272 Mr KELLAND, ON THE MOTION OF 



so that if h be greater than Jh n is greater than ?<,, or for the same 

 leno-th of wave (on this hypothesis) the velocities increase with the 

 increase of the depth of fluid. 



I return to the equations in (34). 



39. It is possible, that the original disturbance may have been 

 such as to make a = 0, that is, entirely transversal ; such an hypothesis 

 will in no way affect our investigations, as it does not interfere with 

 the other equations, and moreover in the case of light is probably 

 correct. 



Again, the original disturbance may have been such as to impel 

 forwards the particles, at the same time that a transversal vibration is 

 communicated to them. Integrating the first equation, we have 



^:)' = *«'"• -^ ^' 



V = C; 

 V being the velocity communicated; hence, we have 



a = Vf, 



and if we assume that a = mt + ere", cos ^x, we have 

 Sa = — ae" . 2 sin*—— cos fcx -f tSm 



= — 2 (a - mt) sin^-^- + torn ; 



,. ^=2>r(a - mt) + tf(x), 

 the latter term arising from m being a function of x; 



d'a 



but -r- = a(^e"coskx = c'ia - mt); 

 dt- 



.-. e{a- mt) = 2u'{a - mt) + t .fix) ; 

 and by equating coefficients of a we get 



c' = 2u\ 



