ia tes 
By change of integration variable to R, equation (11) can be written in the form 
i - BV aE et f R,) oR 
scant (ctienR) gy ta(ct = RY) _ 5 4) a= B(x - a) oh apie Ania nee 
R R' R' / R vig 
(13) 
ct > sRY 24k 
The solution for the velocity potential ¢ is given simply by substituting — t/p c 
for f in (13) where t, Is defined by 
tf, @) =" tO) 46) (14) 
Application to underwater explosion wave. 
For an underwater explosion wave we assume as in Report A that the incident wave has 
form 
f(ct-R) = pp Re c (15) 
1177 
the 
where p_ is the maximum pressure in the incident wave at distanc2 R_ from the explosion. We 
shall consider only the pressure and velocity at the plate since this is the item of major practical 
importance. 
Now from (13) and (15) we have at x = 0, 
= Feo) Chg By Ry - +n Rafe 
SS c SB Re Ea e d Ry 
° — Es 
a Werner ee 
° 
R 
x = 0, t22 (16) 
where Ro is the distance of a point P of the plate from tne explosion centre and is given by 
Resmi ita (17) 
The velocity v communicated to the plate is from (3) and (4%) given by 
m = pdt = -p¢ (18) 
and - 9 cd is obtained by putting f, for f where from (14) and (15) 
f, (ct -R) = ae (eee) (19) 
Hence - n O¢+ p is equal to the pressure when the incident wave is of constant pressure py 
i.e. when n= in (16). Hence 
Roe 
