Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/431

Rh with a limited train, it is difficult to see in what manner this pressure can be confined to the region occupied by the wave train; according to thermodynamic principles it must be distributed uniformly and press equally in every direction. If this is true, the wave train as a whole will expand, and the remainder of the fluid will be compressed, so that the mean density of the wave train will become less than that of the undisturbed fluid. On this basis, employing the principle of § 5, a wave train under the conditions we are now supposing must be regarded as conveying negative momentum.

In an article on radiation in the "Encyclopaedia Britannica," Larmor gives a theorem which purports to be a general proof of the transmission or communication of momentum by wave motion. Poynting has given a condensed edition of this alleged proof, which may be quoted, as follows:—"Let us suppose that a train of waves is incident normally on a perfectly reflecting surface. Then, whether the reflecting surface is at rest, or is moving to or from the source, the perfect reflection requires that the disturbance at its surface shall be annulled by the superposition of the direct and reflected trains. The two trains must therefore have equal amplitudes. Suppose now that the reflector is moving forward towards the source. By Döppler's principle the waves of the reflected train are shortened, and so contain more energy than those of the incident train. The extra energy can only be accounted for by supposing that there is a pressure against the reflector, that work has to be done in pushing it forward. . . . A similar train of reasoning gives us a pressure on the source, increasing when the source is moving forward, decreasing when it is receding."