The atmosphere, because of its great tenuity, mobility, and comparative imponderability, presents little resistance to bodies passing through it at low velocities. If, however, the speed be greatly accelerated, the passage of even an ordinary cane is sensibly impeded.

This comes of the action and reaction of matter, the resistance experienced varying according to the density of the atmosphere and the shape, extent, and velocity of the body acting upon it. While, therefore, scarcely any impediment is offered to the progress of an animal in motion, it is often exceedingly difficult to compress the air with sufficient rapidity and energy to convert it into a suitable fulcrum for securing the onward impetus. This arises from the fact that bodies moving in the air experience the minimum of resistance and occasion the maximum of displacement. Another and very obvious difficulty is traceable to the great disparity in the weight of air as compared with any known solid, this in the case of water being nearly as 1000 to 1. According to the density of the medium so is its buoying or sustaining power.

The Wing a Lever of the Third Order.—To meet the peculiarities stated above, the insect, bat, and bird are furnished with extensive surfaces in the shape of pinions or wings, which they can apply with singular velocity and power, as levers of the third order (fig. 3, p. 20),61 at various angles, or by alternate slow and sudden movements, to obtain the necessary degree of resistance and non-resistance. Although the third order of lever is particularly inefficient when the fulcrum is rigid and immobile, it possesses singular advantages when these conditions are reversed, i.e. when the fulcrum, as happens with the air, is elastic and yielding. In this case a very slight movement at the root of the pinion, or that end of the lever directed towards the body, is succeeded by an immense sweep of the extremity of the wing, where its elevating and propelling power is greatest. This arrangement insures that the large quantity of air necessary for propulsion and support shall be compressed under the most favourable conditions.

It follows from this that those insects and birds are endowed with the greatest powers of flight whose wings are the longest. The dragon-fly and albatross furnish examples. The former on some occasions dashes along with amazing velocity and wheels with incredible rapidity; at other times it suddenly checks its headlong career and hovers or fixes itself in the air after the manner of the kestrel and humming-birds. The flight of the albatross is also remarkable. This magnificent bird, I am informed on reliable authority, sails about with apparent unconcern for hours together, and rarely deigns to flap its enormous pinions, which stream from its body like ribbons to the extent, in some cases, of seven feet on either side.

The manner in which the wing levers the body upwards and forwards in flight is shown at fig. 52.

In this fig. f f´ represent the moveable fulcra furnished by the air; p p´ the power residing in the wing, and b the body to be flown. In order to make the problem of flight more intelligible, I have prolonged the lever formed by the wing beyond the body (b), and have applied to the root of the wing so extended the weight w w´. x represents the universal joint by which the wing is attached to the body. When the wing ascends, as shown at p, the air (= fulcrum f) resists its upward passage, and forces the body (b), or its representative (w), slightly downwards. When the wing descends, as shown at p´, the air (= fulcrum f´) resists its downward passage, and forces the body (b), or its representative (w´), slightly upwards. From this it follows, that when the wing rises the body falls, and vice versâ; the wing describing the arc of a large circle (f f´), the body (b), or the weights representing it (w w´) describing the arc of a much smaller circle. The body, therefore, as well as the wing, rises and falls in flight. When the wing descends it elevates the body, the wing being active and the body passive; when the body descends it elevates the wing, the body being active and the wing passive. The elevator muscles, and the reaction of the air on the under surface of the wing, contribute to its elevation. It is in this manner that weight forms a factor in flight, the wing and the weight of the body reciprocating and mutually assisting and relieving each other. This is an argument for employing four wings in artificial flight, the wings being so arranged that the two which are up shall always by their fall mechanically elevate the two which are down. Such an arrangement is calculated greatly to conserve the driving power, and, as a consequence, to reduce the weight. It is the upper or dorsal surface of the wing which more especially operates upon the air during the up stroke, and the under or ventral surface which operates during the down stroke. The wing, which at the beginning of the down stroke has its surfaces and margins (anterior and posterior) arranged in nearly the same plane with the horizon,62 rotates upon its anterior margin as an axis during its descent and causes its under surface to make a gradually increasing angle with the horizon, the posterior margin (fig. 53, c) in this movement descending beneath the anterior one. A similar but opposite rotation takes place during the up stroke. The rotation referred to causes the wing to twist on its long axis screw-fashion, and to describe a figure-of-8 track in space, one-half of the figure being described during the ascent of the wing, the other half during its descent. The twisting of the wing and the figure-of-8 track described by it when made to vibrate, are represented at fig. 53. The rotation of the wing on its long axis as it ascends and descends causes the under surface of the wing to act as a kite, both during the up and down strokes, provided always the body bearing the wing is in forward motion. But the upper surface of the wing, as has been explained, acts when the wing is being elevated, so that both the upper and under surfaces of the wing are efficient during the up stroke. When the wing ascends, the upper surface impinges against the air; the under surface impinging at the same time from its being carried obliquely forward, after the manner of a kite, by the body, which is in motion. During the down stroke, the under surface only acts. The wing is consequently effective both during its ascent and descent, its slip being nominal in amount. The wing acts as a kite, both when it ascends and descends. It acts more as a propeller than an elevator during its ascent; and more as an elevator than a propeller during its descent. It is, however, effective both in an upward and downward direction. The efficiency of the wing is greatly increased by the fact that when it ascends it draws a current of air up after it, which current being met by the wing during its descent, greatly augments the power of the down stroke. In like manner, when the wing descends it draws a current of air down after it, which being met by the wing during its ascent, greatly augments the power of the up stroke. These induced currents are to the wing what a stiff autumn breeze is to the boy’s kite. The wing is endowed with this very remarkable property, that it creates the current on which it rises and progresses. It literally flies on a whirlwind of its own forming.

