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the wing has to elevate as well as propel; the oar of a boat when employed as a scull only propelling. In order to elevate more effectually, the oars formed by the wings are made to oscillate on a level with and under the volant animal rather than above it; the posterior margins of the wings being made to oscillate on a level with and below the anterior margins (pp. 150, 151).

Borelli, and all who have written since his time, are unanimous in affirming that the horizontal transference of the body of the bird is due to the perpendicular vibration of the wings, and to the yielding of the posterior or flexible margins of the wings in an upward direction as the wings descend. I am, however, as already stated, disposed to attribute the transference, 1st, to the fact that the wings, both when elevated and depressed, leap forwards in curves, those curves uniting to form a continuous waved track; 2d, to the tendency which the body of the bird has to swing forwards, in a more or less horizontal direction, when once set in motion ; 3d, to the construction of the wings (they are elastic helices or screws, which twist and untwist when they are made to vibrate, and tend to bear upwards and onwards any weight suspended from them); 4th, to the reaction of the air on the under surfaces of the wings, which always act as kites; 5th, to the ever-varying power with which the wings are urged, this being greatest at the beginning of the down stroke, and least at the end of the up one; 6th, to the contraction of the voluntary muscles and elastic ligaments; 7th, to the effect produced by the various inclined surfaces formed by the wings during their oscillations ; 8th, to the weight of the bird—weight itself, when acting upon inclined planes (wings), becoming a propelling power, and so contributing to horizontal motion. This is proved by the fact that if a sea bird launches itself from a cliff with expanded motionless wings, it sails along for an incredible distance before it reaches the water (fig. 103, p. 186).

The authors who have adopted Borelli's plan of artificial wing, and who have indorsed his mechanical views of the action of the wing most fully, are Chabrier, Straus-Durckheim, Girard, and Marey. Borelli's artificial wing, as already explained (p. 220, fig. 113), consists of a rigid rod (e, r) in

front, and a flexible sail (a, o) composed of feathers, behind. It acts upon the air, and the air acts upon it, as occasion demands.

Chabrier's Views.—Chabrier states that the wing has only one period of activity—that, in fact, if the wing be suddenly lowered by the depressor muscles, it is elevated solely by the reaction of the air. There is one unanswerable objection to this theory—the bats and birds, and some, if not all the insects, have distinct elevator muscles. The presence of welldeveloped elevator muscles implies an elevating function, and, besides, we know that the insect, bat, and bird can elevate their wings when they are not flying, and when, consequently, no reaction of the air is induced.

Straus-Durckheim's Views.—Durckheim believes the insect abstracts from the air by means of the inclined plane a component force (composant) which it employs to support and direct itself. In his Theology of Nature he describes a schematic wing as follows:-It consists of a rigid ribbing in front, and a flexible sail behind. A membrane so constructed will, according to him, be fit for flight. It will suffice if such a sail elevates and lowers itself successively. It will, of its own accord, dispose itself as an inclined plane, and receiving obliquely the reaction of the air, it transfers into tractile force a part of the vertical impulsion it has received. These two parts of the wing are, moreover, equally indispensable to each other. If we compare the schematic wing of Durckheim with that of Borelli they will be found to be identical, both as regards their construction and the manner of their application.

Professor Marey, so late as 1869, repeats the arguments and views of Borelli and Durckheim, with very trifling alterations. Marey describes two artificial wings, the one composed of a rigid rod and sail—the rod representing the stiff anterior margin of the wing; the sail, which is made of paper bordered with card-board, the flexible posterior portion. The other wing consists of a rigid nervure in front and behind of thin parchment which supports fine rods of steel. He states, that if the wing only elevates and depresses itself, “ the resistance of the air is sufficient to produce all the other movements. In effect the wing of an insect has not the power of equal resistance in every part. On the anterior margin the extended nervures make it rigid, while behind it is fine and flexible. During the vigorous depression of the wing the nervure has the power of remaining rigid, whereas the flexible portion, being pushed in an upward direction on account of the resistance it experiences from the air, assumes an oblique position, which causes the upper surface of the wing to look forwards." ...“At first the plane of the wing is parallel with the body of the animal. It lowers itself—the front part of the wing strongly resists, the sail which follows it being flexible yields. Carried by the ribbing (the anterior margin of the wing) which lowers itself, the sail or posterior margin of the wing being raised meanwhile by the air, which sets it straight again, the sail will take an intermediate position, and incline itself about 45° plus or minus according to circumstances. The wing continues its movements of depression inclined to the horizon, but the impulse of the air which continues its effect, and naturally acts upon the surface which it strikes, has the power of resolving itself into two forces, a vertical and a horizontal force, the first suffices to raise the animal, the second to move it along."1 The reverse of this, Marey states, takes place during the elevation of the wing—the resistance of the air from above causing the upper surface of the wing to look backwards. The fallaciousness of this reasoning has been already pointed out, and need not be again referred to. It is not a little curious that Borelli's artificial wing should have been reproduced in its integrity at a distance of nearly two centuries.

