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]
Fig. 114.
Fig. 115.
The manner in which the natural wing (and the artificial wing properly constructed and propelled) evades the resistance of the air during the up stroke, and gives continuous support and propulsion, is very remarkable. Fig. 115 illustrates the true principle. Let a b represent the horizon; m n the direction of vibration; x s the wing ready to make the down stroke, and x t the wing ready to make the up stroke. When the wing x s descends, the posterior margin (s) is screwed downwards and forwards in the direction s, t; the forward angle which it makes with the horizon increasing as the wing descends (compare with fig. [85] (a b c), p. 160, and fig. [88] (c d e f), p. 166). The air is thus seized by a great variety of inclined surfaces, and as the under surface of the wing, which is a true kite, looks upwards and forwards, it tends to carry the body of the bird upwards and forwards in the direction x w. When the wing x t makes the up stroke, it rotates in the direction t s to prepare for the second down stroke. It does not, however, ascend in the direction t s. On the contrary, it darts up like a true kite, which it is, in the direction x v, in virtue of the reaction of the air, and because the body of the bird, to which it is attached, has a forward motion communicated to it by the wing during the down stroke (compare with g h i of fig. [88], p. 166). The resultant of the forces acting in the directions x v and x b, is one acting in the direction x w, and if allowance be made for the operation of gravity, the flight of the bird will correspond to a line somewhere between w and b, probably the line x r. This result is produced by the wing acting as an eccentric—by the upper concave surface of the pinion being always directed upwards, the under concave surface downwards—by the under surface, which is a true kite, darting forward in wave curves both during the down and up strokes, and never making a backward angle with the horizon (fig. [88], p. 166); and lastly, by the wing employing the air under it as a fulcrum during the down stroke, the air, on its own part, reacting on the under surface of the pinion, and when the proper time arrives, contributing to the elevation of the wing.
If, as Borelli and his successors believe, the posterior margin of the wing yielded to a marked extent in an upward direction during the down stroke, and more especially if it yielded to such an extent as to cause the under surface of the wing to make a backward angle with the horizon of 45°, one of two things would inevitably follow—either the air on which the wing depends for support and propulsion would be permitted to escape before it was utilized; or the wing would dart rapidly downward, and carry the body of the bird with it. If the posterior margin of the wing yielded in an upward direction to the extent described by Marey during the down stroke, it would be tantamount to removing the fulcrum (the air) on which the lever formed by the wing operates.
If a bird flies in a horizontal direction the angles made by the under surface of the wing with the horizon are very slight, but they always look forwards (fig. [60], p. 126). If a bird flies upwards the angles in question are increased (fig. [59], p. 126). In no instance, however, unless when the bird is everted and flying downwards, is the posterior margin of the wing on a higher level than the anterior one (fig. [106], p. 203). This holds true of natural flight, and consequently also of artificial flight.