These remarks apply more especially to the wings of bats and birds, and those insects whose wings are made to vibrate in a more or less vertical direction. The action of the wing is readily imitated, as a reference to fig. 53 will show.

If, for example, I take a tapering elastic reed, as represented at a b, and supply it with a flexible elastic sail (c d), and a ball-and-socket joint (x), I have only to seize the reed at a and cause it to oscillate upon x to elicit all the wing movements. By depressing the root of the reed in the direction n e, the wing flies up as a kite in the direction j f. During the upward movement the wing flies upwards and forwards, and describes a double curve. By elevating the root of the reed in the direction m a, the wing flies down as a kite in the direction i b. During the downward movement the wing flies downwards and forwards, and describes a double curve. These curves, when united, form a waved track, which represents progressive flight. During the rise and fall of the wing a large amount of tractile force is evolved, and if the wings and the body of the flying creature are inclined slightly upwards, kite-fashion, as they invariably are in ordinary flight, the whole mass of necessity moves upwards and forwards. To this there is no exception. A sheet of paper or a card will float along if its anterior margin is slightly raised, and if it be projected with sufficient velocity. The wings of all flying creatures when made to vibrate, twist and untwist, the posterior thin margin of each wing twisting round the anterior thick one, like the blade of a screw. The artificial wing represented at fig. 53 (p. 107) does the same, c d twisting round a b, and g h round e f. The natural and artificial wings, when elevated and depressed, describe a figure-of-8 track in space when the bodies to which they are attached are stationary. When the bodies advance, the figure-of-8 is opened out to form first a looped and then a waved track. I have shown how those insects, bats, and birds which flap their wings in a more or less vertical direction evolve tractile or propelling power, and how this, operating on properly constructed inclined surfaces, results in flight. I wish now to show that flight may also be produced by a very oblique and almost horizontal stroke of the wing, as in some insects, e.g. the wasp, blue-bottle, and other flies. In those insects the wing is made to vibrate with a figure-of-8 sculling motion in a very oblique direction, and with immense energy. This form of flight differs in no respect from the other, unless in the direction of the stroke, and can be readily imitated, as a reference to fig. 54 will show.

