Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/137

Rh momentum to the fluid passing into the region to the left of $$S\ S$$. But this fluid is the same as that to which counterclockwise momentum had previously been imparted. And the two couples are of equal magnitude, and act on any portion of the fluid for equal time. Consequently the clockwise couple will exactly take away the angular momentum communicated by the counterclockwise couple, and the final state of fluid will be the same as its initial state. Also it will possess counterclockwise momentum whilst in the neighbourhood of the applied force. But this implies either a cyclic motion or a rotation, and we know the latter to be impossible; therefore a transverse force acting between the filament and the fluid implies a cyclic motion around the filament. It is evident that the foregoing theorem involves as a corollary the converse, i.e., that a cyclic motion in translation will give a transverse reaction. We have yet to investigate in what manner, if it is possible, the cyclic motion can be generated.