Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/426

App. II. of the all-pervading ether are essentially involved, such a term as a self-contained system ceases to have any signification. There is only one self-contained system known to us—the Universe.

From another point of view we know that according to modern theory the momentum of any finite quantity of matter, however small, moving with the velocity of light is infinite ; consequently a finite quantity of momentum will be carried at this velocity by a quantity of matter smaller than can be expressed in finite units, or, physically speaking, communication of momentum at the velocity of light becomes independent of the displacement or transference of matter. Thus the present application of the principle of no momentum is in no way antagonistic to modern views and discovery as to the transference of momentum by light and other manifestations of electric radiation.

Boyle's law, let us examine the case of an isolated compression wave travelling to and fro in a prismatic box of unit cross section and length $$= l .$$ Let the mass of the fluid in this wave, in excess of the normal contents of the region it occupies, be $$m .$$

Now since the wave carries an excess of fluid it will carry momentum, and this momentum will be represented by the mass $$m$$ transported with the velocity of wave propagation, which we denote by the symbol $$U .$$

And the presence of this excess of fluid in the enclosure will raise the mean pressure throughout the enclosure to the same extent as if it were uniformly diffused. (This has already been demonstrated.)

The proposition is to show that the pressure increase due to