In this figure (54) the conditions represented at fig. 53 (p. 107) are exactly reproduced, the only difference being that in the present figure the wing is applied to the air in a more or less horizontal direction, whereas in fig. 53 it is applied in a more or less vertical direction. The letters in both figures are the same. The insects whose wings tack upon the air in a more or less horizontal direction, have an extensive range, each wing describing nearly half a circle, these half circles corresponding to the area of support. The body of the insect is consequently the centre of a circle of motion. It corresponds to x of the present figure (fig. 54). When the wing is seized by the hand at a, and the root made to travel in the direction n e, the body of the wing travels in the direction j f. While so travelling, it flies upwards in a double curve, kite-fashion, and elevates the weight l. When it reaches the point f, it reverses suddenly to prepare for a return stroke, which is produced by causing the root of the wing to travel in the direction m a, the body and tip travelling in the direction i b. During the reverse stroke, the wing flies upwards in a double curve, kite-fashion, and elevates the weight k. The more rapidly these movements are repeated, the more powerful the wing becomes, and the greater the weight it elevates. This follows because of the reciprocating action of the wing,—the wing, as already explained, always drawing a current of air after it during the one stroke, which is met and utilized by it during the next stroke. The reciprocating action of the wing here referred to is analogous in all respects to that observed in the flippers of the seal, sea-bear, walrus, and turtle; the swimming wing of the penguin; and the tail of the whale, dugong, manatee, porpoise, and fish. If the muscles of the insect were made to act at the points a e, the body of the insect would be elevated as at k l, by the reciprocating action of the wings. The amount of tractile power developed in the arrangement represented at fig. 53 (p. 107), can be readily ascertained by fixing a spring or a weight acting over a pulley to the anterior margin (a b or e f) of the wing; weights acting over pulleys being attached to the root of the wing (a or e).

The amount of elevating power developed in the arrangement represented at fig. 54, can also be estimated by causing weights acting over pulleys to operate upon the root of the wing (a or e), and watching how far the weights (k or l) are raised. In these calculations allowance is of course to be made for friction. The object of the two sets of experiments described and figured, is to show that the wing can exert a tractile power either in a nearly horizontal direction or in a nearly vertical one, flight being produced in both cases. I wish now to show that a body not supplied with wings or inclined surfaces will, if left to itself, fall vertically downwards; whereas, if it be furnished with wings, its vertical fall is converted into oblique downward flight. These are very interesting points. Experiment has shown me that a wing when made to vibrate vertically produces horizontal traction; when made to vibrate horizontally, vertical traction; the vertical fall of a body armed with wings producing oblique traction. The descent of weights can also be made to propel the wings either in a vertical or horizontal direction; the vibration of the wings upon the air in natural flight causing the weights (body of flying creature) to move forward. This shows the very important part performed by weight in all kinds of flight.

Weight necessary to Flight.—However paradoxical it may seem, a certain amount of weight is indispensable in flight.

In the first place, it gives peculiar efficacy and energy to the up stroke, by acting upon the inclined planes formed by the wings in the direction of the plane of progression. The power and the weight may thus be said to reciprocate, the two sitting, as it were, side by side, and blending their peculiar influences to produce a common result.

Secondly, it adds momentum,—a heavy body, when once fairly under weigh, meeting with little resistance from the air, through which it sweeps like a heavy pendulum.

Thirdly, the mere act of rotating the wings on and off the wind during extension and flexion, with a slight downward stroke, apparently represents the entire exertion on the part of the volant animal, the rest being performed by weight alone.

This last circumstance is deserving of attention, the more especially as it seems to constitute the principal difference between a living flying thing and an aërial machine. If a flying-machine was constructed in accordance with the principles which we behold in nature, the weight and the propelling power of the machine would be made to act upon the sustaining and propelling surfaces, whatever shape they assumed, and these in turn would be made to operate upon the air, and vice versâ. In the aërial machine, as far as yet devised, there is no sympathy between the weight to be elevated and the lifting power, whilst in natural flight the wings and the weight of the flying creature act in concert and reciprocate; the wings elevating the body the one instant, the body by its fall elevating the wings the next. When the wings elevate the body they are active, the body being passive. When the body elevates the wings it is active, the wings being passive. The force residing in the wings, and the force residing in the body (weight is a force when launched in space and free to fall in a vertical direction) cause the mass of the volant animal to oscillate vertically on either side of an imaginary line—this line corresponding to the path of the insect, bat, or bird in the air. While the wings and body act and react upon each other, the wings, body, and air likewise act and react upon each other. In the flight of insects, bats, and birds, weight is to be regarded as an independent moving power, this being made to act upon the oblique surfaces presented by the wings in conjunction with the power expended by the animal—the latter being, by this arrangement, conserved to a remarkable extent. Weight, assisted by the elastic ligaments or springs, which recover all wings in flexion, is to be regarded as the mechanical expedient resorted to by nature in supplementing the efforts of all flying things.63 Without this, flight would be of short duration, laboured, and uncertain, and the almost miraculous journeys at present performed by the denizens of the air impossible.

