Contribution to the aileron theory

In an attempt to treat theoretically the effect of ailerons, difficulty arises because an aileron may begin at any point of the wing. Hence the question arises as to how the transition of the lift distribution proceeds at such a point, since the effect of the aileron (i.e., the moment generated about the longitudinal axis) depends largely on this distribution. In order to answer this question regarding the lift distribution during irregular variations in the angle of attack at first independently of other influences, especially those of the wing tips, we have taken as the basis of the following theoretical discussion a wing of infinite span and constant chord which exhibits at one point an irregular variation in the angle of attack. As regards the mathematical treatment, we will first consider a wing with periodically recurring angle of attack.