THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 131 



For the root 6 = 2".916080, we get, 

 , 0.3678561 , 



0.3544989 



tftr. 



-i'R , Z,; 



581.0130 



Whence /3 6 =133 56' 26".3; and log. #,"=6.9441240. 



N e -=+0.003086, N a " =+0.000879273", 



JV 6 ' =+0.001797, N 6 V =+0.000717874, 



# 6 " =+0.001615, N 6 ri = 0.0176858, 



JV 6 '"=+0.001157, # r "=+0.00190082. 



For the root 7 = 25".934782, we get, 



0.2996357 



. 



N"; 2/ 7 = 



0.2203002 



59.02984 



Whence /3 T =306 19' 27".6 ; and log. JV/ r =7.7993611. 



JV 7 =0.0002690, N, ir =+0.00630030, 



NJ =0.0002227, N 7 T =0.01569181, 



^"=0.0027550, N, =+0.000688861, 



JV/"= 0.0093164, JV/"= +0.0000771929. 



16. For an increment of ^ to the mass of the earth, we have the preliminary 

 computations by merely making all the coefficients positive in equations (251-256). 

 We shall then obtain the following 



Fundamental Equations for ^"=-1 ; or /orm"=l-r-335172. 



10' 



4=^+40.092595.0 +195.673045; 

 A =# 2 +23.4348156.#+100.8391921 ; 



4"=0 2 +19.4622137.(7+ 77.7179078; 

 4!=^+ 18.4089042.0+ 60.3313475; 

 4j=0 2 + 13 - 1935918 -#+ 8.982096; 

 4 3 =0 2 +26.3829396.0+ 9.895893. 



D =0 2 +46.0863772.#+633.1 39825; 

 Z7=0 2 +52.837 2995.^+622.776921 ; 

 j9" == /+32.4903462.^+261.2498776 ; 

 A^+43.8987902.^+1 72.463686 ; 

 D 2 =0 2 +46.4944263^+ 32.948508 ; 

 Z> 3 =0 2 + 3.4291886.^+ 1.69252948. 



B= |0+34.38795 16; B' = ^+17.7555387} b ) 



B"= ^+13.801975 1 b j 



C =^+27.173766| [9.4381 149]5'; 

 C"= J0+17.7855450 } [9.1138076]6' ; 

 6"'=+[0.3976676]6'; 

 C""=+[0.4411620]6'. 



(455) 



(456) 



(457) 



(458) 



