THE ORBITS OF TEE EIGHT PRINCIPAL PLANETS. 



65 



For the root </ 4 =0".6166870, we get, 

 , 3.35791 2 



x * — H jqio ; Vi — + 



Whence &"=67° 56' 42".3 ; log. N t ir z 

 JV 4 =+0.000007676 

 ^'=+0.000011687: 

 iV 4 " =4-0.000013561 

 iV 4 '"=+0.000021841 



For the root f7 5 =2".7277089, we get, 

 , 0.6477216 



1.360959 _56997.71 



10"™' Z4— ~10 lu * 

 =95.8032384. 



N/ r =+0.000063565; 

 AY =4-0.000071695; 

 AY' =4-0.00155764; 

 iV 4 r "=+0.01003850. 



°~ i l()io 



Whence /? 8 =105° 6' 59". 3 ; log. 

 JV 5 =+0.00055404 

 JV 6 ' =4-0.00054913 

 iV 5 " =+0.00057941 

 iV 5 '"=4-0.00077160 



iVV r = 



0.174 9684 



— W° ; 

 97.2882538. 



345.4842 



tf/" =+0.0019420 



N 6 r =4-0.0017682 

 JV 5 " =+0.0297289 

 iV 5 r/ = -0.00290997. 



For the root ^=3". 7 172386, we get, 



_ 0.4583439 _ , 0.8566511 _22.50983 



X{i ' io 10 ' ^° — ' 10™ ; z% — io T ° — 



Whence /? 6 =28° 8' 55". 1 ; log. iV 6 /r =98.6350978. 



N 6 =+0.0233180; N 6 IV =+0.0431616 



JV 6 ' =+0.0162078 ; N 6 r =+0.0341038 



N: =+0.0161491 ; NJ 1 = -0.0448343 



iV 6 '"=+0.0186903 ; ^"'=+0.00141840. 



For the root # 7 =22". 46 11216, we get, 



1.009450 



v--- 



0.7872062 



7— 10 10 



Whence /3 7 =307° 56' 54".3 ; log. N/ 

 N 7 =—0.00011217; 

 N,' =+0.00051216; 

 iV 7 "=— 0.0024585; 

 N'"=— 0.0155133; 



81.85450 



10 10 ' 7 

 :98.1942049. 



^=+0.0156388: 

 N 7 T =—0.0483500: 

 N 7 n =+0.0018057; 

 iV 7 "'=+0.0001 3650.' 



32. We shall now suppose u" 



Using this mass, we shall find, 



A|T^=— 0".Q279815 

 A(T7T] =— 0.1020355 

 A[7j0=— .2982001 

 A[iTJ]= 0. 



9 November, 1871. 



=+1 ; and the mass of Mars will become, 



. 1 + 1 _J 



2680637 - 1340318.5" 



A|TT] = _ 0".0031027 

 AE3=— 0.0003297 

 ART^=— 0.000Q275 

 AQTT]=— .0000057. j 



\- (269) 



