Generation, Growth and Propagation of Waves 69 



a relatively long period of time, the values of the functions C(\v) and S(w) 

 are simplified to the extent that we obtain approximately 



Lamb (1932, p. 385) writes: "It is evident that any particular phase of the 

 surface disturbance, e. g. a zero or a maximum or a minimum of r\ is 

 associated with a definite value of vv and therefore that the phase in question 

 travels over the surface with a constant acceleration. Consequently, an endless 

 series of waves travels from the disturbed region, and the amplitude of these 

 waves would rapidly decrease with increasing distance from the origin, if 

 only the distance was taken into consideration. However, inasmuch as the 

 amplitude is at the same time proportional to the time ?, it constantly in- 

 creases. This result, at first sight, seems contradictory, but finds its explanation 

 in the assumption of the initial accumulation, of a finite volume of elevated 

 water on an infinitely narrow base which implies an unlimited store of energy." 

 It is mathematically possible to consider an initial elevation distributed over 

 a band of finite breadth; then all pecularities of a concentrated linesource 

 of disturbance disappear, but the formulae become much more complicated 

 without altering essentially the results. Thorade has given in Fig. 36 a graphical 



km from origin of disturbance 

 4 5 6 7 



T 



Fig. 36. Progress of a single disturbance according to Poisson and Chauchy's theory 



(computed by Thorade). (130 and 140 sec after the disturbance. One has to assume that 



the right part of the curves are extended so far that they cross the x-axis, go through 



a minimum and then tend asymptotically towards the x-axis.). 



presentation, according to (IV. 2), of the front waves computed for a distance 

 of 10 km from the origin after 130 sec and after 140 sec and also the surface 

 wave. We can no longer speak of a simple-harmonic wave profile. The wave 

 crests and wave troughs have different lengths; the wave crests flatten out 

 and at the same time lengthen as the disturbance moves on, as observed in 