Weight contributes to Horizontal Flight.—That the weight of the body plays an important part in the production of flight may be proved by a very simple experiment.

If I take two primary feathers and fix them in an ordinary cork, as represented at fig. 55, and allow the apparatus to drop from a height, I find the cork does not fall vertically downwards, but downwards and forwards in a curve. This follows, because the feathers a, b are twisted flexible inclined planes, which arch in an upward direction. They are in fact true wings in the sense that an insect wing in one piece is a true wing. (Compare a, b, c of fig. 55, with g, g´, s of fig. 82, p. 158.) When dragged downwards by the cork (c), which would, if left to itself, fall vertically, they have what is virtually a down stroke communicated to them. Under these circumstances a struggle ensues between the cork tending to fall vertically and the feathers tending to travel in an upward direction, and, as a consequence, the apparatus describes the curve d e f g before reaching the earth h, i. This is due to the action and reaction of the feathers and air upon each other, and to the influence which gravity exerts upon the cork. The forward travel of the cork and feathers, as compared with the space through which they fall, is very great. Thus, in some instances, I found they advanced as much as a yard and a half in a descent of three yards. Here, then, is an example of flight produced by purely mechanical appliances. The winged seeds fly in precisely the same manner. The seeds of the plane-tree have, e.g. two wings which exactly resemble the wings employed for flying; thus they taper from the root towards the tip, and from the anterior margin towards the posterior margin, the margins being twisted and disposed in different planes to form true screws. This arrangement prevents the seed from falling rapidly or vertically, and if a breeze is blowing it is wafted to a considerable distance before it reaches the ground. Nature is uniform and consistent throughout. She employs the same principle, and very nearly the same means, for flying a heavy, solid seed which she employs for flying an insect, a bat, or a bird.

When artificial wings constructed on the plan of natural ones, with stiff roots, tapering semi-rigid anterior margins, and thin yielding posterior margins, are allowed to drop from a height, they describe double curves in falling, the roots of the wings reaching the ground first. This circumstance proves the greater buoying power of the tips of the wings as compared with the roots. I might refer to many other experiments made in this direction, but these are sufficient to show that weight, when acting upon wings, or, what is the same thing, upon elastic twisted inclined planes, must be regarded as an independent moving power. But for this circumstance flight would be at once the most awkward and laborious form of locomotion, whereas in reality it is incomparably the easiest and most graceful. The power which rapidly vibrating wings have in sustaining a body which tends to fall vertically downwards, is much greater than one would naturally imagine, from the fact that the body, which is always beginning to fall, is never permitted actually to do so. Thus, when it has fallen sufficiently far to assist in elevating the wings, it is at once elevated by the vigorous descent of those organs. The body consequently never acquires the downward momentum which it would do if permitted to fall through a considerable space uninterruptedly. It is easy to restrain even a heavy body when beginning to fall, while it is next to impossible to check its progress when it is once fairly launched in space and travelling rapidly in a downward direction.

