Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/152

§ 102 motion as constituting an absolute and patent disproof of the doctrine of discontinuity, which in reality do not seem capable of any such interpretation. One of the supposed cases is given in Fig. 55, which represents a projectile having a gap in its mid-body dividing it into two halves which are assumed to be rigidly connected; this has been indicated in the present reproduction by a stem or spindle.

Now it appears to the author that this example can be construed in favour, rather than otherwise, of the Helmholtz doctrine. Let us suppose the gap bridged initially by a telescopic sheath represented by the dotted line and the projectile set in uniform motion in a perfect fluid. Next let us suppose the sheath to be withdrawn (by sliding it longitudinally), then we have a system of flow involving a surface of discontinuity, a system of flow alternative to that of the ordinary Eulerian theory, and contrary to the theorem of least energy, and one that has many points in common with that which obtains in practice.

§ 103. The Position Summarised.—We may summarise the possible causes of the departure from the theoretical Eulerian form of flow as follows:—

(1) The observed departure is due to viscosity, and:

(a) The departure is less the less the viscosity, as might be readily imagined (to harmonise with the Eulerian theory).

(b) The departure is greater the less the viscosity.

(2) The departure not necessarily connected with viscosity, and either:

(c) Due to cavitation (as suggested by Helmholtz).

(d) Due to compressibility (alternatively suggested by Helmholtz).