drag, the fluid in the interior has difficulty in finding its way back to take its place. This difficulty is greatest in the region from which the discontinuity springs, where the dead-water runs off to a "feather edge," and it is evident that some point of attenuation is reached at which the return flow becomes impossible, and the fluid will be "pumped out" or ejected from the region forward of this point. This brings the discontinuity further aft on the body, where the process can be supposed repeated, so that eventually the whole dead-water has been pumped away, and streamline motion supervenes. It is evident that the process will not occur in stages, as above suggested, but will be continuous.
It might be supposed from the foregoing argument that the degree of curvature of the surface of the body would not be a matter of importance, as in any case the feather edge of the deadwater would be sufficiently fine to ensure the ejection of some small amount of the fluid, and this process by continuous repetition would eventually clear the wake of its contents. If the surface of the body were frictionless, doubtless this might be the case, but it is established that there is continuity between the surface of an immersed body and the surrounding fluid; that is to say, there is the same degree of viscous connection between the fluid and the surface as there is between one layer of the fluid and another. The consequence of this is that the deadwater never fines off entirely, but extends forward as a sort of sheath enveloping the whole surface of the body, and if the curvature at any point is too rapid, the ejection may not prove effective, and the discontinuity will persist. It is evident therefore that there will be some relation between the bluffness of form permissible and the viscosity of the fluid, and, other things being equal, the less the viscosity the finer will have to be the lines of the body. The theory evidently also points to the importance of smoothness of surface when the critical conditions are approached.
The subject is not yet exhausted. We know that the thickness
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