THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 121 



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



0.1018241 0.2719087 24.19508 



' io° ' u — ' io 10 * 5 — — fo 1 — 6 ' 



Whence /? 5 =20° 32' 21".0; and log. i\y r =7.0792052. 



iV 6 =+0.001482, N 6 1V =+0.00120007, 



N>' =+0.001362, JV 5 r =+0.00115846, 



iV 5 " =+0.001333, N b ri =-0.001 12554, 



iV 5 '"=+ 0.00 1260, iV 5 "=— 0.0117964. 



For the root g B = — 2".916041, we get, 



0.3683810 0.3540483 581.3949 



1 J ()io -"a i I/a — jqio ly e > z o — Jqio iv 6 • 



Whence &=133° 51' 48".4; and log. N 6 ' r =6.9438946. 



jV 6 =+0.003247, N 6 ' r =+0.0008788, 



JV 6 ' =+0.001900, N 6 r =+0.0007174, 



iV/ =+0.001679, iV 6 r '=— 0.0176820, 



iV 6 " =+0.001 166, N™ =+0.0019005. 



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



0.2996641 0.2202989 _ 59^03124 



'— 10 !0 "I . ^7 — ^ 1()1 o «t ' -7— Jq 



Whence /? T =306° 19' 17".6; and log. iV/ r =7.7993764. 



N 7 =—0.000265, N/ r =+0.00630052, 



N,' =—0.000287, N 7 V =—0.0156923, 



N 7 "=— 0.002741, #/' =+0.0006891, 



iV/"=— 0.007355, ^"'=+0.00007720. 



12. For an increment of ^l, in the mass of Venus, 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 «fs=-| ; or for m = 



i J F -r 20 > J 371428.6 



A =^+38.4851145.^+188.270582; 

 ^'=^+23.3470945.(7+101.1013581 

 ^"=(/ 2 +18.9541253.r7+ 75.3044562 

 ^=^+18.4082271.^+ 60.3282264 

 A= i / 2 +13.1929198. i 7+ 8.981600; 

 _4 3 =(7 2 +26.3821932.(7-|- 9.882701. 



B =^+45.3182858.(7+610.942268; 

 /y =^+53.1 764531. </+626.087193; 

 Z>"=^ 2 +32.4522201.(7+261. 0475918; 

 A=^ 2 +43.8987079.(7+172.463115; 



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

 D 3 =g~\- 3.4291807.^+ 1.69252138 



16 February, 1872. 



(431) 



i (432) 