Weight, Momentum, and Power, to a certain extent, synonymous in Flight.—When a bird rises it has little or no momentum, so that if it comes in contact with a solid resisting surface it does not injure itself. When, however, it has acquired all the momentum of which it is capable, and is in full and rapid flight, such contact results in destruction. My friend Mr. A. D. Bartlett informed me of an instance where a wild duck terminated its career by coming violently in contact with one of the glasses of the Eddystone Lighthouse. The glass, which was fully an inch in thickness, was completely smashed. Advantage is taken of this circumstance in killing sea-birds, a bait being placed on a board and set afloat with a view to breaking the neck of the bird when it stoops to seize the carrion. The additional power due to momentum in heavy bodies in motion is well illustrated in the start and progress of steamboats. In these the slip, as it is technically called, decreases as the speed of the vessel increases; the strength of a man, if applied by a hawser attached to the stern of a moderate-sized vessel, being sufficient to retard, and, in some instances prevent, its starting. In such a case the power of the engine is almost entirely devoted to “slip” or in giving motion to the fluid in which the screw or paddle is immersed. It is consequently not the power residing in the paddle or screw which is cumulative, but the momentum inhering in the mass. In the bird, the momentum, alias weight, is made to act upon the inclined planes formed by the wings, these adroitly converting it into sustaining and propelling power. It is to this circumstance, more than any other, that the prolonged flight of birds is mainly due, the inertia or dead weight of the trunk aiding and abetting the action of the wings, and so relieving the excess of exertion which would necessarily devolve on the bird. It is thus that the power which in living structures resides in the mass is conserved, and the mass itself turned to account. But for this reciprocity, no bird could retain its position in the air for more than a few minutes at a time. This is proved by the comparatively brief upward flight of the lark and the hovering of the hawk when hunting. In both these cases the body is exclusively sustained by the action of the wings, the weight of the trunk taking no part in it; in other words, the weight of the body does not contribute to flight by adding its momentum and the impulse which momentum begets. In the flight of the albatross, on the other hand, the momentum acquired by the moving mass does the principal portion of the work, the wings for the most part being simply rotated on and off the wind to supply the proper angles necessary for the inertia or mass to operate upon. It appears to me that in this blending of active and passive power the mystery of flight is concealed, and that no arrangement will succeed in producing flight artificially which does not recognise and apply the principle here pointed out.

Air-cells in Insects and Birds not necessary to Flight.—The boasted levity of insects, bats, and birds, concerning which so much has been written by authors in their attempts to explain flight, is delusive in the highest degree.

Insects, bats, and birds are as heavy, bulk for bulk, as most other living creatures, and flight can be performed perfectly by animals which have neither air-sacs nor hollow bones; air-sacs being found in animals never designed to fly. Those who subscribe to the heated-air theory are of opinion that the air contained in the cavities of insects and birds is so much lighter than the surrounding atmosphere, that it must of necessity contribute materially to flight. I may mention, however, that the quantity of air imprisoned is, to begin with, so infinitesimally small, and the difference in weight which it experiences by increase of temperature so inappreciable, that it ought not to be taken into account by any one endeavouring to solve the difficult and important problem of flight. The Montgolfier or fire-balloons were constructed on the heated-air principle; but as these have no analogue in nature, and are apparently incapable of improvement, they are mentioned here rather to expose what I regard a false theory than as tending to elucidate the true principles of flight.

When we have said that cylinders and hollow chambers increase the area of the insect and bird, and that an insect and bird so constructed is stronger, weight for weight, than one composed of solid matter, we may dismiss the subject; flight being, as I shall endeavour to show by-and-by, not so much a question of levity as one of weight and power intelligently directed, upon properly constructed flying surfaces.

The bodies of insects, bats, and birds are constructed on strictly mechanical principles,—lightness, strength, and durability of frame being combined with power, rapidity, and precision of action. The cylindrical method of construction is in them carried to an extreme, the bodies and legs of insects displaying numerous unoccupied spaces, while the muscles and solid parts are tunnelled by innumerable air-tubes, which communicate with the surrounding medium by a series of apertures termed spiracles.

