Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/88

§ 51 body. In Figs. 29 and 30 the curve does not extend to the $$V^2$$ stage; in Fig. 31 we have the three stages represented diagrammatically, firstly, by a straight line departure from the origin where $$R \propto V$$—this is the Stokes stage; next we have a section of the curve following the $$R \propto V^{1.5}$$ law, the Allen stage, and lastly the curve will approximate to a parabola where $$R \propto V^2 .$$ The latter stage is that investigated both theoretically and experimentally by Newton ("Principia," Book II., Section VII.), determinations being made both in water and air; also in the year 1719 by Dr. Desaguliers, who employed spherical bladders let fall from the cupola of St. Paul's. Newton's theoretical investigations were based on the hypothetical medium of discrete particles, but the experimental verification was sufficiently close, qualitatively, to establish the velocity squared law as substantially correct, so far at least as the sizes of sphere and velocities employed in his own and Desaguliers' experiments are concerned.

§ 52. Physical Meaning of Change of Index.—The nature of the alteration in the system of disturbance that accompanies each change of "law" is a matter of considerable interest. The