Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/172

§ 114 disturbance approximates to its evanescent form, that which we now propose to investigate. We therefore base the initial argument upon the case of an aeroplane gliding horizontally and edgewise, supporting a load smaller than can be specified infinite units.

§ 115, Aeroplane of Infinite Lateral Extent.—We have in the previous chapter become familiar with the simplification that results from the consideration of cases in which the motion takes place in two dimensions only, and with the conception of bodies of infinite lateral extent as a special case involving such a condition.

In Fig. 64, let $$A$$ represent the forward and $$B$$ the after-edge of an aeroplane extending to infinity in the direction at right angles to the plane of the paper; or, if preferred, we may consider the plane to be of finite extent, but bounded laterally by two continuous parallel walls rising vertically from the surface of the earth.

Let us examine a portion of the field $$e\ e\ e$$ enclosed between two adjacent lines of force, $$J_1, J_2.$$ Then the intensity of the field in the region $$e\ e\ e$$ is inversely proportional to the distance between the hounding lines of force. For let $$q_1, q_2,$$ be the normal distances at any two points $$G$$ and $$H,$$ and let us suppose a small displacement