﻿342 Prof. P. Lowell on the Asteroids. 



0. Taking up now the terms in 20, 30, &c, 20', 30', &c, 

 we find that their expressions are as follows : — 



(4) B=^x 



[_|(46( 2 )+V 2) )cos0 



- (0 3 ( - 14 ^ (2) - | ^ 2 > + 3 b 2 W + * & 3 < 2 >) cos 

 + | (j) { 64 7/ 2 > + 6 /V 2) - 8 & 2 (2) ~ />3 (2) } cos 



+ ~{ 3^-f-^W } cos {0- (>-<*')} 



+ (rX e 2 { -12 ^ {1) 4-4 V 1 ) + 7 & 2 (D 4- & a fl> } cos {0-(^-<)} 

 + ( k yY{-14^)+2^ l )4-^ 2 W + ^ 3 W}cos{0-(^--^')} 



~6)^ {^r* ( - 3> + t Ai( " s) - ^ w_s °- ^3 ( - 3) }cos{0-f(^-^')} 



+ (|J { 22 &W -1- 7 ^< 4) -r ~ & 2 (4) } cos 20 



~l~{ 42^+146^)+ l^ }cos{20-(*r-w')} 



4- (f Y{19 ^ (2) + 7 & i (2) + v^ (2) J cos {20-2(«-*r') } 



- (£ V (134 // 6 > 4- ~ />i (,3) + 5 & s «0 + J V 6) } cos 30 



+ G) 2 2 { ^^^ +2 ? 6i(5) + 7 ^ + I ^ 5) jcos{30-( OT -^} 



- \ (j\ {416 &« + 151 &,(*) + 16 b^) + * &,« } cos {30-2(^-^0 } 



4- (j) {136 6^ + 52^+ i 1 ^ 3) + 1 ^}cos{30-3(^-^ / )}]. 

 To determine the value of the right side in this case we 



