That no fixed relation exists between the area of the wings and the size and weight of the body, is evident on comparing the dimensions of the wings and bodies of the several orders of insects, bats, and birds. If such comparison be made, it will be found that the pinions in some instances diminish while the bodies increase, and the converse. No practical good can therefore accrue to aërostation from elaborate measurements of the wings and trunks of any flying thing; neither can any rule be laid down as to the extent of surface required for sustaining a given weight in the air. The wing area is, as a rule, considerably in excess of what is actually required for the purposes of flight. This is proved in two ways. First, by the fact that bats can carry their young without inconvenience, and birds elevate surprising quantities of fish, game, carrion, etc. I had in my possession at one time a tame barn-door owl which could lift a piece of meat a quarter of its own weight, after fasting four-and-twenty hours; and an eagle, as is well known, can carry a moderate-sized lamb with facility.

The excess of wing area is proved, secondly, by the fact that a large proportion of the wings of most volant animals may be removed without destroying the power of flight. I instituted a series of experiments on the wings of the fly, dragon-fly, butterfly, sparrow, etc., with a view to determining this point in 1867. The following are the results obtained:—

Blue-bottle Fly.—Experiment 1. Detached posterior or thin half of each wing in its long axis. Flight perfect.

Exp. 2. Detached posterior two-thirds of either wing in its long axis. Flight still perfect. I confess I was not prepared for this result.

Exp. 3. Detached one-third of anterior or thick margin of either pinion obliquely. Flight imperfect.

Exp. 4. Detached one-half of anterior or thick margin of either pinion obliquely. The power of flight completely destroyed. From experiments 3 and 4 it would seem that the anterior margin of the wing, which contains the principal nervures, and which is the most rigid portion of the pinion, cannot be mutilated with impunity.

Exp. 5. Removed one-third from the extremity of either wing transversely, i.e. in the direction of the short axis of the pinion. Flight perfect.

Exp. 6. Removed one-half from either wing transversely, as in experiment 5. Flight very slightly (if at all) impaired.

Exp. 7. Divided either pinion in the direction of its long axis into three equal parts, the anterior nervures being contained in the anterior portion. Flight perfect.

Exp. 8. Notched two-thirds of either pinion obliquely from behind. Flight perfect.

Exp. 9. Notched anterior third of either pinion transversely. The power of flight destroyed. Here, as in experiment 4, the mutilation of the anterior margin was followed by loss of function.

Exp. 10. Detached posterior two-thirds of right wing in its long axis, the left wing being untouched. Flight perfect. I expected that this experiment would result in loss of balancing-power; but this was not the case.

Exp. 11. Detached half of right wing transversely, the left one being normal. The insect flew irregularly, and came to the ground about a yard from where I stood. I seized it and detached the corresponding half of the left wing, after which it flew away, as in experiment 6.

Dragon-Fly.—Exp. 12. In the dragon-fly either the first or second pair of wings may be removed without destroying the power of flight. The insect generally flies most steadily when the posterior pair of wings are detached, as it can balance better; but in either case flight is perfect, and in no degree laboured.

Exp. 13. Removed one-third from the posterior margin of the first and second pairs of wings. Flight in no wise impaired.

If more than a third of each wing is cut away from the posterior or thin margin, the insect can still fly, but with effort.

Experiment 13 shows that the posterior or thin flexible margins of the wings may be dispensed with in flight. They are more especially engaged in propelling. Compare with experiments 1 and 2.

Exp. 14. The extremities or tips of the first and second pair of wings may be detached to the extent of one-third, without diminishing the power of flight. Compare with experiments 5 and 6.

If the mutilation be carried further, flight is laboured, and in some cases destroyed.

Exp. 15. When the front edges of the first and second pairs of wings are notched or when they are removed, flight is completely destroyed. Compare with experiments 3, 4, and 9.

This shows that a certain degree of stiffness is required for the front edges of the wings, the front edges indirectly supporting the back edges. It is, moreover, on the front edges of the wings that the pressure falls in flight, and by these edges the major portions of the wings are attached to the body. The principal movements of the wings are communicated to these edges.

