THE ORBITS OF THE EIGHT PRINCIPAL PLACETS. 



81 



For the root g^ we get, 



^ 4 =0".62228135; 

 N t =+ 0. 1215129 N t ir 

 N t ' =+ 0.1845219iV 4 "' 

 iV 4 " =-f 0.2130944^/" 

 N t '" =+ 0.3455668iV 4 ' r 

 NJ =+ 1.133130^/" 

 N i r '=-\- 24.593006iV 4 /r 

 iV 4 "'=+160.6301 1JV 4 ' F 



For the root g b , wc get, 



^ 5 =2".7623108; 

 N b =+ 0.2979185JV 6 ' r 

 iV 5 ' =+ 0.2890480iV 6 "' 

 iV 6 " =+ 0.3020508JV 5 /r 

 JV 5 '" =+ 0.4005457iV 6 ' r 

 N b v =+ 0.9164754iV 6 ' r 

 iV 5 " =+15.69060^'" 

 iV 5 r "=— 1.514217iV/ r 



For the root g e , we get, 



# 6 =3".7862093 ; 

 JV 6 =+0.6004756iV 6 /F 

 iV 6 ' =+0.3937991iV/ F 

 JV 6 " =+0.3856959iV ' r 

 JV 6 '" =+0.4382820i\r' F 

 # d r =+0.794009iV/ r 

 JV 6 "=— 1.022221JV/ r 

 iy 6 r/ =+0.03054184iV/ r 



For the root g 7 , we get, 



^ 7 =22".5759799 ; 

 JV 7 =— 0.006116321iV/ r 

 JV/ =+0.01912057iV/ F 

 N 7 " =— 0.1503075iV 7 ' r 

 N 7 "' =— 0.9432520iV/ r 

 N 7 r =— 3.002313iV 7 ' F 

 iV 7 r/ =+0.1143927iV/ r 

 iV 7 r '=+0.00864081iV/ r 



log. 9.0846223 



" 9.2660478 



" 9.3297932 



" 9.5385321 



" 0.0542790 



« 1.3908116 



" 2.2058270. 



losr. 



log. 



9.4740975 

 9.4609699 

 9.4800800 

 9.6026522 

 9.9621209 

 1.1956394 

 0.1801882h 



9.7784954; 



9.5952747; 



9.5862450 : 



9.6417536; 



9.8998255; 



0.0095448m ; 



8.4848952. 



log. 7.7864903m ; 



" 8.2815008; 



« 9.1769806m; 



« 9.9746277m ; 



« 0.4774559m ; 



" 9.0583982; 



« 7.9365546. 



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



must also add the logarithm of l+</\ to those of - 



to obtain the numbers to be used in this computation. 



11 December, 1871. 



_« r A*, and J^l\ in order 

 n a n a 



