H. Wysor Marsh 197 
of any wave field into plane waves. Wiener's formulas are, in fact, used through- 
out my development, although a delta function is used for convenience in the 
final stages, since the power spectrumis more easily utilized than the integrated 
spectrum. 
The question of rigor in the use of Wiener's method is another matter. With- 
out doubt, sufficient qualifications could be made to guarantee validity, except 
for circumstances of vanishing probability. The fact is that the results are 
formally valid. 
It is not surprising that it is difficult to reconcile my results with those of 
others. Only Rayleigh has results which are comparable, and, then, only for a 
sinusoidal surface. My results agree with Rayleigh's when compared under 
equivalent conditions. My results are not comparable to calculations based on 
the distribution of heights because the height distribution is, in general, not 
determined by the surface spectrum, and vice versa. A Gaussian surface cannot 
be sinusoidal and, therefore, any agreement between a Gaussian surface and 
Rayleigh's results is fortuitous. 
The important point, as Eckart pointed out, is that the low-frequency scatter- 
ing is determined by the surface spectrum, and not by the height distribution. 
My formula shows that energy is conserved, since the negative integral of 
the nonspecular scattering over all direction cosines plus the specular term 
is unity. 
DR. H. CHARNOCK asked the lecturer whether there was any evidence that 
the so-called "equilibrium sea" is horizontally isotropic. 
DR. MARSH: I do not know whether the equilibrium sea is isotropic. How- 
ever, the mean scattering of sound waves, for random orientation of the incident 
wave, is surely isotropic in azimuth. This is the situation developed in my 
lecture. 