Butterfly.—Exp. 16. Removed posterior halves of the first pair of wings of white butterfly. Flight perfect.

Exp. 17. Removed posterior halves of first and second pairs of wings. Flight not strong but still perfect. If additional portions of the posterior wings were removed, the insect could still fly, but with great effort, and came to the ground at no great distance.

Exp. 18. When the tips (outer sixth) of the first and second pairs of wings were cut away, flight was in no wise impaired. When more was detached the insect could not fly.

Exp. 19. Removed the posterior wings of the brown butterfly. Flight unimpaired.

Exp. 20. Removed in addition a small portion (one-sixth) from the tips of the anterior wings. Flight still perfect, as the insect flew upwards of ten yards.

Exp. 21. Removed in addition a portion (one-eighth) of the posterior margins of anterior wings. The insect flew imperfectly, and came to the ground about a yard from the point where it commenced its flight.

House Sparrow.—The sparrow is a heavy small-winged bird, requiring, one would imagine, all its wing area. This, however, is not the case, as the annexed experiments show.

Exp. 22. Detached the half of the secondary feathers of either pinion in the direction of the long axis of the wing, the primaries being left intact. Flight as perfect as before the mutilation took place. In this experiment, one wing was operated upon before the other, in order to test the balancing-power. The bird flew perfectly, either with one or with both wings cut.

Exp. 23. Detached the half of the secondary feathers and a fourth of the primary ones of either pinion in the long axis of the wing. Flight in no wise impaired. The bird, in this instance, flew upwards of 30 yards, and, having risen a considerable height, dropped into a neighbouring tree.

Exp. 24. Detached nearly the half of the primary feathers in the long axis of either pinion, the secondaries being left intact. When one wing only was operated upon, flight was perfect; when both were tampered with, it was still perfect, but slightly laboured.

Exp. 25. Detached rather more than a third of both primary and secondary feathers of either pinion in the long axis of the wing. In this case the bird flew with evident exertion, but was able, notwithstanding, to attain a very considerable altitude.

From experiments 1, 2, 7, 8, 10, 13, 16, 22, 23, 24, and 25, it would appear that great liberties may be taken with the posterior or thin margin of the wing, and the dimensions of the wing in this direction materially reduced, without destroying, or even vitiating in a marked degree, the powers of flight. This is no doubt owing to the fact indicated by Sir George Cayley, and fully explained by Mr. Wenham, that in all wings, particularly long narrow ones, the elevating power is transferred to the anterior or front margin. These experiments prove that the upward bending of the posterior margins of the wings during the down stroke is not necessary to flight.

Exp. 26. Removed alternate primary and secondary feathers from either wing, beginning with the first primary. The bird flew upwards of fifty yards with very slight effort, rose above an adjoining fence, and wheeled over it a second time to settle on a tree in the vicinity. When one wing only was operated upon, it flew irregularly and in a lopsided manner.

Exp. 27. Removed alternate primary and secondary feathers from either wing, beginning with the second primary. Flight, from all I could determine, perfect. When one wing only was cut, flight was irregular or lopsided, as in experiment 26.

From experiments 26 and 27, as well as experiments 7 and 8, it would seem that the wing does not of necessity require to present an unbroken or continuous surface to the air, such as is witnessed in the pinion of the bat, and that the feathers, when present, may be separated from each other without destroying the utility of the pinion. In the raven and many other birds the extremities of the first four or five primaries divaricate in a marked manner. A similar condition is met with in the Alucita hexadactyla, where the delicate feathery-looking processes composing the wing are widely removed from each other. The wing, however, ceteris paribus, is strongest when the feathers are not separated from each other, and when they overlap, as then they are arranged so as mutually to support each other.

Exp. 28. Removed half of the primary feathers from either wing transversely, i.e. in the direction of the short axis of the wing. Flight very slightly, if at all, impaired when only one wing was operated upon. When both were cut, the bird flew heavily, and came to the ground at no very great distance. This mutilation was not followed by the same result in experiments 6 and 11. On the whole, I am inclined to believe that the area of the wing can be curtailed with least injury in the direction of its long axis, by removing successive portions from its posterior margin.

