THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. U5 



For the root g x = — 6".6358742, we get, 



. 0.685590 ._ 0.6767428 Ar 34.48222 ATO 



x i=+ 10 u -*\l Vi= jQiT- N r, ^—— 1QU — N i- 



Whence &= 134° 37' 40". 5 ; and log. ^=8.4461821. 



N x =4-0.027937, ^"'=+0.00000958766, 



N; =-0.0079385, N x 7 =+0.0000135304, 



AY' =—0.0063791, N," =—0.0000069640, 



^'"=—0.00132626, ^,"=—0.00000042454. 



For the root g 2 = — 17".520779, we get, 



69.06713 A7 . 26.31099 Ar 4443.491 AT9 



**=— 10 i4 #; 2/2= H — 1QU a 2 ; *= . 1Q1S ffi. 



Whence &=290° 51' 15".3; and log. ^=7.2209728. 



N 2 =+0.0016633, iV r 2 "'=— 0.0000026543, 



JV 2 ' =—0.0093605, N 2 r =—0.000022202, 



N a " =+0.0078636, N 2 TI =+0.0000021487, 



iV 2 '"=+0.0517583, i^ 2 F/ =+0.00000024767. 



For the root g 8 =— 18".486192, we get, 



67.51436 . T 23.46891 Ar 20391.171 . T , 

 *»=- iqu &s; !/*= iQi^^ ; 2 3= — Wl W. 



Whence /3 3 =250° 49' 54".7 ; and log. iV 3 =7.5447249 



JV 3 =+0.0035053, N./ r =+0.00000000335, 



N 3 ' =—0.0215019, N 3 r =+0.0000006499, 



N 3 " =+0.0236359, N 3 " =—0.00000005957, 



iV 3 '"=— 0.0395973, N 3 " =—0.0000000071*0. 



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



. 7.294416 A _ 2.119410 A7 274.1191 AT2 



x *=-\ — jqu- -#; y*= ro^~^ ; Zi= — iw~ * 



Whence /? 4 =106° 12' 4".8; and iV 4 =iV 4 '=iV 4 "= &c, 

 =+0.02771087, log. 8.4426502. 



For the root # 5 = — 0".6633671, we get, 



1.016103 _ 2.742753 _ 245.2401 



x 6— T 10 u iv 5 . 2/s— i jqTI iV 5 , %— Jqi5 — ^v 5 . 



Whence /? 6 =20° 19' 41".0 ; and log. JV/ r =7.0765225 



N, =+0.0014684, N s ir =+0.00119268, 



N b ' =+0.0013482, JV/ =+0.00115141, 



JV 6 " =+0.0013207, iV 6 r/ = — 0.00112652, 



JV 5 W =+0.0012511, N b TII z=— 0.0118074. 



19 March, 1870. 



