exceedingly fragile, and because of the prodigious force required to propel them usually break after a few trials. Fig. 112, p. 217, embodies M. de la Landelle's ideas.

In the helicopteric models made by MM. Nadar, Pontin d'Amécourt, and de la Landelle, the screws (mnopqrst of figure) are arranged in tiers, i.e. the one screw is placed above the other. In this respect they resemble the aëroplanes recommended by Mr. Wenham, and tested by Mr. Stringfellow (compare m n o p q r s t of fig. 112, with a bc of fig. 110, p. 213). The superimposed screws, as already explained, were first figured and described by Sir George Cayley (p. 215). The French screws, and that employed by Mr. Phillips, are rigid or unyielding, and strike the air at a given angle, and herein, I believe, consists their principal defect. This arrangement results in a ruinous expenditure of power, and is accompanied by a great amount of slip. The aërial screw, and the machine to be elevated by it, can be set in motion without any preliminary run, and in this respect it has the advantage over the machine supported by mere sustaining planes. It has, in fact, a certain amount of inherent motion, its screws revolving, and supplying it with active or moving surfaces. It is accordingly more independent than the machine designed by Henson, Wenham, and Stringfellow.

I may observe with regard to the system of rigid inclined planes wedged forward at a given angle in a straight line or in a circle, that it does not embody the principle carried out in nature.

The wing of a flying creature, as I have taken pains to show, is not rigid; neither does it always strike the air at a given angle. On the contrary, it is capable of moving in all its parts, and attacks the air at an infinite variety of angles (pp. 151 to 154). Above all, the surface exposed by a natural wing, when compared with the great weight it is capable of elevating, is remarkably small (fig. 89, p. 171). This is accounted for by the length and the great range of motion of natural wings; the latter enabling the wings to convert large tracts of air into supporting areas (figs. 64, 65, and 66, p. 139). It is also accounted for by the multiplicity of the movements of natural wings, these enabling the pinions to create and rise upon currents of their own

forming, and to avoid natural currents when not adapted for propelling or sustaining purposes (fig. 67, 68, 69, and 70, p. 141).

If any one watches an insect, a bat, or a bird when dressing its wings, he will observe that it can incline the under surface of the wing at a great variety of angles to the horizon. This it does by causing the posterior or thin margin of the wing to rotate around the anterior or thick margin as an axis. As a result of this movement, the two margins are forced into double and opposite curves, and the wing converted into a plastic helix or screw. He will further observe that the bat and bird, and some insects, have, in addition, the power of folding and drawing the wing towards the body. during the up stroke, and of pushing it away from the body and extending it during the down stroke, so as alternately to diminish and increase its area; arrangements necessary to decrease the amount of resistance experienced by the wing during its ascent, and increase it during its descent. It is scarcely requisite to add, that in the aeroplanes and aërial screws, as at present constructed, no provision whatever is made for suddenly increasing or diminishing the flying surface, of conferring elasticity upon it, or of giving to it that infinite variety of angles which would enable it to seize and disentangle itself from the air with the necessary rapidity. Many investigators are of opinion that flight is a mere question of levity and power, and that if a machine could only be made light enough and powerful enough, it must of necessity fly, whatever the nature of its flying surfaces. A grave fallacy lurks here. Birds are not more powerful than quadrupeds of equal size, and Stringfellow's machine, which, as we have seen, only weighed 12 lbs., exerted one-third of a horse power. The probabilities therefore are, that flight is dependent to a great extent on the nature of the flying surfaces, and the mode of applying those surfaces to the air.

Artificial Wings (Borelli's Views).—With regard to the production of flight by the flapping of wings, much may and has been said. Of all the methods yet proposed, it is unquestionably by far the most ancient. Discrediting as apocryphal the famous story of Dedalus and his waxen wings, we cer

tainly have a very graphic account of artificial wings in the De Motu Animalium of Borelli, published as far back as 1680, i.e. nearly two centuries ago.1

Indeed it will not be too much to affirm, that to this distinguished physiologist and mathematician belongs almost all the knowledge we possessed of artificial wings up till 1865. He was well acquainted with the properties of the wedge, as applied to flight, and he was likewise cognisant of the flexible and elastic properties of the wing. To him is to be traced the purely mechanical theory of the wing's action. He figured a bird with artificial wings, each wing consisting of a rigid rod in front and flexible feathers behind. I have thought fit to reproduce Borelli's figure both because of its great antiquity, and because it is eminently illustrative of his text.2

