The subject of artificial flight, notwithstanding the large share of attention bestowed upon it, has been particularly barren of results. This is the more to be regretted, as the interest which has been taken in it from early Greek and Roman times has been universal. The unsatisfactory state of the question is to be traced to a variety of causes, the most prominent of which are—

1st, The extreme difficulty of the problem.

2d, The incapacity or theoretical tendencies of those who have devoted themselves to its elucidation.

3d, The great rapidity with which wings, especially insect wings, are made to vibrate, and the difficulty experienced in analysing their movements.

4th, The great weight of all flying things when compared with a corresponding volume of air.

5th, The discovery of the balloon, which has retarded the science of aërostation, by misleading men’s minds and causing them to look for a solution of the problem by the aid of a machine lighter than the air, and which has no analogue in nature.

Flight has been unusually unfortunate in its votaries. It has been cultivated, on the one hand, by profound thinkers, especially mathematicians, who have worked out innumerable theorems, but have never submitted them to the test of experiment; and on the other, by uneducated charlatans who, despising the abstractions of science, have made the most ridiculous attempts at a practical solution of the problem.

Flight, as the matter stands at present, may be divided into two principal varieties which represent two great sects or schools—

1st, The Balloonists, or those who advocate the employment of a machine specifically lighter than the air.

2d, Those who believe that weight is necessary to flight. The second school may be subdivided into

(a) Those who advocate the employment of rigid inclined planes driven forward in a straight line, or revolving planes (aërial screws); and

(b) Such as trust for elevation and propulsion to the vertical flapping of wings.

Balloon.—The balloon, as my readers are aware, is constructed on the obvious principle that a machine lighter than the air must necessarily rise through it. The Montgolfier brothers invented such a machine in 1782. Their balloon consisted of a paper globe or cylinder, the motor power being super-heated air supplied by the burning of vine twigs under it. The Montgolfier or fire balloon, as it was called, was superseded by the hydrogen gas balloon of MM. Charles and Robert, this being in turn supplanted by the ordinary gas balloon of Mr. Green. Since the introduction of coal gas in the place of hydrogen gas, no radical improvement has been effected, all attempts at guiding the balloon having signally failed. This arises from the vast extent of surface which it necessarily presents, rendering it a fair conquest to every breeze that blows; and because the power which animates it is a mere lifting power which, in the absence of wind, must act in a vertical line. The balloon consequently rises through the air in opposition to the law of gravity, very much as a dead bird falls in a downward direction in accordance with it. Having no hold upon the air, this cannot be employed as a fulcrum for regulating its movements, and hence the cardinal difficulty of ballooning as an art.

Finding that no marked improvement has been made in the balloon since its introduction in 1782, the more advanced thinkers have within the last quarter of a century turned their attention in an opposite direction, and have come to regard flying creatures, all of which are much heavier than the air, as the true models for flying machines. An old doctrine is more readily assailed than uprooted, and accordingly we find the followers of the new faith met by the assertion that insects and birds have large air cavities in their interior; that those cavities contain heated air, and that this heated air in some mysterious manner contributes to, if it does not actually produce, flight. No argument could be more fallacious. Many admirable fliers, such as the bats, have no air-cells; while many birds, the apteryx for example, and several animals never intended to fly, such as the orang-outang and a large number of fishes, are provided with them. It may therefore be reasonably concluded that flight is in no way connected with air-cells, and the best proof that can be adduced is to be found in the fact that it can be performed to perfection in their absence.

The Inclined Plane.—The modern school of flying is in some respects quite as irrational as the ballooning school.

The favourite idea with most is the wedging forward of a rigid inclined plane upon the air by means of a “vis a tergo.”

The inclined plane may be made to advance in a horizontal line, or made to rotate in the form of a screw. Both plans have their adherents. The one recommends a large supporting area extending on either side of the weight to be elevated; the surface of the supporting area making a very slight angle with the horizon, and the whole being wedged forward by the action of vertical screw propellers. This was the plan suggested by Henson and Stringfellow.

