Manchester Memoirs, Vol. xliv. ( i <S99), No. 5. 9 



be only approximate. Apart from frictional losses, the 

 maintenance of a given level im|)lies the continual forma- 

 tion of a downward aerial current, and consequent expen- 

 diture of energ)-. We ha\e next to consider the magnitude 

 of these losses, taking the case of a plane moving at a uni- 

 form speed. And, in the first instance, we shall neglect the 

 frictional forces, assuming that the reaction of the air 

 upon the plane is truly normal. 



Before we can advance a step in the desired direction 

 we must know how the normal pressure upon an aero- 

 plane is related to the size and shape of the plane, to the 

 velocity of the motion, and above all to the angle between 

 the plane and the direction of motion. According to an 

 erroneous theory, to some extent sanctioned by Newton, 

 the mean pressure would depend only upon the area of the 

 plane and the resolved part of the velocity in a direction 

 perpendicular to the plane. If V be the velocity, a the 

 angle between V and the plane, p the density of the air 

 (or other fluid concerned), the pressure/ would be given by 



p = \oV'^%\\\-n (4). 



That this formula is quite erroneous, especially 

 when a is small, has long been known.* At small 

 angles the pressure is more nearl)- proportional to 

 sin a than to sin'-a and, as was strongly emphasized by 

 Wenham in an early and important paper on aerial loco- 

 motion,-|- the question of shape and presentation is by no 

 means indifferent. In the case of an elongated shape 

 moving \\ith given velocity f", and at a given small 

 inclination a, the pressure is much greater when the long 

 dimension of the plane is perpendicular than when it is 

 (nearly) parallel to V. 



* A further ilisciission will be fournl in Phil. J/ti,^":, vol. ii. , p. 430, 1S76, 

 Scientific Papers, vol. i., p. 287, and in Nature, vol. xlv. , p. loS, 1892. 

 t Report of Aeronautical Society, 1S66, p. 10. 



