The theoretical interpretation of the experiments rests on the solution of the hydrodynamical problem of determining the motion and pressure throughout the body of water in a rectangular tank to which is given an arbitrary small oscillation parallel to its length. The solution is similar to that given by H. M. Westergaard for a channel of infinite length, reducing to Westergaard's solution as a limiting case. It is shown that if the length of the tank is two and one-half times the depth of the water, the total pressure on one end is about 4 per cent less than for a channel of infinite length.
In order that the accelerative force due to the inertia of the body of water may be measured, the tank is mounted on rollers on a shaking table in such a way that, with negligible friction, the motion of the shaking table is communicated to the tank by means of an elastic connection which also serves the function of a spring dynamometer. The motion of the tank is therefore never exactly the same as the motion of the shaking table. With increasing rigidity of the dynamometer, the motions of the tank and the table become more and more alike.
If the tank is empty of water, the force measured by the dynamometer is due wholly to the inertia of the tank together with any solid bodies attached to it; but if the tank contains water, the force is due in part to the varying pressure of the water upon the ends of the tank. By comparing the dynamometer record when water is present with records obtained when the water is replaced by solid bodies of known mass, it is possible to determine what part of the force acting on the dynamometer is due to water pressure.
The motion of the shaking table is produced by an elastic impact of a pendulum moving with known velocity against a bumper spring on the shaking table. The starting motion during the impact time interval is fairly simple, and the subsequent motion is a free, damped vibration. The motion can be produced experimentally again and again with great accuracy, and, inasmuch as the starting motion lasts for a relatively short time, the system of reflected, gravitational waves from the ends of the tank does not come into existence for a time relatively long as compared to the impact time interval. This type of motion is probably the simplest element of actual earthquake motions which it is feasible to reproduce with repeated accuracy in the laboratory. The maximum acceleration of the tank during the impact interval ranged from 0.7 to 1.2 times that of gravity.
Altogether seven different experimental combinations of three table periods and three tank-dynamometer periods were used. If the experimental combinations be related to conditions existing in nature, the period of the table corresponds to the period of the earthquake motion, and the frequency of the tank-dynamometer system corresponds approximately to the frequency of the free vibration of a dam.
The experimental results show a satisfactory agreement with the theory. If the ratio of the experimental value of the equivalent water load to the theoretical value of the equivalent water load be called W′/W, the average of eighty-three observations on the tank with a single compartment gave W′/W = 0.78, and the average of 104 observations on the tank with two compartments gave W′/W = 0.85. One of the obvious reasons for the ratio of W′/W being smaller than unity is the lack of rigidity of the tanks.
Not only the total hydrodynamic load, but also the distribution of the pressure on the ends of the tank was measured, and a satisfactory verification of the theory in this regard has been obtained.