[Illustration: Fig. 65.--The aeroplane here shown is a mathematical paradox. This aeroplane lifts, no matter in which direction it is driven. It encounters air which is stationary and leaves it with a downward trend; therefore it must lift. However, if we remove the section _b_, and only subject _a_ to the blast, as shown at Fig. 66, no lifting effect is produced. On the contrary, the air has a tendency to press _a_, downwards. The path which the air takes is clearly shown; this is most important, as it shows that the shape of the top side is a factor which has to be considered. All the lifting effect in this case is produced by the top side.] [Illustration: Fig. 66.] [Illustration: Fig. 67.--In this drawing _a_ represents an aeroplane, or a bird’s wing. Suppose that the wind is blowing in the direction of the arrows; the real path of the bird as relates to the air is from _i_ to _j_,--that is, the bird is falling as relates to the air although moving on the line _c_, _d_, against the wind. In some cases, a bird is able to travel along the line _g_, _h_, instead of in a horizontal direction, thus rising and apparently flying into the teeth of the wind at the same time.] SOME RECENT MACHINES. Professor S. P. Langley, of the Smithsonian Institute, Washington, D.C., made a small flying model in 1896. This, however, only weighed a few pounds; but as it did actually fly and balance itself in the air, the experiment was of great importance, as it demonstrated that it was possible to make a machine with aeroplanes so adjusted as to steer itself automatically in a horizontal direction. In order to arrive at this result, an innumerable number of trials were made, and it was only after months of careful and patient work that the Professor and his assistants succeeded in making the model fly in a horizontal direction without rearing up in front, and then pitching backwards, or plunging while moving forward.