everyone who has experimented has observed, can m no wise be accounted for by the continuous and uniform action of [viscous] friction.”
This does not express the position of affairs one whit too strongly; in fact, before the date of the recent additions to the mathematical theory relating to discontinuous motion (largely initiated by Helmholtz himself), it might almost have been said that the hydrodynamic theory of the text-book had nothing at all to do with the motions of any known liquid or gas.
In the paper in question Helmholtz states that it is necessary to take account of a condition in the integration of the hydrodynamic equations, which had up till then been neglected. In the hydrodynamic equations, velocity and pressure are treated as continuous functions of the co-ordinates, but in reality there is nothing to prevent in a true inviscid fluid two layers slipping past one another with finite velocity. The author of the paper, referring to his previous work on gyratory movement, suggests that the surface of separation is a gyration surface, the conception being that the surface consists of an infinite distribution of lines of gyration at which the mass of fluid is vanishingly small (or evanescent), and the moment of rotation finite. It is pointed out that such a system involves a discontinuity, such as might be initiated by incipient cavitation, and under these circumstances the conditions of mathematical hypothesis are violated. The theory of discontinuous motions, such as outlined, is afterwards dealt with at some length, with results similar to those already given.
§ 100. The Doctrine of Discontinuity attacked by Kelvin.—The theory of discontinuity has been regarded by some authorities as a questionable innovation, and it has been violently attacked by Lord Kelvin in a series of articles to Nature in the year 1894, and so the subject has become a matter of controversy.
So far as the author is aware, this controversy has never been authoritatively settled; it is therefore necessary to give the