A somewhat similar disposition of parts is met with in birds, these being in many cases furnished not only with hollow bones, but also (especially the aquatic ones) with a liberal supply of air-sacs. They are likewise provided with a dense covering of feathers or down, which adds greatly to their bulk without materially increasing their weight. Their bodies, moreover, in not a few instances, particularly in birds of prey, are more or less flattened. The air-sacs are well seen in the swan, goose, and duck; and I have on several occasions minutely examined them with a view to determine their extent and function. In two of the specimens which I injected, the material employed had found its way not only into those usually described, but also into others which ramify in the substance of the muscles, particularly the pectorals. No satisfactory explanation of the purpose served by these air-sacs has, I regret to say, been yet tendered. According to Sappey,64 who has devoted a large share of attention to the subject, they consist of a membrane which is neither serous nor mucous, but partly the one and partly the other; and as blood-vessels in considerable numbers, as my preparations show, ramify in their substance, and they are in many cases covered with muscular fibres which confer on them a rhythmic movement, some recent observers (Mr. Drosier65 of Cambridge, for example) have endeavoured to prove that they are adjuncts of the lungs, and therefore assist in aërating the blood. This opinion was advocated by John Hunter as early as 1774,66 and is probably correct, since the temperature of birds is higher than that of any other class of animals, and because they are obliged occasionally to make great muscular exertions both in swimming and flying. Others have viewed the air-sacs in connexion with the hollow bones frequently, though not always, found in birds,67 and have come to look upon the heated air which they contain as being more or less essential to flight. That the air-cells have absolutely nothing to do with flight is proved by the fact that some excellent fliers (take the bats, e.g.) are destitute of them, while birds such as the ostrich and apteryx, which are incapable of flying, are provided with them. Analogous air-sacs, moreover, are met with in animals never intended to fly; and of these I may instance the great air-sac occupying the cervical and axillary regions of the orang-outang, the float or swimming-bladder in fishes, and the pouch communicating with the trachea of the emu.68

The same may be said of the hollow bones,—some really admirable fliers, as the swifts, martins, and snipes, having their bones filled with marrow, while those of the wingless running birds alluded to have air. Furthermore and finally, a living bird weighing 10 lbs. weighs the same when dead, plus a very few grains; and all know what effect a few grains of heated air would have in raising a weight of 10 lbs. from the ground.

How Balancing is effected in Flight, the Sound produced by the Wing, etc.—The manner in which insects, bats, and birds balance themselves in the air has hitherto, and with reason, been regarded a mystery, for it is difficult to understand how they maintain their equilibrium when the wings are beneath their bodies. Figs. 67 and 68, p. 141, throw considerable light on the subject in the case of the insect. In those figures the space (a, g) mapped out by the wing during its vibrations is entirely occupied by it; i.e. the wing (such is its speed) is in every portion of the space at nearly the same instant, the space representing what is practically a solid basis of support. As, moreover, the wing is jointed to the upper part of the body (thorax) by a universal joint, which admits of every variety of motion, the insect is always suspended (very much as a compass set upon gimbals is suspended); the wings, when on a level with the body, vibrating in such a manner as to occupy a circular area (vide r d b f of fig. 56, p. 120), in the centre of which the body (a e c) is placed. The wings, when vibrating above and beneath the body occupy a conical area; the apex of the cone being directed upwards when the wings are below the body, and downwards when they are above the body. Those points are well seen in the bird at figs. 82 and 83, p. 158. In fig. 82 the inverted cone formed by the wings when above the body is represented, and in fig. 83 that formed by the wings when below the body is given. In these figures it will be observed that the body, from the insertion of the roots of the wings into its upper portion, is always suspended, and this, of course, is equivalent to suspending the centre of gravity. In the bird and bat, where the stroke is delivered more vertically than in the insect, the basis of support is increased by the tip of the wing folding inwards and backwards in a more or less horizontal direction at the end of the down stroke; and outwards and forwards at the end of the up stroke. This is accompanied by the rotation of the outer portion of the wing upon the wrist as a centre, the tip of the wing, because of the ever varying position of the wrist, describing an ellipse. In insects whose wings are broad and large (butterfly), and which are driven at a comparatively low speed, the balancing power is diminished. In insects whose wings, on the contrary, are long and narrow (blow-fly), and which are driven at a high speed, the balancing power is increased. It is the same with short and long winged birds, so that the function of balancing is in some measure due to the form of the wing, and the speed with which it is driven; the long wing and the wing vibrated with great energy increasing the capacity for balancing. When the body is light and the wings very ample (butterfly and heron), the reaction elicited by the ascent and descent of the wing displaces the body to a marked extent. When, on the other hand, the wings are small and the body large, the reaction produced by the vibration of the wing is scarcely perceptible. Apart, however, from the shape and dimensions of the wing, and the rapidity with which it is urged, it must never be overlooked that all wings (as has been pointed out) are attached to the bodies of the animals bearing them by some form of universal joint, and in such a manner that the bodies, whatever the position of the wings, are accurately balanced, and swim about in a more or less horizontal position, like a compass set upon gimbals. To such an extent is this true, that the position of the wing is a matter of indifference. Thus the pinion may be above, beneath, or on a level with the body; or it may be directed forwards, backwards, or at right angles to the body. In either case the body is balanced mechanically and without effort. To prove this point I made an artificial wing and body, and united the one to the other by a universal joint. I found, as I had anticipated, that in whatever position the wing was placed, whether above, beneath, or on a level with the body, or on either side of it, the body almost instantly attained a position of rest. The body was, in fact, equally suspended and balanced from all points.

