(4 = 27r/T) and thus obtain some special case non-periodic 
solutions. 
For infinitely deep water (for practical purposes about 
five hundred feet for waves with periods of ten seconds or less), 
the potential function, the free surface, the pressure (z de- 
creases from zero), the wave speed and the wave length are given 
by equations (2.24), (2.25), (2.26), (2.27) and (2.28) where 
ft = 2r/T. The equations follow from equations (2.7), (2.9), 
(Qol2)5 (Bore (aout) eiael (Boils))s 
In these equations (Plate III), ® is a function of the 
three space coordinates and time. © also depends upon the para- 
meters, , 0, A, and 6. If ®, = D 5 (x79 29by oe 304 28784)” 
is one potential function, and if Dy = @5(xX,y¥,2,t, pp 51959Ao965) 
is a second potential function, then ® = @, + @, is a third 
potential function. 
Moreover, if A and 6 are functions of » and ©, then a 
double integral of ® over p# and © is also a potential function. 
A(p ,®) and 5( 4,8) must behave properly in a mathematical sense 
for largey» . In particular aqne sien (2.29) is a potential 
function which satisfies equation (2.6) and (for z = -@) 
equation (2.8). Also7 can be found from equation (2.9) and 
the pressure can be found from equation (2.7). The condition, 
(2.10), is satisfied. 
If one picks some functional form for A(y,6) and b(t 58) 
and if then the indicated integration can be performed on equa- 
tion (2.29), the resulting expression for the potential function 
Pgs ora ® is a function of the time and space variables and one 
set of fixed values for the parameters. 
Sas 
