“a 
Chapter 2. RESUME OF CLASSICAL WAVE THEORY 
Introduction 
Classical wave theory has discussed rotational waves such 
as Gerstner's waves and irrotational waves such as shallow water 
waves, waves of finite height, deep water waves of infinitesimal 
height, and solitary waves. This paper will be concerned with the 
theory of deep water waves of infinitesimal height at first, and 
later the refraction and diffraction of these waves will be dis- 
cussed. 
Before the theory of waves of infinitesimal height is applied 
to the sea surface, a reason should be given for not using the 
theory of waves of finite height. The reason is simply that the 
waves of infinitesimal height combine linearly whereas waves of 
finite height do not combine linearly. The irregularity of the 
sea surface is its dominant feature. As such, it can be treated 
mathematically. The non-linearity of the sea surface cannot be 
treated mathematically without suppressing the irregularity of 
the sea surface. These points will be clarified in the resume of 
the theory of waves which follows. 
Non-linear equations 
If irrotational motion is assumed, the problems connected 
with gravity wave motion on a free surface approximated by a plane 
despite the curvature of the earth can all be considered to be 
solutions of equations (2.1), (2.2), (2.3), (2.4), and (2.5) which 
are shown in Plate I and which for example are given by Lamb [1932]. 
