THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



129 



For the root g^ we get, 



g t = 0".G61665, 



N t ' =+1.130316JV 5 " p 

 N," =+1.107793iV r , /F 

 N s " =+1.049700JV 5 /r 

 N a r =4-0.96532472V 5 /r 

 #5"= 0.9380148iV 5 /r 

 Nt ra = 9.829793i\r 6 



5 

 ' r 



For the root g^ we get, 



</ 6 = 2".916080, 

 2V 6 =+ 3.5096032V a " 

 2V 6 ' =4- 2.0433762V 6 ' r 

 2V 6 " =+ 1.8368842V." 

 2V 6 '" =4- 1.3157522V/ r 

 2V a r =-j- 0.81644042V a ' r 



2V 8 F "=-|- 2.161811^" 



For the root g 7 , we get, 



7 = 25".934782, 

 N, = 0.04268995iV/ F 

 2V/ = 0.035352232V/ r 

 2V r " = 0.43727582V/ r 

 2V/" = 1.4787182V T " 

 2V/ = 2.49()6482V/ r 



log. 0.0900640, 



" 0.0531999, 



" 0.0444583, 



" 0.0210647, 



" 9.9846734, 



" 9.9722097n, 



" 0.9925444. 



log. 0.5452580, 



" 0.3103480, 



" 0.2640819, 



" 0.1191740, 



" 9.9119245, 



" 1.3035012, 



" 0.3348177. 



log. 8.6303257n, 

 " 8.5484168n, 

 " 9.6407554n, 



" 0.3963122^, 

 " 9.0387706, 

 8.0882161. 



15. If we ndw substitute these values in equations (408) and (409), we shall 

 obtain the following quantities : 



For the root g= 5". 1701 89, we get, 



, 0.581731 . , 1.5880256 ,. 14.050229 , 



*=H JQU N < y=-\ 10^ ; z= I7m ^ 



Whence /3=20 7' 8".3, and log. 2V=9.0805176. 



N =-(-0.120370, 2V /r = 0.00002524, 



2V =4-0.014605, N v =0.00003221, 



N" =+0.010530, N VI =+0.00002767, 



2V" =4-0.002167, 2V m =+0.00000080l5. 



17 February, 1872. 



