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.

These remarks are more especially applicable to the flight of the bat and bird where the wing is made to vibrate more or less perpendicularly (fig. 17, p. 36; figs. 82 and 83, p. 158. Compare with fig. 85, p. 160, and fig. 88, p. 166). If a bird or a bat wishes to fly upwards, its flying surfaces must always be inclined upwards. It is the same with the fish. A fish can only swim upwards if its body is directed upwards. In the insect, as has been explained, the wing is made to vibrate in a more or less horizontal direction. In this case the wing has not to contend directly against gravity (a wing which flaps vertically must). As a consequence it is made to tack upon the air obliquely zigzag fashion as horse and carriage would ascend a steep hill (vide figs. 67 to 70, p. 141. Compare with figs. 71 and 72, p. 144). In this arrangement gravity is overcome by the wing reversing its planes and acting as a kite which flies alternately forwards and backwards. The kites formed by the wings of the bat and bird always fly forward (fig. 88, p. 166). In the insect, as in the bat and bird, the posterior margin of the wing never rises above the horizon so as to make an upward and backward angle with it, as stated by Borelli, Marey, and others (ca a of fig. 114, p. 228).

While Borelli and his successors are correct as to the wedgeaction of the wing, they have given an erroneous interpretation of the manner in which the wedge is produced. Thus Borelli states that when the wings descend their posterior margins ascend, the two wings forming a cone whose base is represented by cbe of fig. 113, p. 220); its apex being represented by af of the same figure. The base of Borelli's cone, it will be observed, is inclined forwards in the direction of

the head of the bird. Now this is just the opposite of what ought to be. Instead of the two wings forming one cone, the base of which is directed forwards, each wing of itself forms two cones, the bases of which are directed backwards and outwards, as shown at fig. 116.

m

qo

n

b

FIG. 116.

In this figure the action of the wing is compared to the sculling of an oar, to which it bears a considerable resemblance. 1 The one cone, viz., that with its base directed outwards, is represented at x bd. This cone corresponds to the area mapped out by the tip of the wing in the process of elevating. The second cone, viz., that with its base directed backwards, is represented at qpn. This cone corresponds to the area mapped out by the posterior margin of the wing in the process of propelling. The two cones are produced in virtue of the wing rotating on its root and along its anterior margin as it ascends and descends (fig. 80, p. 149; fig. 83, p. 158). The present figure (116) shows the double twisting action of the wing, the tip describing the figure-of-8 indicated at befgh d ijkl; the posterior margin describing the figure-of-8 indicated at prn. It is in this manner the cross pulsation or wave referred to at p. 148 is produced. To represent the action of the wing the sculling oar (a b, xs, cd) must have a small scull (mn, qr, op) working at right angles to it. This follows because 1 In sculling strictly speaking, it is the upper surface of the oar which is most effective; whereas in flying it is the under.

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

1 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