Mr. Henson designed his aërostat in 1843. “The chief feature of the invention was the very great expanse of its sustaining planes, which were larger in proportion to the weight it had to carry than those of many birds. The machine advanced with its front edge a little raised, the effect of which was to present its under surface to the air over which it passed, the resistance of which, acting upon it like a strong wind on the sails of a windmill, prevented the descent of the machine and its burden. The sustaining of the whole, therefore, depended upon the speed at which it travelled through the air, and the angle at which its under surface impinged on the air in its front. . . . The machine, fully prepared for flight, was started from the top of an inclined plane, in descending which it attained a velocity necessary to sustain it in its further progress. That velocity would be gradually destroyed by the resistance of the air to forward flight; it was, therefore, the office of the steam-engine and the vanes it actuated simply to repair the loss of velocity; it was made therefore only of the power and weight necessary for that small effect” (fig. 109). The editor of Newton’s Journal of Arts and Science speaks of it thus:—“The apparatus consists of a car containing the goods, passengers, engines, fuel, etc., to which a rectangular frame, made of wood or bamboo cane, and covered with canvas or oiled silk, is attached. This frame extends on either side of the car in a similar manner to the outstretched wings of a bird; but with this difference, that the frame is immovable. Behind the wings are two vertical fan wheels, furnished with oblique vanes, which are intended to propel the apparatus through the air. The rainbow-like circular wheels are the propellers, answering to the wheels of a steam-boat, and acting upon the air after the manner of a windmill. These wheels receive motion from bands and pulleys from a steam or other engine contained in the car. To an axis at the stern of the car a triangular frame is attached, resembling the tail of a bird, which is also covered with canvas or oiled silk. This may be expanded or contracted at pleasure, and is moved up and down for the purpose of causing the machine to ascend or descend. Beneath the tail is a rudder for directing the course of the machine to the right or to the left; and to facilitate the steering a sail is stretched between two masts which rise from the car. The amount of canvas or oiled silk necessary for buoying up the machine is stated to be equal to one square foot for each half pound of weight.”

Wenham103 has advocated the employment of superimposed planes, with a view to augmenting the support furnished while it diminishes the horizontal space occupied by the planes. These planes Wenham designates Aëroplanes. They are inclined at a very slight angle to the horizon, and are wedged forward either by the weight to be elevated or by the employment of vertical screws. Wenham’s plan was adopted by Stringfellow in a model which he exhibited at the Aëronautical Society’s Exhibition, held at the Crystal Palace in the summer of 1868.

The subjoined woodcut (fig. 110), taken from a photograph of Mr. Stringfellow’s model, gives a very good idea of the arrangement; a b c representing the superimposed planes, d the tail, and e f the vertical screw propellers.

Its engine represented a third of a horse power, and the weight of the whole (engine, boiler, water, fuel, superimposed planes, and propellers) was under 12 lbs. Its sustaining area, if that of the tail (d) be included, was something like thirty-six square feet, i.e. three square feet for every pound—the sustaining area of the gannet, it will be remembered (p. 134), being less than one square foot of wing for every two pounds of body.

The model was forced by its propellers along a wire at a great speed, but, so far as I could determine from observation, failed to lift itself notwithstanding its extreme lightness and the comparatively very great power employed.104

