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

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.

Fig. 113.§ 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

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