THE ORBITS OF THE EIGHT PRINCIPAL PLANETS, 

 log- Ji 11 =86.2924049 ; log. ?-=85.7169075 ; 



/ill ^ tiff. * 



35 



na 

 l0g> 7 W =85.9487046 ; log. Z'-^ =85.8645162,* ; 



in 



n a 



l0g - ^'=86.5381661 ; log. r~=85.8002322» ; 



l0g - r ^=86.1723213« ; log. ^—=86.4707346 ; 



bg - 7< Va- =89 - 2232280 S l °S- ?';7^7T-=89.8989416 ; 



l0g - V n'a v =89-5809761 ; log. Z r ^=86.8370944n ; 



l0g - 7i "^=88.0117101 ; log. Z r/ j^=88.7914476»; 



l0g - 7iW ~t" a r,=88.2010654; log. r"^ ril = 88. 1206031. 



18. These quantities are now to be substituted in equations (136) and (137), in 

 connection with the values of N', N", N'", Sec, corresponding to the different roots. 

 For the root <7=5".4638027, we find 



1847539 64178.9 10467760 



T" 10 20 iV ' 9—T ]() 20 iV > Z — \ 10 23 — -^ ■ 



Whence /?=88° 0' 37".8, and log. iV=9.2470063. 



Therefore for root g, we have the following values, 



N =+0.1766064, N' r =-0.0000090002, 



N' =+0.0085906, N r =-0.0000080335, 



N" =+0.0054825, N TI =+0.0000035168, 



N'" =+0.00084182, #"'=+0.000000063131. 



In like manner we shall find for the root ^=7". 2484269, 



1654860.4 4347600.6 .173037154^ 



Whence /? 1= 20° 50' 19".4, and log. #=8.4294913. 



Therefore for the root g x we have 



Hr t =+0.02688384, N,' r =+0.000010644, 



#' =-0.02014438, # r =+0.000010875, 



N," =-0.01536192, JV, " = -0.000002744, 



N{' =-0.00254509, JV, "'=-0.0000001122. 



For the root # 2 =17".0143734, we find, 



18893046 40873423 3.068840 

 2 jo 20 2 ' y~ i ~^ io 20 2 ' z 2— n JqTo — #2 • 



&=335° 1 1' 31".4, log. #=7.1665150. 



# =+0.001467287, N 2 ' v =-0.000001059, 



#'=-0.01121706, N 2 V =-0.000006401, 



#"=+0.01131047, N™ =+0.000000392, 



#'"=+0.02257186, #/ i =+0.0000000288. 