The idea embodied by Henson, Wenham, and Stringfellow is plainly that of a boy’s kite sailing upon the wind. The kite, however, is a more perfect flying apparatus than that furnished by Henson, Wenham, and Stringfellow, inasmuch as the inclined plane formed by its body strikes the air at various angles—the angles varying according to the length of string, strength of breeze, length and weight of tail, etc. Henson’s, Wenham’s, and Stringfellow’s methods, although carefully tried, have hitherto failed. The objections are numerous. In the first place, the supporting planes (aëroplanes or otherwise) are not flexible and elastic as wings are, but rigid. This is a point to which I wish particularly to direct attention. Second, They strike the air at a given angle. Here, again, there is a departure from nature. Third, A machine so constructed must be precipitated from a height or driven along the surface of the land or water at a high speed to supply it with initial velocity. Fourth, It is unfitted for flying with the wind unless its speed greatly exceeds that of the wind. Fifth, It is unfitted for flying across the wind because of the surface exposed. Sixth, The sustaining surfaces are comparatively very large. They are, moreover, passive or dead surfaces, i.e. they have no power of moving or accommodating themselves to altered circumstances. Natural wings, on the contrary, present small flying surfaces, the great speed at which wings are propelled converting the space through which they are driven into what is practically a solid basis of support, as explained at pp. 118, 119, 151, and 152 (vide figs. 64, 65, 66, 82, and 83, pp. 139 and 158). This arrangement enables natural wings to seize and utilize the air, and renders them superior to adventitious currents. Natural wings work up the air in which they move, but unless the flying animal desires it, they are scarcely, if at all, influenced by winds or currents which are not of their own forming. In this respect they entirely differ from the balloon and all forms of fixed aëroplanes. In nature, small wings driven at a high speed produce the same result as large wings driven at a slow speed (compare fig. 58, p. 125, with fig. 57, p. 124). In flight a certain space must be covered either by large wings spread out as a solid (fig. 57, p. 124), or by small wings vibrating rapidly (figs. 64, 65, and 66, p. 139).

“As it may be an amusement to some of your readers to see a machine rise in the air by mechanical means, I will conclude my present communication by describing an instrument of this kind, which any one can construct at the expense of ten minutes’ labour.

“a and b (fig. 111, p. 215) are two corks, into each of which are inserted four wing feathers from any bird, so as to be slightly inclined like the sails of a windmill, but in opposite directions in each set. A round shaft is fixed in the cork a, which ends in a sharp point. At the upper part of the cork b is fixed a whalebone bow, having a small pivot hole in its centre to receive the point of the shaft. The bow is then to be strung equally on each side to the upper portion of the shaft, and the little machine is completed. Wind up the string by turning the flyers different ways, so that the spring of the bow may unwind them with their anterior edges ascending; then place the cork with the bow attached to it upon a table, and with a finger on the upper cork press strong enough to prevent the string from unwinding, and, taking it away suddenly, the instrument will rise to the ceiling.”

Cayley’s screws were peculiar, inasmuch as they were superimposed and rotated in opposite directions. He estimated that if the area of the screws was increased to 200 square feet, and moved by a man, they would elevate him. Cayley’s interesting experiment is described at length, and the apparatus figured in Nicholson’s Journal for 1809, p. 172. In 1842 Mr. Phillips also succeeded in elevating a model by means of revolving fans. Mr. Phillips’s model was made entirely of metal, and when complete and charged weighed 2 lbs. It consisted of a boiler or steam generator and four fans supported between eight arms. The fans were inclined to the horizon at an angle of 20°, and through the arms the steam rushed on the principle discovered by Hero of Alexandria. By the escape of steam from the arms, the fans were made to revolve with immense energy, so much so that the model rose to a great altitude, and flew across two fields before it alighted. The motive power employed in the present instance was obtained from the combustion of charcoal, nitre, and gypsum, as used in the original fire annihilator; the products of combustion mixing with water in the boiler, and forming gas charged steam, which was delivered at a high pressure from the extremities of the eight arms. This model is remarkable as being probably the first which actuated by steam has flown to a considerable distance.105 The French have espoused the aërial screw with great enthusiasm, and within the last ten years (1863) MM. Nadar,106 Pontin d’Amécourt, and de la Landelle have constructed clockwork models (orthopteres), which not only raise themselves into the air, but carry a certain amount of freight. These models are 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 (m n o p q r s t 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 b c 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 aëroplanes 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 Dædalus and his waxen wings, we certainly 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.107

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.108

The wings (b c f, o e a), are represented as striking vertically downwards (g h). They remarkably accord with those described by Straus-Durckheim, Girard, and quite recently by Professor Marey.109

