(α), neglecting the counter-current, is sensible; if, however, the proportion were to become considerable, the departure from theory would become serious. The validity of the present application of the Newtonian method depends definitely upon the fact that is small.
Considering next (b) the problem of propulsion in its full relation to the body propelled: if a vessel be towed through a fluid, the pull on the tow line being applied from without, the whole energy is, in the sense of § 198, usefully employed, and the condition of affairs is that tacitly taken in § 198 to represent unit efficiency.
The energy expended passes into the fluid and is swallowed up partly in overcoming viscous stress and partly in setting the fluid in motion; the first part vanishes at once into the thermodynamic system and is lost; the second part remains in the fluid as kinetic energy until in turn it is spent in overcoming viscosity, when by degrees it also vanishes.
Now the energy that is left in the kinetic form takes some time to disappear, and in the meantime it constitutes a wake current with a corresponding counterwake whose momenta are equal and opposite, the wake current being situated in the immediate track of the vessel, and the counterwake further afield and extending theoretically to the confines of the fluid region, but only sensible for a limited distance. This kinetic energy is not irretrievably lost; after the fluid has passed in effect out of dynamic connection with the vessel, there is ample time for the recovery of the energy if a suitable method could be devised, and then, by returning it to the source of power, it is evident that the vessel will be propelled with a less expenditure of power than previously, and the “efficiency” will become greater than that somewhat arbitrarily chosen as unity.
§ 200. A Hypothetical Study in Propulsion.—Let us consider the case in which the propeller is constrained to act on the wake current (or, as it is sometimes termed, “the frictional wake”),
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