It is a fact of common experience that a body in motion relative to a gas or liquid is subject to a resultant force, and it is customary to resolve this force into two components, the drag opposing the relative motion and the lift at right-angles to the direction of this motion. In general the drag is the pre-dominant component, but the class of bodies known as aerofoils and used for the construction of aeroplane wings, is such that the lift is considerably in excess of the drag. The present discussion relates solely to this class of bodies whose essential characteristic is the production of a large lift correlated with a relatively small drag. It is a matter of very considerable importance to develop a theory which will explain the origin of the forces experienced by an aerofoil, and will provide a method of calculating the characteristics of any aerofoil structure from a knowledge of its geometrical form and of the physical properties of the fluid through which it moves. It is proposed to discuss the behaviour of aerofoils in two and in three dimensions, and in particular to discuss the vortex theory of lift and induced drag. The general nature of the flow pattern on which the theory is based has been described by Lanchester, but the mathematical development of the thcorv is due to Prandtl and his colleagues.