= 
893 
and the material velocity, v » may be derived. 
(3.2) 9, ) = G eed, pO) 
Wy may be divided into two partes: 
(3,2) ws Wt Vy 
where Lae is the disturbance produced by e in the absence of 
g, and where SiGe 1s the perturbation due to the presenoe of g. 
Let the normal component of the fluid velocity across T toward 
g be v,. Then 
(35.3) y= - Uh 2h 
z, 252 ce hes 
4. The velocity potential satisfies the wave equation. Hence 
(2.3) is apolicable to  , and Ys (2,3) gives for the points 
P and Q in Fig. 3. 
cr) = ay fae Dad 
ua HALAL 
(442) cee lee keeles 
am) 
gd (4,1) and (4,2) are valid on 
T 4tself inside of the WY g wave 
Y. WAVE 
front. Let P snd & coincide on 
FRONT Yq WAVE FRONT 
T behind the Y g wave front. Then 
by (4.1), (4.2), (8.2) and (pe3)5 
yoo = an) (ee4)- 2 BEN 4s 
ew) 
af {40d -2 BES 
(T) 
&O 
he 
Ve 
fa) 
= jo) 
