The preceding discussion as to how tides are generated in the oceans clearly suggests that to determine the exact tide-generating forces is in fact, an astronomical problem. Very complex mathematical equations are involved in the solution of this problem.
Scientists, in order to find a solution to this complicated problem have taken help from the laws of hydrodynamics, physics and astrophysics. However, the effect of tide-generating forces on the waters of seas and oceans is determined by observations.
The oceanographers and other scientists are making efforts to find an answer to such problems as the differences in the heights of tides generated in the oceans, their types and variations, and their movements in the open oceans.
The experimental verification on earth has been achieved by measurements with horizontal pendulae and gravimeters, with not as much of accuracy as has been obtained by computations on the basis of astronomical data.
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The situation is entirely different as regards our knowledge of the functioning of the system of tide- producing forces. The question of how the amplitudes and phases of tides at the coasts, which vary from one location to another, are generated and how they propagate in the open ocean is still unanswered.
Undoubtedly, the main problem of the theory of tides is the determination of how this system of forces works. In fact, this represents a hydrodynamic instead of an astronomical problem.
Since Newton, the theory of ocean tides has attracted great mathematicians like Bernoulli, Laplace, Airy, Poincar, and many others. They have succeeded in elucidating the fundamental problems.
However, in order to surmount the mathematical problems, they considered model oceanic areas of simple geometrical shapes. But their solutions are not applicable to such seas that are irregularly shaped.
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During the last few decades altogether fresh attempts have been made, and these have been based on geophysical considerations. Scientists who made valuable contributions to this new approach include A.Von Sterneck, Defant, Thorade, Proudman and W.Hansen etc.