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 vibration of its wings, the wings during their action forming a wedge, the base of which (c b e) is directed towards the head of the bird; the apex (a f) being directed towards the tail. This idea is worked out in propositions 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 (i.e. with a tendency to glide downwards) from falling, it will be urged in a horizontal direction. This follows because the two osseous rods (virgæ) 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 b e), which is equivalent 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 when flying towards the tail with a horizontal motion like that of oars, but always bend them downwards, and so describe circles raised perpendicularly to the horizon.110

“Besides, in boats the horizontal motion of the oars is easily made, and a perpendicular stroke on the water would be perfectly useless, inasmuch as their descent would be impeded by the density of the water. But in birds, such a horizontal motion (which indeed would rather hinder flight) would be absurd, since it would cause the ponderous bird to fall headlong to the earth; whereas it can only be suspended in the air by constant vibration of the wings perpendicular to the horizon. Nature was thus forced to show her marvellous skill in producing a motion which, by one and the same action, should suspend the bird in the air, and carry it forward in a horizontal direction. This is effected by striking the air below perpendicularly to the horizon, but with oblique strokes—an action which is rendered possible only by the flexibility of the feathers, for the fans of the wings in the act of striking acquire the form of a wedge, by the forcing out of which the bird is necessarily moved forwards in a horizontal direction.”

The points which Borelli endeavours to establish are these:—

First, That the action of the wing is a wedge action.

Second, That the wing consists of two portions—a rigid anterior portion, and a non-rigid flexible portion. The rigid portion he represents in his artificial bird (fig. 113, p. 220) as consisting of a rod (e r), the yielding portion of feathers (a o).

Third, That if the air strikes the under surface of the wing perpendicularly in a direction from below upwards, the flexible portion of the wing will yield in an upward direction, and form a wedge with its neighbour.

Fourth, Similarly and conversely, if the wing strikes the air perpendicularly from above, the posterior and flexible portion of the wing will yield and be forced in an upward direction.

Fifth, That this upward yielding of the posterior or flexible margin of the wing results in and necessitates a horizontal transference of the body of the bird.

Sixth, That to sustain a bird in the air the wings must strike vertically downwards, as this is the direction in which a heavy body, if left to itself, would fall.

Seventh, That to propel the bird in a horizontal direction, the wings must descend in a perpendicular direction, and the posterior or flexible portions of the wings yield in an upward direction, and in such a manner as virtually to communicate an oblique action to them.

Eighth, That the feathers of the wing are bent in an upward direction when the wing descends, the upward bending of the elastic feathers contributing to the horizontal travel of the body of the bird.

I have been careful to expound Borelli’s views for several reasons:—

1st, Because the purely mechanical theory of the wing’s action is clearly to be traced to him.

2d, Because his doctrines have remained unquestioned for nearly two centuries, and have been adopted by all the writers since his time, without, I regret to say in the majority of cases, any acknowledgment whatever.

3d, Because his views have been revived by the modern French school; and

4th, Because, in commenting upon and differing from Borelli, I will necessarily comment upon and differ from all his successors.

As to the Direction of the Stroke, yielding of the Wing, etc.—The Duke of Argyll111 agrees with Borelli in believing that the wing invariably strikes perpendicularly downwards. His words are—“Except for the purpose of arresting their flight birds can never strike except directly downwards; that is, against the opposing force of gravity.” Professor Owen in his Comparative Anatomy, Mr. Macgillivray in his British Birds, Mr. Bishop in his article “Motion” in the Cyclopedia of Anatomy and Physiology, and M. Liais “On the Flight of Birds and Insects” in the Annals of Natural History, all assert that the stroke is delivered downwards and more or less backwards.

To obtain an upward recoil, one would naturally suppose all that is required is a downward stroke, and to obtain an upward and forward recoil, one would naturally conclude a downward and backward stroke alone is requisite. Such, however, is not the case.

In the first place, a natural wing, or a properly constructed artificial one, cannot be depressed either vertically downwards, or downwards and backwards. It will of necessity descend downwards and forwards in a curve. This arises from its being flexible and elastic throughout, and in especial from its being carefully graduated as regards thickness, the tip being thinner and more elastic than the root, and the posterior margin than the anterior margin.

