THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



81 



For the root g, we get, 



# 4 =0".62228135; 

 jV 4 = 4_ o. 1215129 # 4 ' r 

 N{ =4- 0.1845219^'" 

 JV 4 " =4- 0.2136944JV/ r 

 N t " =+ 0.3455668^ 

 NJ =4- 1.133130JV/" 

 N t "=+ 24.593006^ 4 /^ 

 JV 4 r// =4-160.63011JV 4 /r 



For the root f/ 6 , we get, 



N, =+ ().2979185JV/ r 

 ^V 5 ' =4- 0.2890480^" 

 ^V 5 " =4- 0.3020508JV 6 ;r 

 N,'" =-)- 0.4005457JV 6 ' r 

 N t r =4- 0.9164754^ 5 ' r 

 J ZV 6 "=4-15.69060W 5 /r 

 N= 1.514217^ 6 /r 



For the root g w we get, 



N 6 = 



=+().3937991^V 6 J 

 =+0.3856959^ 

 =4-0.4382820^ 

 =4-0.794009JV 6 7F 



For the root <JT T , we get, 



^ 7 =22".5759799 ; 

 N 7 =0.0061 16321 JV/ 

 N,' =-f0.01912057JV/ r 

 N 7 " = 0.1503075JV/ F 

 Nj" = 0.9432520JV/' 



^"=+0.1143927^ 



^"'=-1-0.00864081^ 



log. 9.0846223 ; 



" 9.2660478; 



" 9.3297932; 



" 9.5385321 ; 



" 0.0542796 ; 



" 1.3908116; 



" 2.2058270. 



log. 9.4740975 ; 



" 9.4609699 ; 



" 9.4800800 ; 



" 9.6026522; 



" 9.9621209; 



" 1.1956394; 



" 0.1801882n. 



log. 9.7784954; 



" 9.5952747 ; 



" 9.5862450; 



" 9.6417536; 



" 9.8998255; 



" 0.0095448n 



" 8.4848952. 



log. 7.7864903w ; 



" 8.2815008; 



" 9.1769806; 



' 9.9746277w ; 



" 0.4774559n ; 



" 9.0583982 ; 



" 7.9365546. 



37. These numbers are now to be substituted in equations (134) and (135). We 



r , in order 



must also add the logarithm of l4-u\ to those of- ~ r , - -_ h v , and -^- 



n a na n a 



to obtain the numbers to be used in this computation. 



11 December. 1871. 



