THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



83 



For the root #=2". 762311, we get, 



0.6624109 

 10 10 



' 2/6=- 



0.1988506 

 10' 



_36J..8939 r2 

 Z 6 -^QIO * X 6 " 



Whence &=106 42 1 33".6 ; log. J\V r =7.2812824. 



N s =+0.00056935; N,' r =+0.00191110; 



N s ' =+0.00055240 ; N & r =+0.00175147 ; 



JV 5 " =+0.00057725; N b ri =+0.0299862; 



^'"=+0.00076548; 

 For the root ^=3". 786 209, we get, 



JV r . ir "= 0.00289381. 



X 6 + 



0.4675181 



r 



^'s ; z/o 



0.8555864 



22.61242 



, 



\' 



" 



T _, 



' * 



Whence &=28 39' 12".7 ; log. ^ 7 r =8.6346522. 



N 6 =+0.0258909 ; # 6 /r =+0.0431174; 



JV 8 ' =+0.0169796 ; N 6 r =-\-Q.032356 ; 



N e " =+0.0166303; JV 6 " = 0.0440755 ; 



JV 6 '"=+0.0188976 ; 2V 6 m =+0.0013169. 



For the root gr 7 =22".575980, we get, 



1.004018 , , 0.7872757 



JQ1 



JQ1 



r _ 



"I > Z 7 



79.68195 



10 



io 



Whence /3 7 =308 6' 3".2 ; log. ^ /r = 8. 2044480. 



N 7 =0.0000979; 

 Nj' =+0.0003062 ; 

 JV 7 "= 0.00240674; 

 N,'"= 0.0151034 ; 



38. We shall now suppose that ^"=+^5 and the mass of Uranus will become 



N,' r =+0.0160121 ; 

 N, r =0.0480733 ; 

 N 7 rr =+0.0018317; 

 tf m =:- 0.0001384 



1 i TI 1 

 i r/ =^j~^=HoYTq- Using this value of the mass of Uranus, we shall find, 



A[o7o]= 0".0000666; 

 A[TTT1= 0.0001705; 

 A[UJ= 0.0002778 ; 

 AQ73]= .0005261 ; 



Whence we get, 



{^]=g 5".5703224; 

 OIO=7 11 .3149387; 

 [^}=(jl3. 0724508; 

 [373=^17.5533906; 



[47*1 = O ff .OQ37881; 

 1775]= 0.0139141; 



= _0 .0130554. 



71]=^- 7".5161635; 

 ^\ =g 18. 6101270; 

 7e]=i7 2.7662522; 

 T=^ 0.6610123. 



(326) 



(327) 