In the second place, there is only one direction in which the wing could strike so at once to support and carry the bird forward. The bird, when flying, is a body in motion. It has therefore acquired momentum. If a grouse is shot on the wing it does not fall vertically downwards, as Borelli and his successors assume, but downwards and forwards. The flat surfaces of the wings are consequently made to strike downwards and forwards, as they in this manner act as kites to the falling body, which they bear, or tend to bear, upwards and forwards.

So much for the direction of the stroke during the descent of the wing.

Let us now consider to what extent the posterior margin of the wing yields in an upward direction when the wing descends. Borelli does not state the exact amount. The Duke of Argyll, who believes with Borelli that the posterior margin of the wing is elevated during the down stroke, avers that, “whereas the air compressed in the hollow of the wing cannot pass through the wing owing to the closing upwards of the feathers against each other, or escape forwards because of the rigidity of the bones and of the quills in this direction, it passes backwards, and in so doing lifts by its force the elastic ends of the feathers. In passing backwards it communicates to the whole line of both wings a corresponding push forwards to the body of the bird. The same volume of air is thus made, in accordance with the law of action and reaction, to sustain the bird and carry it forward.”112 Mr. Macgillivray observes that “to progress in a horizontal direction it is necessary that the downward stroke should be modified by the elevation in a certain degree of the free extremities of the quills.”113

Marey’s Views.—Professor Marey states that during the down stroke the posterior or flexible margin of the wing yields in an upward direction to such an extent as to cause the under surface of the wing to look backwards, and make a backward angle with the horizon of 45° plus or minus according to circumstances.114 That the posterior margin of the wing yields in a slightly upward direction during the down stroke, I admit. By doing so it prevents shock, confers continuity of motion, and contributes in some measure to the elevation of the wing. The amount of yielding, however, is in all cases very slight, and the little upward movement there is, is in part the result of the posterior margin of the wing rotating around the anterior margin as an axis. That the posterior margin of the wing never yields in an upward direction until the under surface of the pinion makes a backward angle of 45° with the horizon, as Marey remarks, is a matter of absolute certainty. This statement 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 on no occasion looks backwards, as stated by Marey. On the contrary, he will find that the under surface of the wing (during the down stroke) invariably looks forwards—the posterior margin of the wing being inclined downwards and backwards; as shown at figs. 82 and 83, p. 158; fig. 103, p. 186; fig. 85 (a b c), p. 160; and fig. 88 (c d e f g), p. 166.

The under surface of the wing, as will be seen from this account, not only always looks forwards, but it 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 d, e, f, g; j, k, l, m of fig. 88, p. 166. I am therefore opposed to Borelli, Macgillivray, Owen, Bishop, M. Liais, the Duke of Argyll, and Marey as to the direction and nature of the down stroke. I differ also as to the direction and nature of the up stroke.

Professor Marey states that not only does the posterior margin of the wing yield in an upward direction during the down stroke until the under surface of the pinion makes a backward angle of 45° with the horizon, but that during the up stroke it yields to the same extent in an opposite direction. The posterior flexible margin of the wing, according to Marey, passes through a space of 90° every time the wing reverses its course, this space being dedicated to the mere adjusting of the planes of the wing for the purposes of flight. The planes, moreover, he asserts, are adjusted not by vital and vito-mechanical acts but by the action of the air alone; this operating on the under surface of the wing and forcing its posterior margin upwards during the down stroke; the air during the up stroke acting upon the posterior margin of the upper surface of the wing, and forcing it downwards. This is a mere repetition of Borelli’s view. Marey delegates to the air the difficult and delicate task of arranging the details of flight. The time, power, and space occupied in reversing the wing alone, according to this theory, are such as to render flight impossible. That the wing does not act as stated by Borelli, Marey, and others may be readily proved by experiment. It may also be demonstrated mathematically, as a reference to figs. 114 and 115, p. 228, will show.

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

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.

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 (c x a of fig. 114, p. 228).

While Borelli and his successors are correct as to the wedge-action 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 c b e of fig. 113, p. 220; its apex being represented by a f 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.