THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



89 



For the root £ 5 =2".726518, we get, 



0.6486453 0.1822083 337.9588 



- ■ 1Q I0 -a . if»— 1Q 



Whence /? 5 =105° 41' 25".3 ; log. ^"=7.2996358 

 JV 5 =+0.00058277 

 iV 5 ' =+0.00057135 

 N 6 "= 4-0.00059807 

 ^"=+0.00079643 



i\V =+0.00199359; 

 NJ =+0.00181568; 

 iV 5 " =+0.0292788; 

 W'=— 0.0030292. 



For the root g 6 =S". 725131, we get, 



0.4579378 



y« 



.. 0.8593662 



: T" jqio -*V 



22.55046 



10 10 ' 



Whence ^=28° 3' 7".9 ; log. N 6 ,v =8.6352986. 



JV a =+0.0246773 

 iV 6 ' =+0.0166620 

 iV " =+0.0163874 

 JV "=+0.0188199 



For the root <7 7 =22".4729002, we get, 



+0.043 IN 16 

 N/ =+0.0340853 

 N a VT =— 0.0444971 

 JV 6 ""=+0.00154190 



1.010089 

 10 10 



•• — , 0.7868583 , r 



81.93419 



N' 



j (110 -"7 



Whence ,J 7 =307° 55' 6".8; log. iV/ r =8. 1938807. 



N 7 = -0.0000972 ; N/ F =+0.0156272 ; 



N 7 T =—0.0483433 ; 

 iV 7 " =+0.0018046; 

 ^V 7 r "=+0.0001357. 



Nj' =+0.0003152 

 iV 7 "=— 0.0023732 

 ^"=—0.0149913 



40. We shall now suppose ^"'=+^5 and the mass of Neptune will become 

 18780 17072.73 



Using this value of Neptune's mass, we shall find, 



A[^T]=— 0".0()00460 : 

 A(TTT] = — 0.0001177; 

 A[^\=— 0.0001914; 

 Ar?771=— 0.0003611; 



Whence we get, 



[°Z]=#— 5".5703018; 

 HID =9— H.3148859; 

 [TJ\ =7—13.0723644; 

 M =</— 17.5532256; 



A[TT]=— C.0024017; 

 AQ7±]=— 0.0068740; 

 A^l =— 0.04333257: 



ApTT| = 0. 



(345) 



\H±\=g— 7".5147771 ; 1 

 \EH\=9— 18.6030869; [ 



\±Zl=g— 2.8095779; 

 GZ1=^— 0.6479569. 



12 December, 1871. 