Rapidity of Wing Movements partly accounted for.—Much surprise has been expressed at the enormous rapidity with which some wings are made to vibrate. The wing of the insect is, as a rule, very long and narrow. As a consequence, a comparatively slow and very limited movement at the root confers great range and immense speed at the tip; the speed of each portion of the wing increasing as the root of the wing is receded from. This is explained on a principle well understood in mechanics, viz. that when a rod hinged at one end is made to move in a circle, the tip or free end of the rod describes a much wider circle in a given time than a portion of the rod nearer the hinge. This principle is illustrated at fig. 56. Thus if a b of fig. 56 be made to represent the rod hinged at x, it travels through the space d b f in the same time it travels through j k l; and through j k l in the same time it travels through g h i; and through g h i in the same time it travels through e a c, which is the area occupied by the thorax of the insect. If, however, the part of the rod b travels through the space d b f in the same time that the part a travels through the space e a c, it follows of necessity that the portion of the rod marked a moves very much slower than that marked b. The muscles of the insect are applied at the point a, as short levers (the point referred to corresponding to the thorax of the insect), so that a comparatively slow and limited movement at the root of the wing produces the marvellous speed observed at the tip; the tip and body of the wing being those portions which occasion the blur or impression produced on the eye by the rapidly oscillating pinion (figs. 64, 65, and 66, p. 139), But for this mode of augmenting the speed originally inaugurated by the muscular system, it is difficult to comprehend how the wings could be driven at the velocity attributed to them. The wing of the blow-fly is said to make 300 strokes per second, i.e. 18,000 per minute. Now it appears to me that muscles to contract at the rate of 18,000 times in the minute would be exhausted in a very few seconds, a state of matters which would render the continuous flight of insects impossible. (The heart contracts only between sixty and seventy times in a minute.) I am, therefore, disposed to believe that the number of contractions made by the thoracic muscles of insects has been greatly overstated; the high speed at which the wing is made to vibrate being due less to the separate and sudden contractions of the muscles at its root than to the fact that the speed of the different parts of the wing is increased in a direct ratio as the several parts are removed from the driving point, as already explained. Speed is certainly a matter of great importance in wing movements, as the elevating and propelling power of the pinion depends to a great extent upon the rapidity with which it is urged. Speed, however, may be produced in two ways—either by a series of separate and opposite movements, such as is witnessed in the action of a piston, or by a series of separate and opposite movements acting upon an instrument so designed, that a movement applied at one part increases in rapidity as the point of contact is receded from, as happens in the wing. In the piston movement the motion is uniform, or nearly so; all parts of the piston travelling at very much the same speed. In the wing movements, on the contrary, the motion is gradually accelerated towards the tip of the pinion, where the pinion is most effective as an elevator, and decreased towards the root, where it is least effective—an arrangement calculated to reduce the number of muscular contractions, while it contributes to the actual power of the wing. This hypothesis, it will be observed, guarantees to the wing a very high speed, with comparatively few reversals and comparatively few muscular contractions.

In the bat and bird the wings do not vibrate with the same rapidity as in the insect, and this is accounted for by the circumstance, that in them the muscles do not act exclusively at the root of the wing. In the bat and bird the muscles run along the wing towards the tip for the purpose of flexing or folding the wing prior to the up stroke, and for opening out and expanding it prior to the down stroke.

