Equilibrium or Lake Tides
The surface of a small and sufficiently deep body of water will arrange itself normal to the direction of apparent gravity; that is, normal to the direction of terrestrial gravity when disturbed by the moon and sun, or, in other words, normal to the disturbed plumb line. If such a body of water be situated upon the earth's equator, high water will occur at its east end three lunar hours before the upper or lower culmination of the moon and low water, three hours after such times. When it is high water at the east end, it will be low water at the west end, and vice versâ. The amount of the rise and fall (i. e., the range of tide) at either end will be one thirteen-millionth part of the length of the body of water. If the body of water be not upon the equator, the range of tide will be somewhat less, and the times of high water around its margin will be progressive, following the order of the hands of a watch in the northern hemisphere and the opposite order in the southern. At the center of gravity of the surface of such a body will be a point having no rise and fall of tide, and so styled a "no-tide point." Tides produced in this way are called "equilibrium tides"; the minute tide found in Lake Superior constitutes an excellent example of this class. The observed rise and fall of the lunar tide at Duluth amounts to 1.6 inches, while the value computed directly from the forces amounts to 1.4 inches.
As commonly taught in schools and colleges, the expression "equilibrium tide" is used to denote a fluctuation in the ocean's surface resulting from an instantaneous arrangement of all water particles such that the surface of the ocean is everywhere apparently level, or normal to the direction of the earth's gravity when slightly disturbed by the action of the moon. It is taught that, but for the resistance caused by the continents and ocean bed, high water at a given place would occur when the moon crosses the local meridian. As may be gathered from what follows, this conception is fundamentally wrong. The semidaily fluctuation of the ocean's surface does not even approximate towards a surface of equilibrium, because the inertia of the water, and the shallowness of the ocean, when its depths are compared with its horizontal dimensions or with the distance from the surface to the center of the earth, prevent such adjustment from taking place in anything like the half-daily period.
Oscillatory or Ocean Tides
Most tides are not equilibrium tides; they are waves either stationary or progressive. The forces just described act upon portions of the oceans which are susceptible of taking up stationary oscillations having about the same period as the period of the forces. In this way the dominant tides originate. But irregularities in depth and coast line, particularly openings through the latter, cause the tides generated in
