THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. U5 



For the root #,= 6".6358742, we get, 



0.685590 _0.6767428 34.48222 



U -u y\ U" iv i> z i 14 ~ 1% 



Whence ^=134 3T40".5; and log. #=8.4461821. 



# =+0.027937, #'"=+0.00000958766, 



#'=0.0079385, # r =+0.0000135304, 



#"=0.0063791, #"=0.0000069640, 



#'"=0.00132626, # r// = 0.00000042454. 



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



69.06713 A7 , 26.31099 .. 4443.491 , 



*2= - #; 2/ 2 =H --- n #; z 2 = - # 



Whence ft=290 51' 15".3; and log. #=7.2209728. 



# =+0.0016633, #' r = 0.0000026543, 



#' =0.0093605, # r =0.000022202, 



#" =+0.0078636, #" =+0.0000021487, 



#'"=+0.0517583, # m =+0.00000024767. 



For the root <7 3 = 18".486192, we get, 



67.51436 23.46891 20391.171 



""""^ ' ^ 3 ~ H - ^ 3 ' Z3 ~ 



Whence /5 3 =250 49' 54".7 ; and log. #=7.5447249 



# =+0.0035053, # /r =+0.00000000335, 

 #' =0.0215019, # r =+0.0000006499, 

 #" =+0.0236359, #" =0.00000005957, 

 #'"=0.0395973, #"'= 0.00000000710. 



For the root #4=0", we get, 



_ , 7.294416 2.119410 274.1191 



x * "r~ jQii -^ii y* JQII #; Z 4 JQII # 



Whence /3 4 =106 12' 4".8; and #=#'=#"= &c., 

 -+0.02771087, log. 8.4426502. 



For the root g 6 = 0".6633671, we get, 



_ 1.016103 _. , 2.742753 . _245.2401 



" - I J^Qll 1V 5 ) 5/5 - ~1 JQII r-"f > Z !> - JQ10 "I ' 



Whence /? 5 =20 19' 41".0 ; and log. # /r =7.0765225 



# =+0.0014684, #' r =+0.00119268, 

 #'=+0.0013482, #"=+0.00115141, 

 #"=+0.0013207, #"=0.00112652, 

 #'"=+0.0012511, # m = 0.0118074. 



19 March, 1870. 



