THE ORBITS OF THE EIGHT PRINCIPAL PLANETS 125 



For the root g±— — 6".634795, we get, 



, 0.637032 ._ 0.4606865.- 27.744169 „, 



^=H iQu— ^i; 2/i= jQii N il z i= iqu #i- 



Whence ft=125° 52' 26".4; and log. #,=8.4523391. 



# x =+0.028336, iV/ r =+0.000008275, 



#/ =—0.006724, #/ =+0.000011726, 



N{ =—0.005485, ^"=—0.000005994, 



Ni" =—0.001160, #/"=— 0.0000003662. 



For the root #>=— 17".459300, we get, 



6.884438 3.578728 _ 6546.046 



Whence /? 2 =297° 28' 0".l; and log. # 8 =7.0738291. 



N 2 =+0.001185, iV/ r =— 0.000002184, 



jV 2 ' =—0.006205, N 2 r =—0.000019227, 



JV 2 " =+0.004991, N" =+0.000001860, 



# 2 '"=+0.047424, ^"=+0.000000214. 



For the root g 3 =— 18".666222, we get, 



6.787567 1.953449 Ar _ 17211619 



X 3 ^Ql3 •"&; V% ^Q13 £*%'■> Z 3 JQ13 ""3 • 



Whence /3 3 =253° 56 ? 39".4; and log. iV 3 =7.61 16607. 



JV 3 =+0.004089, # 3 "'=— 0.000000213, 



iV 3 ' =—0.023880, # 3 r =—0.000003939, 



iV 3 " =+0.026863, N 3 " =+0.000000335, 



#,'"=—0.032221, #,"=+0.0000000385. 



For the root <7 4 =0", we get, 



, 0.7256935 0.2113335 _ 27.24487 Ar2 



•"* ~T~ JQ10 ■"*» i/4 . lQ10 *■'*» "■» JQ10 



Whence /3 4 =100° 14' ll".l ; and log. # 4 =8.4431447. 

 # 4 =#/=#/=#/=#/ , =# 4 , =# 4 "=# 4 "=0.02774244. 



For the root g b = — 0".661664, we get, 



. 0.1017327 A . /r . 0.2717512 „ 24L9334 



*5=H jqxo — # 5 ; 2/ 5 =H jqio — N * 1 z 5= — nF - • • 



Whence &=20° 31' 39",5 ; and log. #/ r =7.0789678. 



# 6 =+0.001475, N b ,v =+0.00119941, 



# 8 ' =+0.001357, #/ =+0.00115783, 



JV 5 " =+0.001330, # 6 " = — 0.00112485, 



# 6 '"=+0.001259, # 5 " =-0.0117895. 