Exp. 29. The carpal or wrist-joint of either pinion rendered immobile by lashing the wings to slender reeds, the elbow-joints being left free. The bird, on leaving the hand, fluttered its wings vigorously, but after a brief flight came heavily to the ground, thus showing that a certain degree of twisting and folding, or flexing of the wings, is necessary to the flight of the bird, and that, however the superficies and shape of the pinions may be altered, the movements thereof must not be interfered with. I tied up the wings of a pigeon in the same manner, with a precisely similar result.

The birds operated upon were, I may observe, caught in a net, and the experiments made within a few minutes from the time of capture.

Some of my readers will probably infer from the foregoing, that the figure-of-8 curves formed along the anterior and posterior margins of the pinions are not necessary to flight, since the tips and posterior margins of the wings may be removed, without destroying it. To such I reply, that the wings are flexible, elastic, and composed of a congeries of curved surfaces, and that so long as a portion of them remains, they form, or tend to form, figure-of-8 curves in every direction.

Captain F. W. Hutton, in a recent paper “On the Flight of Birds” (Ibis, April 1872), refers to some of the experiments detailed above, and endeavours to frame a theory of flight, which differs in some respects from my own. His remarks are singularly inappropriate, and illustrate in a forcible manner the old adage, “A little knowledge is a dangerous thing.” If Captain Hutton had taken the trouble to look into my memoir “On the Physiology of Wings,” communicated to the Royal Society of Edinburgh, on the 2d of August 1870,71 fifteen months before his own paper was written, there is reason to believe he would have arrived at very different conclusions. Assuredly he would not have ventured to make the rash statements he has made, the more especially as he attempts to controvert my views, which are based upon anatomical research and experiment, without making any dissections or experiments of his own.

The Wing area decreases as the Size and Weight of the Volant Animal increases.—While, as explained in the last section, no definite relation exists between the weight of a flying animal and the size of its flying surfaces, there being, as stated, heavy bodied and small-winged insects, bats, and birds, and the converse; and while, as I have shown by experiment, flight is possible within a wide range, the wings being, as a rule, in excess of what are required for the purposes of flight; still it appears, from the researches of M. de Lucy, that there is a general law, to the effect that the larger the volant animal the smaller by comparison are its flying surfaces. The existence of such a law is very encouraging as far as artificial flight is concerned, for it shows that the flying surfaces of a large, heavy, powerful flying machine will be comparatively small, and consequently comparatively compact and strong. This is a point of very considerable importance, as the object desiderated in a flying machine is elevating capacity.

M. de Lucy has tabulated his results, which I subjoin:72—

“It is easy, by aid of this table, to follow the order, always decreasing, of the surfaces, in proportion as the winged animal increases in size and weight. Thus, in comparing the insects with one another, we find that the gnat, which weighs 460 times less than the stag-beetle, has fourteen times more of surface. The lady-bird weighs 150 times less than the stag-beetle, and possesses five times more of surface. It is the same with the birds. The sparrow weighs about ten times less than the pigeon, and has twice as much surface. The pigeon weighs about eight times less than the stork, and has twice as much surface. The sparrow weighs 339 times less than the Australian crane, and possesses seven times more surface. If now we compare the insects and the birds, the gradation will become even much more striking. The gnat, for example, weighs 97,000 times less than the pigeon, and has forty times more surface; it weighs 3,000,000 times less than the crane of Australia, and possesses 149 times more of surface than this latter, the weight of which is about 9 kilogrammes 500 grammes (25 lbs. 5 oz. 9 dwt. troy, 20 lbs. 15 oz. 2 1/4 dr. avoirdupois).

