THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



139 



For the root gr 5 , we get, 



# 5 =— 0".G61664, 

 iV 5 =+1.229368^/" 

 NJ = + 1.129025iV 5 ' 7 

 N s " =+1.105860iV 5 ' F 

 N* =+1.049158iV 5 ' r 

 NJ =-j-0.9653170JV 6 J 

 ^"=—0.9382057^ 

 NJ"=— 9.830882iV 5 /r 



log. 0.0896819, 



" 0.0527036, 



" 0.0436997, 



" 0.0208410, 



" 9.9846700, 



" 9.9722980», 



" 0.99259 25 n. 



For the root g 6 , we get, 





g =— 2".916095, 





JV =-f 3.4798022C lc 



»g. 0.5415546, 



N{ =+ 2.020979 N a " 



' 0.3055617, 



N a " =+ 1.810077JV 6 /V 



' 0.2576970, 



ivy =-)- 1.308654^/" 



' 0.1168248, 



N a T =+ 0.8164215^'" 



' 9.9119144, 



N 6 ri =— 20.115742V 6 " 



' 1.303536071, 



iV li r// =+ 2.156995iV/ r 



' 0.3348492. 



For the root <j~, we get, 



g,=— 25".933517, 

 iV 7 =— 0.04094460iV 7 JV 



JV 7 ' =— 0.04815456iV/ r 

 N 7 " =— 0.4073554.V/" 

 iV/" =— 1.473038JV/ 7 

 Nj r =— 2.490000iV/ r 

 iV 7 rj =+0.1092910iV/ r 

 JV 7 r// =+0.0122-t673iV 7 " 



log. 8.6121966m, 



" 8.6826374», 



" 9.6099734m, 



" 0.1682137», 



" 0.3961992», 



" 9.0385844, 



" 8.0880201. 



19. If we now substitute these values in equations (408) and (409), we shall 

 obtain the following quantities: — 

 For the root rj=— 5".186718, we get, 



134.20637 



6.16813 .. , 15,530471 



10 1 



-N 2 



10 i5 -. a— i 10 i 



Whence /3=21° 39' 31",5 ; and log. JV=9.0952088. 



N = _l.o.124511, N iy =— 0.000024449, 



N ' =+0.0141947 N r =-0.000031240, 



N" =+0.0099895, N r ' =+0.000026642, 



N'" =+0.0020212, N" =+0.00000078455. 



