Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/278

§ 178 state that it is almost unnecessary to specify the precise form to which $$n$$ values are supposed to relate; we may take it that we are dealing with a rectangular plan-form, and that n denotes the lateral breadth in terms of the fore and aft dimension; thus, for planes in pterygoid aspect $$n$$ has a value greater than unity, and for planes in apteroid aspect, less.

Now if $$\kappa$$ is a function of $$n$$ alone, $$\epsilon$$ is also a function of $$n$$ alone, and if we can by experiment or theory establish a form of expression in the one case, the other follows from the equation.

It is evident that the circumstances determining $$\epsilon$$ are foreign to our present hypothesis, and we shall require to temporarily take our stand outside this hypothesis in order to investigate the question.

§ 179. An Auxiliary Hypothesis.—Let us suppose an aerofoil represented in plan in Fig. 113 supported in a continuous medium; then if $$M_a$$ be the upward momentum communicated to the air passing between planes represented by the lines $$b\ b$$ and $$b_1\ b_1$$ at the time when its upward momentum is a maximum—that is, when it comes within the direct influence of the aerofoil (the descending field of Chap. IV.); then, assuming a