Professor Marey states that not only does the posterior margin of the wing yield _in an upward direction_ during the _down stroke_ until the under surface of the pinion makes a backward angle of 45° with the horizon, but that during the _up stroke_ it yields to the same extent _in an opposite direction_. The posterior flexible margin of the wing, according to Marey, passes through a space of 90° every time the wing reverses its course, this space being dedicated to the mere adjusting of the planes of the wing for the purposes of flight. The planes, moreover, he asserts, are adjusted not by vital and vito-mechanical acts but by _the action of the air alone_; this operating on the under surface of the wing and forcing its posterior margin _upwards_ during _the down stroke_; the air during the _up stroke_ acting upon the posterior margin of the upper surface of the wing, and forcing it _downwards_. This is a mere repetition of Borelli’s view. Marey delegates to the air the difficult and delicate task of arranging the details of flight. The time, power, and space occupied in reversing the wing alone, according to this theory, are such as to render flight impossible. That the wing does not act as stated by Borelli, Marey, and others may be readily proved by experiment. It may also be demonstrated mathematically, as a reference to figs. 114 and 115, p. 228, will show.
Let _a b_ of fig. 114 represent the horizon; _m n_ the line of vibration; _x c_ the wing inclined at an upward backward angle of 45° in the act of making the down stroke, and _x d_ the wing inclined at a downward backward angle of 45° and in the act of making the up stroke. When the wing _x c_ descends it will tend to dive downwards in the direction _f_ giving very little of any horizontal support (_a b_); when the wing _x d_ ascends it will endeavour to rise in the direction _g_, as it darts up like a kite (the body bearing it being in motion). If we take the resultant of these two forces, we have at most propulsion in the direction _a b_. This, moreover, would only hold true if the bird was as light as air. As, however, gravity tends to pull the bird downwards as it advances, the real flight of the bird, according to this theory, would fall in a line between _b_ and _f_, probably in _x h_. It could not possibly be otherwise; the wing described and figured by Borelli and Marey is in one piece, and made to vibrate vertically on either side of a given line. If, however, a wing in one piece is elevated and depressed in a strictly perpendicular direction, it is evident that the wing will experience a greater resistance during _the up stroke_, when it is acting _against gravity_, than during _the down stroke_, when it is acting _with gravity_. As a consequence, the bird will be more vigorously depressed during the ascent of the wing than it will be elevated during its descent. That the mechanical wing referred to by Borelli and Marey is _not a flying wing_, but a mere propelling apparatus, seems evident to the latter, for he states that the winged machine designed by him has unquestionably _not motor power enough to support its own weight_.[115]