THE TIDES 527 



Equilibrium or Lake Tides 



The surface of a small and sufficiently deep body of water will ar- 

 range 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 culmi- 

 nation 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 versa. 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 south- 

 ern. 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 " equi- 

 librium tide " is used to denote a fluctuation in the ocean's surface re- 

 sulting 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 shal- 

 lowness 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 anj^thing like the 

 half-daily period. 



Oscillatory or Ocean Tides 

 Most tides are not equilibrium tides ; they are waves either station- 

 ary 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 