The wings (cf, o e a), are represented as striking vertically downwards (gh). They remarkably accord with those described by Straus-Durckheim, Girard, and quite recently by Professor Marey.3

Borelli is of opinion that flight results from the application of an inclined plane, which beats the air, and which has a wedge action. He, in fact, endeavours to prove that a bird wedges itself forward upon the air by the perpendicular vibra

1 Borelli, De Motu Animalium. Sm. 4to, 2 vols. Romæ, 1680.

2 De Motu Animalium, Lugduni Batavorum apud Petrum Vander. Anno MDCLXXXV. Tab. XIII. figure 2. (New edition.)

3 Revue des Cours Scientifiques de la France et de l'Etranger. Mars 1869.

tion of its wings, the wings during their action forming a wedge, the base of which (cbe) is directed towards the head of the bird; the apex (a f) being directed towards the tail. This idea is worked out in propòsitions 195 and 196 of the first part of Borelli's book. In proposition 195 he explains how, if a wedge be driven into a body, the wedge will tend to separate that body into two portions; but that if the two portions of the body be permitted to react upon the wedge, they will communicate oblique impulses to the sides of the wedge, and expel it, base first, in a straight line.

Following up the analogy, Borelli endeavours to show in his 196th proposition, "that if the air acts obliquely upon the wings, or the wings obliquely upon the air (which is, of course, a wedge action), the result will be a horizontal transference of the body of the bird." In the proposition referred to (196) Borelli states- "If the expanded wings of a bird suspended in the air shall strike the undisturbed air beneath it with a motion perpendicular to the horizon, the bird will fly with a transverse motion in a plane parallel with the horizon." In other words, if the wings strike vertically downwards, the bird will fly horizontally forwards. He bases his argument upon the belief that the anterior margins of the wings are rigid and unyielding, whereas the posterior and after parts of the wings are more or less flexible, and readily give way under pressure. "If," he adds, "the wings of the bird be expanded, and the under surfaces of the wings be struck by the air ascending perpendicularly to the horizon, with such a force as shall prevent the bird gliding downwards (ie. with a tendency to glide downwards) from falling, it will be urged in a horizontal direction. This follows because the two osseous rods (virge) forming the anterior margins of the wings resist the upward pressure of the air, and so retain their original form (literally extent or expansion), whereas the flexible after-parts of the wings (posterior margins) are pushed up and approximated to form a cone, the apex of which (vide a f of fig. 113) is directed towards the tail of the bird. In virtue of the air playing upon and compressing the sides of the wedge formed by the wings, the wedge is driven forwards in the direction of its base (c be), which is equiva

lent to saying that the wings carry the body of the bird to which they are attached in a horizontal direction."

Borelli restates the same argument in different words, as follows:

"If," he says, "the air under the wings be struck by the flexible portions of the wings (flabella, literally fly-flaps or small fans) with a motion perpendicular to the horizon, the sails (vela) and flexible portions of the wings (flabella) will yield in an upward direction, and form a wedge, the point of which is directed towards the tail. Whether, therefore, the air strikes the wings from below, or the wings strike the air from above, the result is the same-the posterior or flexible margins of the wings yield in an upward direction, and in so doing urge the bird in a horizontal direction."

In his 197th proposition, Borelli follows up and amplifies the arguments contained in propositions 195 and 196. "Thus," he observes, "it is evident that the object of flight is to impel birds upwards, and keep them suspended in the air, and also to enable them to wheel round in a plane parallel to the horizon. The first (or upward flight) could not be accomplished unless the bird were impelled upwards by frequent leaps or vibrations of the wings, and its descent prevented. And because the downward tendency of heavy bodies is perpendicular to the horizon, the vibration of the plain surfaces of the wings must be made by striking the air beneath them in a direction perpendicular to the horizon, and in this manner nature produces the suspension of birds in the air."

"With regard to the second or transverse motion of birds (i.e. horizontal flight) some authors have strangely blundered; for they hold that it is like that of boats, which, being impelled by oars, moved horizontally in the direction of the stern, and pressing on the resisting water behind, leaps with a contrary motion, and so are carried forward. In the same manner, say they, the wings vibrate towards the tail with a horizontal motion, and likewise strike against the undisturbed air, by the resistance of which they are moved forward by a reflex motion. But this is contrary to the evidence of our sight as well as to reason; for we see that the larger kinds of birds, such as swans, geese, etc., never vibrate their wings