Brief notes on Equilibrium theory of tides

The Equilibrium theory assumes that the entire earth is covered by a uniform layer of water, and that the waters yield, and are heaped up beneath the moon. This theory is based on the assumption that the rotation of the earth relative to the moon is such that the same side of the earth always; faces the moon.

According to this theory, the tide- producing forces would remain stationary relative to the earth. At the points of the earth closest to and farthest away from the moon, there would be permanent reduction of the acceleration of gravity caused by the tide-generating forces.

On the contrary, the same forces would lead to a permanent increase of the acceleration of gravity in the plane at right angles to the line joining the centers of the earth and the moon.

If the earth were completely covered by ocean, the free surface of the water would be in equilibrium only when raised slightly at the points nearest to and farthest away from the moon, and when lowered slightly half way between these two points. By mathematical calculation, this reduced value was found to be 35.6 cm.

If at the point nearest to and farthest away from the moon the undisturbed surface were raised to this height (35.6 cm), there would be equilibrium. Thus, the greatest elevations and the greatest depressions of the equilibrium surface would be 35.6 cm and 17.8 cm respectively.

Thus, the maximum range of the lunar tide amounts to 53.4 cm. According to another calculation the maximum range of the lunar tide is found to be 55 cm, and of the solar tide to be 24 cm. However, this variation is unimportant.

According to the Equilibrium theory, the moon causes the water to be drawn towards the part of the earth facing it, and also towards the opposite side. In this way, the high tide is produced.

Between two high tides, the sea level is lowered causing a low tide. As the earth rotates on its axis every meridian comes in turn beneath each of the high and low tides. Thus, in most places there are two high and two low tides each day.

Because the moon actually revolves around the earth once every 24 hours, 50 minutes, a high tide tends to occur once every 12 hours, 25 minutes. Thus, every lunar day, external force tends to produce two high tides and two low tides approximately every 24 hours, 50 minutes.

The time of consecutive high tides is, therefore, about 50 minutes later. It is also true that similar high tides and low tides are caused by the attractive force of the sun. So the actual tides in the oceans are the combined result of a series of proturbances.

According to Sverdrup et al, “the obvious criticism that can be directed at this theory is that the movement of a flood proturbance over the surface of the earth cannot take place unless water masses actually change positions, but consideration of the movement of the water has been completely disregarded”. There are other objections too.

It is undoubtedly true, however, that the equilibrium theory advanced by I. Newton enables us to explain various characteristics of the oceanic tides. On the basis of observations and actual measurements of tides generated in different kinds of water bodies it has been found that different types of periodic inequalities occur in the tidal ranges in the seas and oceans.

For example, there are fortnightly inequality, monthly inequality, diurnal inequality and declinational inequality and so on. The main cause of these inequalities is some of the astronomical quantities like the phases of moon, its horizontal parallax, and the declination of the sun and moon.

To determine these astronomical quantities it is essential that the records of tides for longer periods, say, of about 19 years are available. There are certain countries which are engaged in the regular publication of astronomical year-books which are of great help in the prediction of tides at various places.