THE ORBITS OP THE EIGHT PRINCIPAL PLANETS. 151 



For the root 6 = 2".9514286, we get, 





0.3712512 



0.3561690 



_ 



Z - 



584.6008 



Whence &=133 48' 43".9 ; log. JV 6 /r =96.9445043. 



N 6 =+0.0032017 

 Nj =+0.0018341 

 #/ =+0.0016409 

 JV 6 '"=+0.0011616 



Nf =+0.000880044 

 N* =+0.000718986 

 N = 0.0177606 ; 

 JV 6 r "=+0.0018826. 



For the root 7 = 26M183694, we get, 



__0.2996395^ 0.2202906 _57.99673 



HF 10 l "TO 15 ; 



Whence /3 7 =306 19' 22".0 ; log. ^"=97.8070262. 



N 7 =0.00002671 ; N," =+0.00641248 ; 



JVY =0.00031380 ; N, r =0.0155812 ; 



Nj" =0.0027363 ; N 7 " =+0.00069663 ; 



#7= 0.0092366 ; # T " '=+0.000078059. 



24. For an increment of ^m", to the assumed mass of Uranus, we shall obtain 

 the preliminary computations by merely making all the coefficients positive in 

 equations (326-331). We shall then obtain the following 





(503) 



Fundamental Equations for ju"=+ ; or for m= . 



\j && 1 1 y 



A =0 2 +38.068970.0 +181.871338; 

 ^'=0 2 +23.1735927.0+ 98.3308977; 

 ^"=// 2 +18.7132214.0+ 72.8344734 ; 

 ^1 1 =0 2 +18.4995010.0+ 61.4402060; 



A 2 I 1 O OAO^v^OQ ^ I Q 1 .471 Oft 



^^=.n -| io.^uyoo*o.^ | y. i-r 1 1*0 , 

 ^ 3 =0 2 +26.3996602.0+ 10.055139. 



D =^+44.5054401.0+588.063848 ; 

 >'=0 2 +51.9992925.0+604.964956 ; 

 Z)"=0 2 +32.1623093.0+256.0208612; 

 Z> 1 =0 2 +43.9809321.0+175.644437 ; 



Z> 2 =0 ! +46.5212935.0+ 33.556164; 

 Z> 3 =0 2 + 3.4429483.0+ 1.72374142. 



5=J0+32.45043|6; ^ = {0+17.5804200^; ) 5Q5 . 



^={0+13.139086^. j 



C =\g+ 22. 255718J [9.4381 189]tf; 



C' = {^+17.6104269 |[9.1138076]ft'; C5Q6) 



C f "=+[0.3976676]6'; 



C""=+[0.4411620]6'. 



(504) 