As the wing must be folded or flexed and opened out or expanded every time the wing rises and falls, and as the muscles producing flexion and extension are long muscles with long tendons, which act at long distances as long levers, and comparatively slowly, it follows that the great short muscles (pectorals, etc.) situated at the root of the wing must act slowly likewise, as the muscles of the thorax and wing of necessity act together to produce one pulsation or vibration of the wing. What the wing of the bat and bird loses in speed it gains in power, the muscles of the bat and bird’s wing acting directly upon the points to be moved, and under the most favourable conditions. In the insect, on the contrary, the muscles act indirectly, and consequently at a disadvantage. If the pectorals only moved, they would act as short levers, and confer on the wing of the bat and bird the rapidity peculiar to the wing of the insect.

The tones emitted by the bird’s wing would in this case be heightened. The swan in flying produces a loud whistling sound, and the pheasant, partridge, and grouse a sharp whirring noise like the stone of a knife-grinder.

It is a mistake to suppose, as many do, that the tone or note produced by the wing during its vibrations is a true indication of the number of beats made by it in any given time. This will be at once understood when I state, that a long wing will produce a higher note than a shorter one driven at the same speed and having the same superficial area, from the fact that the tip and body of the long wing will move through a greater space in a given time than the tip and body of the shorter wing. This is occasioned by all wings being jointed at their roots, the sweep made by the different parts of the wing in a given time being longer or shorter in proportion to the length of the pinion. It ought, moreover, not to be overlooked, that in insects the notes produced are not always referable to the action of the wings, these, in many cases, being traceable to movements induced in the legs and other parts of the body.

It is a curious circumstance, that if portions be removed from the posterior margins of the wings of a buzzing insect, such as the wasp, bee, blue-bottle fly, etc., the note produced by the vibration of the pinions is raised in pitch. This is explained by the fact, that an insect whose wings are curtailed requires to drive them at a much higher speed in order to sustain itself in the air. That the velocity at which the wing is urged is instrumental in causing the sound, is proved by the fact, that in slow-flying insects and birds no note is produced; whereas in those which urge the wing at a high speed, a note is elicited which corresponds within certain limits to the number of vibrations and the form of the wing. It is the posterior or thin flexible margin of the wing which is more especially engaged in producing the sound; and if this be removed, or if this portion of the wing, as is the case in the bat and owl, be constructed of very soft materials, the character of the note is altered. An artificial wing, if properly constructed and impelled at a sufficiently high speed, emits a drumming noise which closely resembles the note produced by the vibration of short-winged, heavy-bodied birds, all which goes to prove that sound is a concomitant of rapidly vibrating wings.

The Wing area Variable and in Excess.—The travelling-surfaces of insects, bats, and birds greatly exceed those of fishes and swimming animals; the travelling-surfaces of swimming animals being greatly in excess of those of animals which walk and run. The wing area of insects, bats, and birds varies very considerably, flight being possible within a comparatively wide range. Thus there are light-bodied and large-winged insects and birds—as the butterfly (fig. 57) and heron (fig. 60, p. 126); and others whose bodies are comparatively heavy, while their wings are insignificantly small—as the sphinx moth and Goliath beetle (fig. 58) among insects, and the grebe, quail, and partridge (fig. 59, p. 126) among birds.

The apparent inconsistencies in the dimensions of the body and wings are readily explained by the greater muscular development of the heavy-bodied short-winged insects and birds, and the increased power and rapidity with which the wings in them are made to oscillate. In large-winged animals the movements are slow; in small-winged ones comparatively very rapid. This shows that flight may be attained by a heavy, powerful animal with comparatively small wings, as well as by a lighter one with enormously enlarged wings. While there is apparently no fixed relation between the area of the wings and the animal to be raised, there is, unless in the case of sailing birds,70 an unvarying relation between the weight of the animal, the area of its wings, and the number of oscillations made by them in a given time. The problem of flight thus resolves itself into one of weight, power, velocity, and small surfaces; versus buoyancy, debility, diminished speed, and extensive surfaces,—weight in either case being a sine quâ non. In order to utilize the air as a means of transit, the body in motion, whether it moves in virtue of the life it possesses, or because of a force superadded, must be heavier than the air. It must tread and rise upon the air as a swimmer upon the water, or as a kite upon the wind. It must act against gravity, and elevate and carry itself forward at the expense of the air, and by virtue of the force which resides in it. If it were rescued from the law of gravity on the one hand, and bereft of independent movement on the other, it would float about uncontrolled and uncontrollable, as happens in the ordinary gas-balloon.