“The Australian crane is the heaviest bird that I have weighed. It is that which has the smallest amount of surface, for, referred to the kilogramme, it does not give us a surface of more than 899 square centimetres (139 square inches), that is to say about an eleventh part of a square metre. But every one knows that these grallatorial animals are excellent birds of flight. Of all travelling birds they undertake the longest and most remote journeys. They are, in addition, the eagle excepted, the birds which elevate themselves the highest, and the flight of which is the longest maintained.”73

Strictly in accordance with the foregoing, are my own measurements of the gannet and heron. The following details of weight, measurement, etc., of the gannet were supplied by an adult specimen which I dissected during the winter of 1869. Entire weight, 7 lbs. (minus 3 ounces); length of body from tip of bill to tip of tail, three feet four inches; head and neck, one foot three inches; tail, twelve inches; trunk, thirteen inches; girth of trunk, eighteen inches; expanse of wing from tip to tip across body, six feet; widest portion of wing across primary feathers, six inches; across secondaries, seven inches; across tertiaries, eight inches. Each wing, when carefully measured and squared, gave an area of 19 1/2 square inches. The wings of the gannet, therefore, furnish a supporting area of three feet three inches square. As the bird weighs close upon 7 lbs., this gives something like thirteen square inches of wing for every 36 1/3 ounces of body, i.e. one foot one square inch of wing for every 2 lbs. 4 1/3 oz. of body.

The heron, a specimen of which I dissected at the same time, gave a very different result, as the subjoined particulars will show. Weight of body, 3 lbs. 3 ounces; length of body from tip of bill to tip of tail, three feet four inches; head and neck, two feet; tail, seven inches; trunk, nine inches; girth of body, twelve inches; expanse of wing from tip to tip across the body, five feet nine inches; widest portion of wing across primary and tertiary feathers, eleven inches; across secondary feathers, twelve inches.

Each wing, when carefully measured and squared, gave an area of twenty-six square inches. The wings of the heron, consequently, furnish a supporting area of four feet four inches square. As the bird only weighs 3 lbs. 3 ounces, this gives something like twenty-six square inches of wing for every 25 1/2 ounces of bird, or one foot 5 1/4 inches square for every 1 lb. 1 ounce of body.

In the gannet there is only one foot one square inch of wing for every 2 lbs. 4 1/3 ounces of body. The gannet has, consequently, less than half of the wing area of the heron. The gannet’s wings are, however, long narrow wings (those of the heron are broad), which extend transversely across the body; and these are found to be the most powerful—the wings of the albatross—which measure fourteen feet from tip to tip (and only one foot across), elevating 18 lbs. without difficulty. If the wings of the gannet, which have a superficial area of three feet three inches square, are capable of elevating 7 lbs., while the wings of the heron, which have a superficial area of four feet four inches, can only elevate 3 lbs., it is evident (seeing the wings of both are twisted levers, and formed upon a common type) that the gannet’s wings must be vibrated with greater energy than the heron’s wings; and this is actually the case. The heron’s wings, as I have ascertained from observation, make 60 down and 60 up strokes every minute; whereas the wings of the gannet, when the bird is flying in a straight line to or from its fishing-ground, make close upon 150 up and 150 down strokes during the same period. The wings of the divers, and other short-winged, heavy-bodied birds, are urged at a much higher speed, so that comparatively small wings can be made to elevate a comparatively heavy body, if the speed only be increased sufficiently.74 Flight, therefore, as already indicated, is a question of power, speed, and small surfaces versus weight. Elaborate measurements of wing, area, and minute calculations of speed, can consequently only determine the minimum of wing for elevating the maximum of weight—flight being attainable within a comparatively wide range.

Wings, their Form, etc.; all Wings Screws, structurally and functionally.—Wings vary considerably as to their general contour; some being falcated or scythe-like, some oblong, some rounded or circular, some lanceolate, and some linear.75

All wings are constructed upon a common type. They are in every instance carefully graduated, the wing tapering from the root towards the tip, and from the anterior margin in the direction of the posterior margin. They are of a generally triangular form, and twisted upon themselves in the direction of their length, to form a helix or screw. They are convex above and concave below, and more or less flexible and elastic throughout, the elasticity being greatest at the tip and along the posterior margin. They are also moveable in all their parts. Figs. 61, 62, 63 (p. 138), 59 and 60 (p. 126), 96 and 97 (p. 176), represent typical bird wings; figs. 17 (p. 36), 94 and 95 (p. 175), typical bat wings; and figs. 57 and 58 (p. 125), 89 and 90 (p. 171), 91 (p. 172), 92 and 93 (p. 174), typical insect wings.

