PROFESSOR KELLAND ON THE THEORY OF WAVES. 135 



l_ e **(*+*) 



Now c 2 =ff n - tt h \=3 f as a first approximation. 



*+* 



_ e 

 Hence, approximately 



= _ 6V> /*" sin/iCa-^Q + Bin/irf gin , , g _^ ( 6_ y ) . 

 7T / V/* 



We can obtain a very important result from this equation when t is a very 

 small quantity. In that case, 



bgt( aa' a' 1 



" V I (a - a') 3 + (b^}* + of 2 + (b-yf } 



or by writing, as we ought, of for a' 



_ 



~ -TT (ar 1 - a) 2 + (6^)2 



Let us transfer the origin to the middle point of the base of the parallelepi- 

 ped originally elevated, and put xf=x + ^; 



a a 



~2 * + ~2 



1. If x be ^ ~ ; -j is negative, or the particles move downwards, as, from 



J ay 



the nature of the case, they must evidently do. 



2. If x be very large, and b y small, the latter may be neglected, and 



d$_bgtl 1 1 \_ bgta 



dy tr \ a a) ~ 



*-2 z+ 2 



Hence sin c /=sin \/y /i t \fg p e~ 2 ^ ^^'^ cos 





3. -- will equal zero if 



a 

 -=0; i. e. 



