THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 121 

 For the root # 6 = 0".661636, we get, 



; 



10' HP 



Whence /3 5 =20 32' 21".0 ; and log. JV 6 ' r =7.0792052. 



N, =+0.001482, N b ' r =+0.00120007, 



NJ =+0.001362, JV7 =+0.00115846, 



N," =+0.001333, N, TI = 0.00112554, 



JV 6 '"=+0.001260, N= 0.0117964. 



For the root # 6 = 2".916041, we get, 



0.3540483 _ 581.3949 



-^*6 ^6 "in " 



_ 0.3683810 



To 



IO 10 IO 10 



Whence /? 6 =133 51' 48".4; and log. N^ =6.9438946. 



N, =+0.003247, N t " =+0.0008788, 



N t ' =+0.001900, N t r =+0.0007174, 



JV 6 "=+0.001679, &"= 0.0176820, 



^ 6 F// =+0.0019005. 



59.03124 



For the root g 7 = 25".934657, we get, 



0.2996641 , , 0.2202989 



10 



,10 



Whence /3 7 =306 19' 17".6; and log. ^V/ r =7.7993764. 



N 7 =0.000265, N, ir =+0.00630052, 



Nj' =0.000287, N 7 r =0.0156923, 



JV T "= 0.002741, N," =+0.0006891, 



^'"=0.007355, J /V 7 m =+0.00007720. 



12. For an increment of ^, in the mass of Venm, we have the preliminary com- 

 putations by merely making all the coefficients positive in equations (193-208). 

 We shall then obtain the following 



Fundamental Equations for ^' = +-_; or for m'= ^. 



20 o714^8.o 



A =^+38.4851145.^+188.270582; 

 ^'=^+23.3470945.^+101.1013581 ; 

 ^1"=/+18.9541253.#+ 75.3044562; 



60.3282264; 



8.981600; 

 ^ 3 =/+26.3821932.^+ 9.882701. 



D =^^45.3182858.^+610.942268 ; 

 J>'=/+53.1764531.#+626.087193 ; 

 D"=/+32. 4522201.^+261. 0475918 ; 

 ^=^+43.8987079.^+1 72. 4631 15 ; 



Z> 2 =^ 2 +46.4943490.^+ 32.948389 ; 

 Z> 3 =^+ 3.4291807.^+ 1.69252138. 



(431) 



(432) 



16 February, 1872. 



