other things being equal, the longer it will take to bring about a given degree of inflation.
(4) The viscous drag experienced between the live fluid and dead water tends to carry the latter away, and if the viscosity exceed a certain value, then, other things being equal, it is found in experience (notably in the case of an ichthyoid form) that the dead water may be ejected and carried away as fast as formed by the viscous drag of the surrounding current. Under these conditions it may be taken that viscosity by its direct drag prevents the surface current from flowing in opposition to the main stream, so that the surface current is consistently rearward, the result being an absence of dead water. The surface of discontinuity may be regarded as having coalesced with the surface film of the body. If the viscosity be sufficiently reduced, the surface of discontinuity will detach itself, and in general the less the viscosity the more complete will he the development of the discontinuous system of flow.
Let us now take the case of a fluid bordering on the inviscid. It is evident, firstly, that the change in the system of flow will be very slow; and, secondly, it would appear that the ultimate transformation of the system will be very complete.
Let us now go further and suppose the viscosity of zero value. Then, on the principle laid down in § 101, we may regard the ultimate condition as one involving discontinuity as investigated by Helmholtz and others, with the reservation that it will require an infinite time for its development.
The transition stages of the system of flow in the inviscid or nearly inviscid fluid are wholly unknown. If we assume the Eulerian and Helmholtz as the initial and final systems of flow, there must be a continuous series of intermediate stages that await investigation. In the Helmholtz theory the dead water region has assigned to it a pressure equal to that of hydrostatic head. Perhaps the intervening stages could be investigated in like manner by assigning other pressure values to the region in question.
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