PROFESSOR KELLAND ON THE THEORY OF WAVES. 113 



r 2 



or c s =^- . X 



\ 



the same result as we obtained before. 



To find the time of describing a given large space, we have 



dx 



= c 

 dt 



t = 



a x 



If/ be the whole length from the origin to the end ;= 7- 



SI -p n % T" ** ""~ ** * 



= rjw = 2 /^ 



J Cn Vl-x c \ 



COR. If x be very small t=, or the variation of depth introduces no vari- 



C o 



ation in the space described. 



21 

 If x=l; t=; or the time occupied by the wave in travelling to the end of 



C o 



the fluid, is exactly double what it would be if the depth were uniformly the 

 same as where the motion is stated to commence. 



57. We are desirous of testing these results by experiment, but find our ma- 

 terials rather scanty. The length of the wave, which is the most simply found 

 from theoretical considerations, is the least easily observed. In lieu thereof we 

 find the height of the wave given. The experiments to which I allude, those of 

 Mr RUSSELL, printed in the Seventh Report of the British Association, contain 

 the variation of height for a number of waves, and the velocity of transmission 

 for a number of others, all of which are what the author designates primary 

 reaves ; that is, waves of translation. We think we are justified in assuming that, 

 for such waves, the whole nave is transferred forwards. By means of this hypo- 

 thesis, we are able to determine the height of the wave in terms of the length. 

 Approximately, the following process will suffice. 



Volume =2f o r z ( ix=2f'fDsmddx 



= - (I COSTT) 

 a 



4/D 



= '- where f is the whole depth of the wave above its 



7T 



hollow. 



Therefore \ remains constant during the motion, 



VOL. XV. PART I. H h 



