THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



141 



For the root O = — 2".9160954, wc get, 



0.3679185 __„ 0.354 4211 „„ 



x u — i ln'.o -"o > iln — iaio -"a 



581.1008 



10 :o ■«■ , jo— 10 , *.. . -o— 10 „ 



Whence &=133 55' 40".2; and log. iV/ =6.9440507. 



JV e =+0.0030592, JV 6 "' =+0.00087912, 



Jft ==+0.0017767, JV 6 r =+0.00071774, 



_ZV 6 "=+0.0015913, W =—0.0170843, 



_ZV '"= +0.00 11505, iV r// =+0.O01900(34. 



W 



0.2995996 __,_ 



59.01481 



For the root T =— 25".936797, we get, 



0.2201126 



10 10 "' 7 ' " 7 ~ '" 10 10 

 Whence /3 7 =306° 18' 15".6 ; and log. iV/ r =7. 7993080. 



JV 7 =—0.0002579, JV/ r =+0.00629953, 



iV 7 ' =—0.00030335, iV/ =—0.0156858, 



iV 7 "=— 0.00256615, JV 7 r ' =+0.00068848, 



JV 7 '"=— 0.0092794. JV 7 " =+0.000077149. 



20. For an increment of +yj-^, to the mass of the Jupiter, wc shall obtain the 

 preliminary computations by merely making all the coefficients positive in equations 

 (280-293). We shall then obtain the following 



Fundamental Equations for ,«" = + • or for in IV =l -5-1037.504. 



A =0 3 +38.155337.0 +182.786001 ; 

 A'=g*-\-2S. 3356274.0+ 99.4308553 ; 

 4=:0*+18. 7710411.0+ 73.2781865 ; 

 4 1 =0 2 +18.4811418.0+ 60.7217122; 

 A=r/+13.2441783.0+ 9.040174 ; 

 ^3=^+26.5649511.0+ 9.944072. 



D =^+44.6177028.0+590.564857 ; 

 Z>'=0 2 +52.1872233.0+61O.731488; 

 Z>"=0 3 +32.378787O.0+259.4OO6143; 

 Z>,=0 2 +44.O9O5279.0+173.591533 ; 



Z>.,=0 2 +46.6785882.0+ 33.163907 ; 

 Z> 3 =0 2 + 3.4403421.0+ 1.70359455. 



B' = J0+17.7264928 16;1 



.B= 1 0+32.52083 J Z>; 



B'z= 1 0+13.180944 } b 



C =—j 0+22.326122 1 [9.4381 189]ft'; 1 

 C =—{0+17.7564991 }[9.1138076]6'; ( 



C"=+[0.3976676]Z/; 

 C""= + [0.4411620]V 



(479) 



(480) 



(481) 

 (482) 



