The dynamical theory of Laplace was developed in 1775 A.D. This theory uses the general equation of motion, taking into account the tidal forces as the external forces. Credit goes to Laplace for having exactly formulated the problems, and having presented solutions.
The comprehension of his mathematical treatment is rather difficult, because it is also connected with other problems of celestial mechanics. However, Poincare, an eminent mathematician, has given the modern representation of Laplace’s tidal theory and has also described the further development of the theory as suggested by the mathematicians of the 19th century.
The dynamical theory of Laplace is also based on the assumption that the earth is surrounded by water. But according to this theory, only the horizontal component of the tide-generating forces is of importance to the movement of water.
This theory attaches little importance to the vertical tide-generating forces, because they have been considered as comprising very small periodical variations of the acceleration of gravity.
The Coriolis force or the deflecting force of the earth’s rotation has been completely neglected. The theory considers that frictional forces nullify the free oscillations.
However, the most important contribution of Laplace to the problem of tides is his recognition of the fact that the depth distribution of a spherical ocean determines the tide significantly in its course of time.
Again, this theory considers that for constant depth, diurnal tides disappear as far as the tidal range is concerned. In contrast to the equilibrium theory, Laplace’s dynamical theory explains the small diurnal tides observed on the coast of the Atlantic Ocean at Brest.
However, the observations confirm this for the Atlantic Ocean only, but not for the Pacific and Indian Oceans. This is due to the peculiar bottom topography of the Atlantic Ocean which creates unfavourable resonance conditions in the entire ocean.
Laplace attached utmost importance to the depth distribution in the oceans in connection with the characteristics of tides. In contrast to the equilibrium theory, according to the dynamical theory of Laplace, for the oceanic depth as it is actually found on earth, a wave trough occurs at that point where the tide-producing heavenly body stands at the zenith or nadir, and not a wave crest.
The dynamical theory of Laplace has offered proof that every partial tide of the tide-generating potential produces an oscillation in the ocean, which has the period of the partial tide. These are the so-called astronomical tides.
However, it may be emphasized that the classic theories as above have, no doubt, provided fundamental insight into the behaviour of the ocean water in response to tide-producing forces in geometrically simple oceans.
But this is equally true that inferences drawn from the classic theories cannot be applied to explain the observed actual tides in natural oceans.