motion of the earth to cause the waters of the oceans to oscillate like water contained in vessels of various shapes and sizes.
While not questioning the fact established by Newton that the tides are primarily due to the attraction of the moon and sun. Admiral Fitz Roy attempts to explain the tides upon the assumption of stationary waves extending in an east-and-west direction across various portions of the several oceans. His wide experience as a navigator had familiarized him with the fact that throughout some extended regions of the ocean, the tides occur at nearly one and the same time; also that even for islands remote from the land, the amount of rise and fall is quite various.
Sir George B. Airy was the first person to make an extensive mathematical study of wave motion implied in tidal phenomena. While he does not point out how the ocean tides are produced, he shows that certain dependent bodies of water, and in particular the Irish Sea, must contain stationary waves. He establishes the theoretical result that the tides in a north-and-south canal extending from the equator to either pole must consist of a stationary wave.
William Ferrel suggests that, because of their unusual size, the tides of the North Atlantic may depend upon stationary waves extending in an east-and-west direction across the ocean; and, in particular, upon one extending between the coasts of Ireland and those of Newfoundland.
These, and other writers who have expressed similar views, failed to consider that an imperfectly bounded strip of the sea must have considerable width (as well as a suitable length) in order to make a stationary wave possible. They also failed to make any connection between the known tidal forces and the times of the tide.
This brings us to the subject proper, which involves an approximate explanation of the dominant ocean tides, it being manifestly unreasonable to expect accurate mathematical solutions of the problems involved.
It should be noted in passing that although Dr. Berghaus propounded no theories concerning the tides, his cotidal chart constructed in 1889 marks a radical departure from those previously constructed, and is in itself highly suggestive.
The Tide-producing Forces
The tide-producing forces of moon and sun can be computed from well-established astronomical data, and there are no uncertainties connected with their determination, at least to a moderate degree of refinement. In this place it is necessary to say only a few words descriptive of these forces. The tide-producing force of the moon upon a particle of unit mass is the difference between the moon's attraction upon this mass and upon a unit mass situated at the earth's center; or