i Compare Marey's description with that of Borelli, a translation of which I subjoin. “Let a bird be suspended in the air with its wings expanded, and first let the under surfaces (of the wings) be struck by the air ascending perpendicularly to the horizon with such a force that the bird gliding down is prevented from falling : I say that it (the bird) will be impelled with a horizontal forward motion, because the two osseous rods of the wings are able, owing to the strength of the muscles, and because of their hardness, to resist the force of the air, and therefore to retain the same form (literally extent, expansion), but the total breadth of the fan of each wing yields to the impulse of the air when the flexible feathers are permitted to rotate around the manubria or osseous axes, and hence it is necessary that the extremities of the wings approximate each other : wherefore the wings acquire the form of a wedge whose point is directed towards the tail of the bird, but whose surfaces are compressed on either side by the ascending air in such a manner that it is driven out in the direction of its base. Since, however, the wedge formed by the wings cannot move forward unless it carry the body of the bird along with it, it is evident that it (the wedge) gives place to the air impelling it, and therefore the bird flies forward in a horizontal direction. But now let the substratum of still air be struck by the fans (feathers) of the wings with a motion perpendicular to the horizon. Since the fans and sails of the wings

The Author's Views:-his Method of constructing and applying Artificial Wings as contra-distinguished from that of Borelli, Chabrier, Durckheim, Marey, etc.The artificial wings which I have been in the habit of making for several years differ from those recommended by Borelli, Durckheim, and Marey in four essential points :

1st, The mode of construction.
2d, The manner in which they are applied to the air.
3d, The nature of the power employed.

4th, The necessity for adapting certain elastic substances to the root of the wing if in one piece, and to the root and the body of the wing if in several pieces.

And, first, as to the manner of construction.

Borelli, Durckheim, and Marey maintain that the anterior margin of the wing should be rigid ; I, on the other hand, believe that no part of the wing whatever should be rigid, not even the anterior margin, and that the pinion should be flexible and elastic throughout.

That the anterior margin of the wing should not be composed of a rigid rod may, I think, be demonstrated in a variety of ways. If a rigid rod be made to vibrate by the hand the vibration is not smooth and continuous; on the contrary, it is irregular and jerky, and characterized by two halts or pauses (dead points), the one occurring at the end of the up stroke, the other at the end of the down stroke. This mechanical impediment is followed by serious consequences as far as power and speed are concerned—the slowing of the wing at the end of the down and up strokes involving a acquire the form of a wedge, the point of which is turned towards the tail (of the bird), and since they suffer the same force and compression from the air, whether the vibrating wings strike the undisturbed air beneath, or whether, on the other hand, the expanded wings (the osseous axes remaining rigid) receive the percussion of the ascending air; in either case the flexible feathers yield to the impulse, and hence approximate each other, and thus the bird moves in a forward direction.—De Motu Animalium, pars prima, prop. 196,

1685.

great expenditure of power and a disastrous waste of time. The wing, to be effective as an elevating and propelling organ, should have no dead points, and should be characterized by a rapid winnowing or fanning motion. It should reverse and reciprocate with the utmost steadiness and smoothness—in fact, the motions should appear as continuous as those of a fly-wheel in rapid motion : they are so in the insect (figs. 64, 65, and 66, p. 139).

To obviate the difficulty in question, it is necessary, in my opinion, to employ a tapering elastic rod or series of rods bound together for the anterior margin of the wing.

If a longitudinal section of bamboo cane, ten feet in length, and one inch in breadth (fig. 117), be taken by the extremity and made to vibrate, it will be found that a wavy serpentine motion is produced, the waves being greatest when the vibration is slowest (fig. 118), and least when it is most rapid (fig. 119). It will further be found that at the extremity of the cane where the impulse is communicated there is a steady reciprocating movement devoid of dead points. The continuous movement in question is no doubt due to the fact that the different portions of the cane reverse at different periods—the undulations induced being to an interrupted or vibratory movement very much what the continuous play of a fly-wheel is to a rotatory motion.

The Wave Wing of the Author.-If a similar cane has added to it, tapering rods of whalebone, which radiate in an outward direction to the extent of a foot or so, and the whalebones be covered by a thin sheet of india-rubber, an artificial wing, resembling the natural one in all its essential points, is at once produced (fig. 120). I propose to designate this wing, from the peculiarities of its movements, the wave wing (fig. 121). If the wing referred to (fig. 121) be made to vibrate at its root, a series of longitudinal (cd e) and transverse (f g h) waves are at once produced; the one series running in the direction of the length of the wing, the other in the direction of its breadth (vide p. 148). This wing further twists and untwists, figure-of-8 fashion, during the up and down strokes, as shown at fig. 122, p. 239 (compare with figs. 82 and 83, p. 158 ; fig. 86, p. 161; and fig. 103, p. 186).

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