In all the wings which I have examined, whether in the insect, bat, or bird, the wing is recovered, flexed, or drawn towards the body by the action of elastic ligaments, these structures, by their mere contraction, causing the wing, when fully extended and presenting its maximum of surface, to resume its position of rest and plane of least resistance. The principal effort required in flight is, therefore, made during extension, and at the beginning of the down stroke. The elastic ligaments are variously formed, and the amount of contraction which they undergo is in all cases accurately adapted to the size and form of the wing, and the rapidity with which it is worked; the contraction being greatest in the short-winged and heavy-bodied insects and birds, and least in the light-bodied and ample-winged ones, particularly such as skim or glide. The mechanical action of the elastic ligaments, I need scarcely remark, insures an additional period of repose to the wing at each stroke; and this is a point of some importance, as showing that the lengthened and laborious flights of insects and birds are not without their stated intervals of rest.

All wings are furnished at their roots with some form of universal joint which enables them to move not only in an upward, downward, forward, or backward direction, but also at various intermediate degrees of obliquity. All wings obtain their leverage by presenting oblique surfaces to the air, the degree of obliquity gradually increasing in a direction from behind forwards and downwards during extension and the down stroke, and gradually decreasing in an opposite direction during flexion and the up stroke.

In the bat and bird the oblique surfaces are produced by the spiral configuration of the articular surfaces of the bones of the wing, and by the rotation of the bones of the arm, forearm, and hand, upon their long axes. The reaction of the air also assists in the production of the oblique surfaces.

That the wing twists upon itself structurally, not only in the insect, but also in the bat and bird, any one may readily satisfy himself by a careful examination; and that it twists upon itself during its action I have had the most convincing and repeated proofs (figs. 64, 65, and 66). The twisting in question is most marked in the posterior or thin margin of the wing, the anterior and thicker margin performing more the part of an axis. As a result of this arrangement, the anterior or thick margin cuts into the air quietly, and as it were by stealth, the posterior one producing on all occasions a violent commotion, especially perceptible if a flame be exposed behind the vibrating wing. Indeed, it is a matter for surprise that the spiral conformation of the pinion, and its spiral mode of action, should have eluded observation so long; and I shall be pardoned for dilating upon the subject when I state my conviction that it forms the fundamental and distinguishing feature in flight, and must be taken into account by all who seek to solve this most involved and interesting problem by artificial means. The importance of the twisted configuration or screw-like form of the wing cannot be over-estimated. That this shape is intimately associated with flight is apparent from the fact that the rowing feathers of the wing of the bird are every one of them distinctly spiral in their nature; in fact, one entire rowing feather is equivalent—morphologically and physiologically—to one entire insect wing. In the wing of the martin, where the bones of the pinion are short and in some respects rudimentary, the primary and secondary feathers are greatly developed, and banked up in such a manner that the wing as a whole presents the same curves as those displayed by the insect’s wing, or by the wing of the eagle where the bones, muscles, and feathers have attained a maximum development. The conformation of the wing is such that it presents a waved appearance in every direction—the waves running longitudinally, transversely, and obliquely. The greater portion of the pinion may consequently be removed without materially affecting either its form or its functions. This is proved by making sections in various directions, and by finding, as has been already shown, that in some instances as much as two-thirds of the wing may be lopped off without visibly impairing the power of flight. The spiral nature of the pinion is most readily recognised when the wing is seen from behind and from beneath, and when it is foreshortened. It is also well marked in some of the long-winged oceanic birds when viewed from before (figs. 82 and 83, p. 158), and cannot escape detection under any circumstances, if sought for,—the wing being essentially composed of a congeries of curves, remarkable alike for their apparent simplicity and the subtlety of their detail.

