PROFESSOR KELLAND ON THE THEORY OF WAVES. 

 ax\ I ax 



c being the value of c when #=0 or a=0; that is, the space described in a given 

 time t in the actual case is less than would be described in the same time with an 



uniform velocity, on two accounts, 1st, because c is changed to c ( 1 -- j } > 



2d, because by the continual change of phase of the wave during the motion 

 from to cc, the motion will not begin from the same place. 



We have, in fact, \=X ( i _ ^L \ 



\ z + hj 



axe t 



that is, 



From these formulae we learn two things, viz. that the velocity of transmission at 

 any point varies as the square root of the depth, or as the square root of the 

 length of the wave. 



56. We might proceed by another method to obtain the variation of c from 

 the variation of \ : thus, 



<?=i- approximately ; 



taking the logarithm of each side, and differentiating it with respect to a?, the re- 



sult is, 



2 dc dD dS da 



_ 

 c dx~Ddx Sdx adx 



But by virtue of equation (8) ; -^ =0, -^ =0 } 



2 dc__ __ 



cdx adx 

 d\ 



\dx 



