Equally difficult to understand are the observations when the disturbance in the sea has occurred several hours after an earthquake; as, for instance, at Batavia, in 1852, when there was an interval of two hours; and to this must be added the observations where the motion of the sea has preceded that of the earthquake—as, for instance, in 1852, at Smyrna. Whilst recognising the fact that it is possible to suggest explanations for many of these anomalies, we must also bear in mind that they are, generally speaking, exceptional, and, in some instances, may possibly be due to errors in observations.
Velocity of propagation of sea waves, and depth of the ocean.—It has long been known to physical science that the velocity with which a given wave is propagated along a trough of uniform depth, holds a relation to the depth of the trough.
If v is the velocity of the wave, and h the depth of the trough, this relation may be expressed as follows:—
h = v2/g or h = (v/k)2
Where g = 32·19 and k = 5·671.
It will be observed that these two formulæ (the first of which is known as Russell’s formula, and the second as Airy’s) are practically identical.
The apparent difference is in the average value assigned to the constant.
For large waves such as we have to deal with, it would be necessary, if we were desirous of great accuracy, to increase the value of h by some small fraction of itself. We might also make allowance for the different values of g, according to our position on the earth’s surface. With these formulæ at our disposal it is an easy matter, after having determined the velocity with which a wave was propagated, to determine the average depth of the area over which it was transmitted.
In making certain earthquake investigations the reverse problem is sometimes useful—namely, determining the velocity with which a sea wave has advanced upon a shown line, from a knowledge of the depth of the water in which it has been propagated.
Calculations of the average depths of the Pacific, dependent on the velocity with which earthquake waves have been propagated, have been made by many investigators.