THE ORBITS OF THE EIGHT 1'IHNCIPAL PLACETS. 



129 



For the root ^ 6 , we get, 



(7 5 =— 0".661665, 

 N b = + 1.230450#/ r 

 N t ' = + 1.130316#/ r 

 2V 6 " =+1.107793# 6 " r 

 #'" = + 1.049700iV 5 ' r 

 #/ =+0.9653247# 5 / 

 #/'=— 0.9380148iV 5 J 

 #"'=— 9.829793# /r 



log. 0.0900640, 



" 0.0531999, 



" 0.0444583, 



" 0.0210647, 



" 9.9846734, 



" 9.9722097n, 



" 0.9925444h. 



for the root g 6 , 



we ge 



t, 



>J 



=—2".9 16080, 



N 6 



=+ 



3.509603# 6 " 



w 



=+ 



2.043376# " 



n: 



=+ 



1.836884JV/ 



w 



=+ 



1.315752#/ 



N/ 



=+ 



0.8164404# 6 



N™ 



— — \ 



20.11413#/ r 



#"=+ 2.16181 l#/ r 



For the root g 7 , we get, 



g 7 =— 25".934782, 

 JV 7 = — 0.04268995#/ 

 #/ =— 0.03535223#/ 

 N 7 " = — 0.4372758#/ F 

 N 7 '" =— 1.478718#/ F 

 N 7 F =— 2.490648iV/ F 

 #/'=+0.1093379#/ r 

 #/"=+0.01225226#/ 



log. 0.5452580, 



" 0.3103480, 



" 0.2640819, 



" 0.1191740, 



" 9.9119245, 



" 1.3035012m, 



" 0.3348177. 



log. 8.6303257w, 



*" 8.5484168m, 



" 9.6407554», 



" 0. 1698852m, 



" 0.3963122m, 



" 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".170189, we get, 



, 0.581731 Ar , 1.5880256 „, 14.050229 

 *=H jgn— N\ V=-\ Jon N > z =— iou N • 



Whence /?=20° 7' 8".3, and log. #=9.0805176. 



N =+0.120370, #'"= — 0.00002524, 



N' =+0.014605, N r =—0.00003221, 



JVT" =+0.010530, #"=+0.00002767, 



N'" =+0.002167, #"=+0.0000008015. 



17 February, 1872. 



