THE OK BITS OF THE EIGHT PRINCIPAL PLANETS. 



113 



p' r =+0.0226127, 

 f =+0.0402201, 

 jp ri =4-0.0129519, 

 jp F "=+0.0238090, 



leg. jp /r =8.3543534; 



log. p v =8.6044432; 

 logy =8. 1123323; 

 logy"=8.3767411; 



V 



=+0.0844678, 



log. q 



=8.9266911; 



4 



=+0.0149991, 



log. q' 



=8.1760051; 



c i" 



= 0. 



log. q" 



= — GC ; 



4" 



=+0.0214548, 



log. 4" 



=8.3315249; 



<r 



=—0.0035434, 



log. q" 



=7.5494159//; 



q r 



=—0.0165138, 



log. q T 



=8.2178478ra; 



7" 



=+0.0039012, 



log. q" 



=7.5911972; 



q vn 



=—0.0200698, 



log. q» 



=8.3025434n. 



Now, adding the logarithms of m-r-na, m'-i-ria', &c, which are given in § 5, 

 we shall obtain the following values of the logarithms of the constants for the given 

 epoch, which enter into the values of x and y. 



log. p 



na 



m 



lo g- P "TT3 



ii a 



log. p' 

 log. p' 

 log. p 

 log. p T 



, in 

 n'"a'" 



n 1T a' y 



■ m T 

 n v a r 



r m ri 



■ m r " 



=85.9443779; 

 =86.9845985 ; 



= GO 



=85.9337058 

 =89.5793573 

 =89.4372661 

 =88.2449047 

 =88.7292393 



k>£ 



b, in 

 g-'J 



it a 



log. q' 

 log. q" 

 log. q n 



in 

 n"ti" 



in'" 

 ri"a'" 

 ■ m' r 



m 



=85.9208552 ; 

 =86.4020721 ; 



= — GO 



=85.8821396; 

 =88.7744198»; 



log. q r ";- T =89.0506707//; 

 n a 



log. ff"-^ =87.7237696; 



log. q r 



— 88.6550416n. 



7. These quantities are now to be substituted in equations (408) and (409), in 

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



For the root ^=—5". 1261 12, we find, 



. 0.612517 , T , 1.5865662 1T 14.046564 xr5 



«=+— Igr-^ y= + 10" N; z =~ m N - 



Whence 0=211° 6' 26". 8 ; and log. iV=9.0830567. 



Therefore, for the root g, we have the following values, 



N =+0.121076, N ir =— 0.00002517, 



N' =+0.0148671, N r =—0.00003200, 



N" =+0.0106496, N r ' =+0.00002804, 



N'" =+0.0021278, A Tr "=+0.00()000775. 



15 February, 1872. 



