by the descending portion of the field aft of P Q will be greater than the upward momentum imparted by the corresponding ascending field aft of the aerofoil. Consequently the portion of the fluid traversing the regions f, f, f, f (Fig. 67) will be ultimately left with some residual downward momentum, which must be equal to the total upward momentum received by the fluid traversing the regions o, o, o, for otherwise there would be a
Fig. 67.
continual accumulation, or else attenuation, of the fluid in the lower strata of the atmosphere, which is impossible. (This otherwise constitutes an application of the principle of no momentum of § 5.) Thus in the case of a loaded aerofoil of finite lateral extent, there is a continual loss of energy occurring, and a source of power is consequently necessary to maintain the aerofoil in horizontal flight.
In addition to the residual vertical motions of the fluid, of which the causes have just been discussed, there must also be horizontal counter-currents formed simultaneously with those in
157
