[Illustration: Fig. 59.--An illustration from another scientific publication also on the Dynamics of Flight. It will be observed that the air in striking the underneath side of the aeroplane is divided into two streams, a portion of it flowing backwards and over the top of the edge of the aeroplane where it becomes compressed. An eddy is formed on the back and top of the aeroplane, and the air immediately aft the aeroplane is neither rising nor falling. Just how these mathematicians reason out that the air in striking the front of the aeroplane would jump backwards and climb up over the top and leading edge against the wind pressure is not clear.] [Illustration: Fig. 60.--This shows another illustration from the same mathematical work, and represents the direction which the air is supposed to take on striking a flat aeroplane. With this, the air is also divided, a portion moving forward and over the top of the aeroplane where it is compressed, leaving a large eddy in the rear, and, as the dotted lines at the back of the aeroplane are horizontal, it appears that the air is not forced downwards by its passage. Here, again, formula founded on such hypothesis is misleading in the extreme.] [Illustration: Fig. 61.--This shows the shape and the practical angle of an aeroplane. This angle is 1 in 10, and it will be observed that the air follows both the upper and the lower surface, and that it leaves the plane in a direction which is the resultant of the top and bottom angle.] [Illustration: Fig. 62.--This shows an aeroplane of great thickness, placed at the highest angle that will ever be used--1 in 4--and even with this the air follows the upper and lower surfaces. No eddies are formed, and the direction that the air takes after leaving the aeroplane is the resultant of the top and bottom angles.] [Illustration: Fig. 63.--Section of a screw blade having a rib on the back. The resistance caused by this rib is erroneously supposed to be skin friction.] [Illustration: Fig. 64.--Shows a flat aeroplane placed at an angle of 45°, an angle which will never be used in practical flight, but at this angle the momentum of the approaching air and the energy necessary to give it an acceleration sufficiently great to make it follow the back of the aeroplane are equal, and at this point, the wind may either follow the surface or not. Sometimes it does and sometimes it does not. See experiments with screws.]