1. Introduction. The analytical study of gravity waves of finite height which are periodic and move without change in shape in an ideal irrotational fluid is a subject which has occupied the attention of physicists and mathematicians ever since Stokes (9) published his classic paper entitled "On the Theory of Oscillatory Waves" in 1847. However, it was not until 1925 that an existence proof for such waves in the case of a basin of infinite depth was published by Levi-Civita (4). The corresponding proof for the case of limited depth was presented by Struik (10) in 1926.