1482 
gives: 
ro) eee. 
she 
Ne: E Ax 
Flt)= WE Wa x (17) 
fie 
The principal value of the integral in equation (17) is identical 
with the negative of the "exponential integral” defined and 
tabulated in reference 3. Thus 
vi (ap olie) (18) 
Vesa PT € 
If a higher order reflection undergoes more than one 
reflection from the bottom at the same angle of incidence, the 
total phase shift to be applied in equation (10) becomes 
ané / w/o where N is the number of times the wave has 
been reflected from the bottom at an angle of incidence corres- 
ponding to the shift € . Each time the wave is reflected 
from the free surface it undergoes a complete inversion; thus 
if M is the number of times the wave has been reflected from 
the surface, the general expression for higher order reflections 
becomes, analagous to equation (11), 
Pear (t) = (-/ ie i (tb) cos 2WE + Flt) Sina ( (19) 
2.4 Conservation of energy. The energy flux in the incident wave 
is given by 
