279.7+173.591533 ; 

 Z> 2 =<7 2 +46.6785882..7+ 33.163967; 

 Z> 3 =<7 2 3.4403421. ' 1.70359455. 



J3=jflr+32.52083}5; 5' = ^+17.7264928^; 1 



B"= ^+13.180944 1 b. \ 



C = {^+22.326122 } [9.4381 189]6'; 

 C'= j7+17.7564991 } [9.1138076]^; 

 <7"=+[0.3976676]6'; 

 (7"'=+[0.4411620]&'. 



20. For an increment of + T 7 , to the mass of the Jupiter, we shall obtain the 

 preliminary computations by merely making all the coefficients positive in equations 

 (280-293). We shall then obtain the following 



Fundamental Equations for fj. ir =-\ ; or /orm /r =l-4- 



^=^+38.155337.^ +182.786001; 

 A =# 2 +23.3356274.#+ 99.4308553 ; 

 ^"=<7 2 +18.7710411.(7+ 73.2781865; 



60.7217122; 



9/040174; 



9.944072- 



(479) 



(480) 



(481) 

 (482) 



