A SYSTEM OF PARTICLES. 279 



By a similar process to (42), we have 



(r + pf r' \ 2 7^ 



2.4 V 'r* 



3.5.7 



{SxSa ^StjSf^ + SxSyy], 



6?^ 

 and by multiplication and reduction, this gives us 



2 ^ V' " 



_ 3.5.7 hjSm 



6 • ~7^]' 



hence, writing ly for ^s: also, putting ^a = 0, this is reduced to 



- ^ ll _ Mr 5 f^/3^ + ^7 ,0^,/ ^/3^ + V ^ 35 ^y ^/3S 1 

 rM r-' 2 I P '"^^ — ^^ — + T^7^j)- 



Now tlie integral of this is not a simple quantity, as in tlie for- 

 mer case, but some knowledge of it, at least, may be obtained by 

 the assumption (whicli is perfectly allowable) that the same form still 

 holds ; 



let then /3 = A cos [ut-kx); 



.J,, _^ . «/eSx 



.: c)/3 = - 2/3 snr— -; 



■ •] It. „ . „k6x 



similarly 6y — - <2.y %\\r — . 



