Abstract
The fundamental normal mode of the free oscillation of water in a lake of elliptic boundary and of uniform depth is investigated exactly by the use of Mathieu functions and modified Mathieu functions in two cases. The relationship between the frequency of the fundamental normal mode of oscillation and the eccentricity of the elliptic boundary of the lake is shown graphically. Also, an approximate formula for said relationship is derived, which may be adequately used to find the approximate value of the frequency.
