will yield all the usual information about the effects of the 
disturbance on the free surface. 
Lamb [1932] summarizes some of the results which have 
been obtained by the use of the Fourier Integral Theorem. Among 
the results, the Cauchy Poisson Wave problems are of the great- 
est interest as far as this paper is concerned. One problem 
gives the wave system propagated from an initially concentrated 
elevation of the free surface, and the other problem gives the 
wave system propagated from an initially concentrated impulse 
applied to the free surface. 
The first problem gives the wave system which would result, 
if at the given time t = 0, an infinitely high, infinitesimally 
wide, infinitely long column of water were to start falling into 
the ocean at the point x = 0. The free surfacey7) » is given by 
equation (2.30) if et-/4x is large. 
| 
ml linn iy al 
At any x as t approaches infinity, 7 oscillates more and 
more rapidly and approaches infinite values of height. Since 
the original formulas upon which this solution is based were 
founded upon the assumption that the height of the initial dis- 
turbance is small, the physical reality of the problem is ser- 
iously open to question. 
The second problem gives the wave system which results 
from the action of an infinitely intense impulse upon the line 
pS eee 
*Note also that the u, Vv, and w components of the fluid 
velocity can be found from@® . 
an Gh = 
