THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 

 For the root ^ 6 = 2". 7 265 18, we get, 



89 



0.6486453 

 ~10' 



0.1822083 

 - 10 w 



337.9588 



Whence .=105 41' 25".3 ; log. #"=7.2996358. 



N & =+0.00058277; #'"=+0.00199359; 



jV 5 ' =+0.00057135 ; # r =+0.00181568 ; 



#" =+0.00059807 ; # rf =+0.0292788 ; 



#'"=+0.00079643 ; #"'= 0.0030292. 



For the root j7 =3".725131, we get, 



. 0.4579378 . 0.8593662 r 22.55046 n 



*e=H YO> ' y = ~l io 10 " 8 ' 2<i= "lo 10 6 ' 



Whence ^,=28 3' 7".9 ; log. ^ c /r =8.6352986. 



JV a =+0.0246773; N,' r =+0.0431816 ; 



NJ =+0.0166620 ; N, r =+0.0340853 ; 



JV e " =+0.0163874; JV 6 "= 0.0444971 ; 



^"'=+0.0188199 ; JV 6 m =+0.00154190. 



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



__1.010_089 /F 0.7868583 



- y, ; 2/7+- iow 



81.93419 



/FJ 



' 



1Q10 *-'7 ' ill I .1010 1Q10 



Whence &=307 55' 6".8 ; log. #'"=8.1938807. 



# =0.0000972; # /F =+0.0156272; 



#' =+0.0003152 ; #" =0.0483433 ; 



#"=0.0023732; #"=+0.0018046 ; 



#'"=0.0149913 ; #""=+0.0001357. 



40. We shall now suppose ^ r ":=-\-^ 5 ; and the mass of Neptune will become. 



'" ii" _ Using this value of Neptutie's mass, we shall find, 



~18780~ 17072.73 



A[oTo]= 0".0000460; 

 A|T7n= 0.0001177; 

 A^3= 0.0001914; 

 A{TT3]= 0.0003611; 



Whence we get, 



[oTo]=? 5".5703018; 

 [TTTj=<? 11 .3148859; 

 [273 =^13.0723644; 

 [775] =(7 17.5532256; 



pTTT|= 0'.0024017; 

 [IT?] =:_(). 0068740; 

 jTTJ] = 0.04333257; 



rrri= o. 



T4]=4 7".5147771 ; 



*7J]=^ 18.6030869; 



3=^~ 2.8095779; 



77= 0.6479569. 



(345) 



12 December, 1871. 



