By fixing the wing to the head of the piston all gearing apparatus is avoided, and the number of joints and working points reduced--a matter of no small importance when it is desirable to conserve the motor power and keep down the weight. _How to apply Artificial Wings to the Air._--Borelli, Durckheim, Marey, and all the writers with whom I am acquainted, assert that the wing should be made to vibrate _vertically_. I believe that if the wing be in one piece it should be made to vibrate _obliquely and more or less horizontally_. If, however, the wing be made to vibrate _vertically_, it is necessary to supply it with a ball-and-socket joint, and with springs at its root (_m n_ of fig. 125, p. 241), to enable it _to leap forward in a curve_ when it descends, and in another and _opposite curve_ when it ascends (_vide a_, _c_, _e_, _g_, _i_ of fig. 81, p. 157). This arrangement practically converts the vertical vibration into _an oblique one_. If this plan be not adopted, the wing is apt to foul at its tip. In applying the wing to the air it ought to have a figure-of-8 movement communicated to it either directly or indirectly. It is a peculiarity of the artificial wing properly constructed (as it is of the natural wing), _that it twists and untwists and makes figure-of-8 curves during its action_ (see _a b_, _c d_ of fig. 122, p. 239), this enabling it to seize and let go the air with wonderful rapidity, and in such a manner as to avoid dead points. If the wing be in several pieces, it may be made to vibrate more vertically than a wing in one piece, from the fact that the outer half of the pinion moves forwards and backwards when the wing ascends and descends so as alternately to become a short and a long lever; this arrangement permitting the wing to avoid the resistance experienced from the air during the up stroke, while it vigorously seizes the air during the down stroke.