A SYSTEM OF PARTICLES. 275 



that velocity if it exist, but merely introduce a portion to be added 

 to the former. 



Now {r + pY = S.v' + (hj + Sl3y + {§x + ^y)' 



= r' + 2(% ^/3 + Sz Sy) + ^13' + Sy' 

 = r^ + p' suppose ; 



and p" = ^{h/^(i' + Sz'Sy') + ^SijSzSliSy; 



hence ^ = 1 /i _ I ZSySfi + QSzSy + ^^ + h' 

 (r + pY ?-M 2 ■ 7' 



1' 



2.4 7^ 



hence ^ = 2 ^^ 



df (r + pf 



[r' 2 r' 



2 r' f' 



but .^ = l.^-^±i|l±l^ nearly, 



3 V 



. ^_y^^ , 3 , 5(5£+V) 3„, S^' + Sy' 



Vol.. VI. Part II. • Nn 