The Wing during its action reverses its Planes, and describes a Figure-of-8 track in space.—The twisting or rotating of the wing on its long axis is particularly observable during extension and flexion in the bat and bird, and likewise in the insect, especially the beetle, cockroach, and such as fold their wings during repose. In these in extreme flexion the anterior or thick margin of the wing is directed downwards, and the posterior or thin one upwards. In the act of extension, the margins, in virtue of the wing rotating upon its long axis, reverse their positions, the anterior or thick margins describing a spiral course from below upwards, the posterior or thin margin describing a similar but opposite course from above downwards. These conditions, I need scarcely observe, are reversed during flexion. The movements of the margins during flexion and extension may be represented with a considerable degree of accuracy by a figure-of-8 laid horizontally.

In the wasp the wing commences the down or forward stroke at a of figs. 67 and 69, and makes an angle of something like 45° with the horizon (x x´). At b (figs. 67 and 69) the angle is slightly diminished, partly because of a rotation of the wing along its anterior margin (long axis of wing), partly from increased speed, and partly from the posterior margin of the wing yielding to a greater or less extent.

At c the angle is still more diminished from the same causes.

At d the wing is slowed slightly, preparatory to reversing, and the angle made with the horizon (x) increased.

At e the angle, for the same reason, is still more increased; while at f the wing is at right angles to the horizon. It is, in fact, in the act of reversing.

At g the wing is reversed, and the up or back stroke commenced.

The angle made at g is, consequently, the same as that made at a (45°), with this difference, that the anterior margin and outer portion of the wing, instead of being directed forwards, with reference to the head of the insect, are now directed backwards.

During the up or backward stroke all the phenomena are reversed, as shown at g h i j k l of figs. 68 and 70 (p. 141); the only difference being that the angles made by the wing with the horizon are somewhat less than during the down or forward stroke—a circumstance which facilitates the forward travel of the body, while it enables the wing during the back stroke still to afford a considerable amount of support. This arrangement permits the wing to travel backwards while the body is travelling forwards; the diminution of the angles made by the wing in the back stroke giving very much the same result as if the wing were striking in the direction of the travel of the body. The slight upward inclination of the wing during the back stroke permits the body to fall downwards and forwards to a slight extent at this peculiar juncture, the fall of the body, as has been already explained, contributing to the elevation of the wing.

The pinion acts as a helix or screw in a more or less horizontal direction from behind forwards, and from before backwards; but it likewise acts as a screw in a nearly vertical direction. If the wing of the larger domestic fly be viewed during its vibrations from above, it will be found that the blur or impression produced on the eye by its action is more or less concave (fig. 66, p. 139). This is due to the fact that the wing is spiral in its nature, and because during its action it twists upon itself in such a manner as to describe a double curve,—the one curve being directed upwards, the other downwards. The double curve referred to is particularly evident in the flight of birds from the greater size of their wings. The wing, both when at rest and in motion, may not inaptly be compared to the blade of an ordinary screw propeller as employed in navigation. Thus the general outline of the wing corresponds closely with the outline of the blade of the propeller, and the track described by the wing in space is twisted upon itself propeller fashion. The great velocity with which the wing is driven converts the impression or blur into what is equivalent to a solid for the time being, in the same way that the spokes of a wheel in violent motion, as is well understood, completely occupy the space contained within the rim or circumference of the wheel (figs. 64, 65, and 66, p. 139).

The figure-of-8 action of the wing explains how an insect, bat, or bird, may fix itself in the air, the backward and forward reciprocating action of the pinion affording support, but no propulsion. In these instances, the backward and forward strokes are made to counterbalance each other.

The Wing, when advancing with the Body, describes a Looped and Waved Track.—Although the figure-of-8 represents with considerable fidelity the twisting of the wing upon its long axis during extension and flexion, and during the down and up strokes when the volant animal is playing its wings before an object, or still better, when it is artificially fixed, it is otherwise when it is free and progressing rapidly. In this case the wing, in virtue of its being carried forward by the body in motion, describes first a looped and then a waved track. This looped and waved track made by the wing of the insect is represented at figs. 71 and 72, and that made by the wing of the bat and bird at fig. 73, p. 144.