318 FLIGHT wing strikes vertically downwards, for, as already explained, the body of a flying bird is a body in motion ; but as a body in motion tends to fall downwards and forwards, the wine* must strike dowmvards and forwards in order effect ually to prevent its fall. Moreover, in point of fact, all natural wings and all artificial wings constructed on the natural type invariably strike doicnwards and fonvards. With regard to the second point, viz., the supposed rigidity of the anterior margin of the wing, it is only necessary to examine the anterior margins of natural wings to be convinced that they are in every case flexible and elastic. Similar remarks apply to properly constructed artificial wings. If the anterior margins of natural and artificial wings were rigid, it would be impossible to make them vibrate smoothly and continuously. This is a matter of experiment. If a rigid rod, or a wing with a rigid anterior margin, be made to vibrate, the vibration is characterized by an unequal jerky motion, which contrasts strangely with the smooth, steady, fanning movement peculiar to natural wings. As to the third point, viz., the upward lending of the posterior margin of the wing during the down stroke, it is necessary to remark that the statement is true if it means a slight upward bending, but that it is untrus if it means an extensive upward bending. Borelli does not state the amount of upward bending, but one of his followers, Profsssor E. J. Marey, maintains that during the down stroke the wing yields until its under surface makes a backward angle ivitli the horizon of 45. Marey further states that during the up stroke the wing yields to a corresponding extent in an opposite direction the posterior margin of the wing, according to him, passing through an angle of 90, plus or minus, according to cir cumstances, every time the wing rises and falls. That the posterior margin of the wing yields to a slight extent during both the down and up strokes will readily be admitted, alike because of the very delicate and highly elastic properties of the posterior margins of wings , and because of the comparatively great force employed in their propulsion ; but that they do not yield to the extent stated by Professor Marey is a matter of absolute certainty. This admits of direct proof. If any one watches the horizontal or upward flight of a large bird he will observe that the posterior or flexible margin of the wing never rises during the down stroke to a perceptible extent, so that the under surface of the wing never looks backwards. On the contrary, he will perceive that the under surface of the wing (during the down stroke) invariably looks forwards and forms a true kite with the horizon, the angles made by the kite varying at every part of the down stroke, as shown more particularly at c d e f g, ij k I m of fig. 30, p. 317. The authors who have adopted Borelli s plan of artificial wing, and who have endorsed his mechanical views of the wing s action most fully, are Chabrier, Straus-Durkheim, Girard, and Marey. Borelli s artificial wing, it will be re membered, consists of a rigid rod in front and a flexible sail behind. It is also made to strike vertically doumwards. According to Chabrier, the wing has only one period of activity. He believes that if the wing be suddenly lowered by the depressor muscles, it is elevated solely by the reac tion 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, and can elevate their wings at pleasure when not flying and when consequently the reaction of the air is not elicited. Straus-Durkheim agrees with Borelli both as to the natural and the artificial wing. Durkheim is of opinion that 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 consisting 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 impidsion it has received. These two parts of the wing, moreover, are equally indispensable to each other. Marey repeats Borelli and Durckheim with very trifling modifications, so late as 1869. 1 He 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 margin. 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 (according to Marey) 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 fl cxible. 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 surf ace- of the iving to look fonvards." The reverse of this, in Marey s opinion, takes place during the elevation of the wing the resistance of the air from above causing the upper surface of the ^v^ng to look backu ards. ... "At first," he says, " 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 move ments 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 resolv ing itself into two forces, a vertical and a horizontal force; the first suffices to raise the animal, the second to more it along." 2 Professor Marey, it will be observed, repro duces Borelli s artificial wing, and even his text, at a dis tance of nearly two centuries. The artificial wing recommended by Professor Petti- grew is a more exact imitation of nature than either of the foregoing. It is of a more or less triangular form, thick at the root and anterior margin, and thin at the tip and posterior margin. No part of it is rigid. It is on the contrary highly elastic and flexible throughout. It is furnished with springs at its root to contribute to its con tinued play, and is applied to the air by a direct piston action in such a way that it descends in a downward and forward direction during the down stroke, and ascends in an upward and forward direction during the up stroke. It elevates and propels both when it rises and falls. It, moreover, ttvists and untwists during its action and des cribes figure-of-8 and ivaved tracks in space, precisely as the natural iving does. The twisting is most marked at the tip and posterior margin, particularly that half of the posterior margin next the tip. The wing when in action may be divided into two portions by a line running diagonally between the tip of the wing anteriorly and the 1 Revue des Cours Scientifiques do In France et de tfitrangcr, 1869, par M. le Docteur Marey, professeur au College de France. 2 Professor E. J. Marey, op. cit., 1869.
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