By W. Froude, ESq., Assoc. I.N.A. Published in 1861
I feel some diffidence in bringing before the experienced members of this society what assumes to be a tolerably complete theoretical elucidation of a difficult and intricate subject, which has hitherto been treated as if unapproachable by the methods of regular investigation.
I may, however, perhaps, bespeak some attention to it, by mentioning that it is the result of an inquiry undertaken at the request of the late Mr. Brunel, with whom I frequently discussed its fundamental principles, while he was engaged on the design and the construction of the Great Eastern, receiving, as no one could fail to receive who discussed such principles with him, the greatest assistance from his broad and masculine perception of their real bearings and of their mutual relations.
The most observable feature in the actual movements of a ship when rolling, and that which had always appeared to me to be specially characteristic of the dynamical laws to which it world be necessary to refer them, is the gradual accumulation of angle during several successive rolls; the cumulative action thus growing up into a maximum, and then dying out by very similar gradations, until the ship becomes for a moment steady, when a nearly similar series of excursions commences and is reproduced: while in reference to the momentary pause, or cessation of motion, it has seemed to me clear that it occurs, not because the waves themselves cease, or cease to act, but because the last oscillation has died out at a moment when the ship and the waves have come to occupy, relatively, a position of momentary equilibrium.
The best information, however, which I have been able to collect from the report of others, and from my own observation, confirms me in the belief that the very large angles of rolling which are occasionally reached are never due to single wave impulses, but are invariably the cumulative results of the operation of successive waves. And I believe, too, that the law of accumulation does, in fact, accord very closely with that which is arrived at in the following investigation.
The investigation, then, of the laws of rolling motion in ships when thus regarded, assumes the form of the inquiry, “What is the cumulative result of the continuous action of “a series on consecutive waves operating on a given ship?”