A UNIFIED MATHEMATICAL THEORY FOR THE ANALYSIS, PROPAGATION, 
AND REFRACTION OF STORM GENERATED OCEAN SURFACE WAVES 
SIR HORACE LAMB M.A., LL.D., SC.D., F.R.S. 
"SINCE THE CONDITIONS ARE UNIFORM WITH RESPECT TO X, THE 
SIMPLEST SUPPOSITION WE CAN MAKE IS THAT @ IS A SIMPLE HARMONIC 
FUNCTION OF X; THE MOST GENERAL CASE CONSISTENT WITH THE ABOVE 
ASSUMPTIONS CAN BE DERIVED BY SUPERPOSITION IN VIRTUE OF 
FOURIER'S THEOREM." 
Chapter 1. INTRODUCTION 
The origin of the remark is lost in antiquity, but many 
persons claim that ocean waves are just bumps on the water. Cer- 
tainly, wave records show that the waves pattern is sometimes 
chaotic, sometimes irregular, and other times smooth. Wave records 
are not sinusoidal, nor are they obviously periodic. In this 
paper the supposition that waves are just bumps on the water will 
be admitted, and then it will be possible to show how waves can 
be represented by the sum of a number of sinusoidal terms in a 
way which will preserve many of their observed properties and 
which will be amenable to theoretical work. 
The overall theory of wave forecasting is a mixture of various 
concepts which do not fit together well at the edges. Waves are 
treated partly as non-conservative waves and partly as classical 
waves. The significant waves are forecasted over a fetch and 
they are supposed to represent the average height and period of 
the one third highest waves. Admittedly, they are not classical 
a Pos 
