^{page 322 note *} On the Various Modes of Flight in relation to Aëronautics.

^{page 324 note *} On the Mechanical Appliances by which Flight is attained in the Animal Kingdom, &c.

^{page 324 note †} Op. cit., from page 199 to page 267 inclusive.

^{page 324 note ‡} Op. cit., Plate XV. figs. 49, 51, 57, 68, 69, 70. Likewise Diagram 18 A d′e′f′, a′b′, page 253.

^{page 324 note §} Op. cit., Plate XV. figs. 58, 59, 61, 73, 74, and 75.

^{page 324 note ∥} Op. cit., Plate XV. fig. 78.

^{page 324 note ¶} I think it proper to state that various anatomists have carefully examined the form of the articular surfaces of the joints in the limbs, more especially in man. The researches of the brothers Weber and Professor Meyer of Zurich are so well known, that it may suffice simply to refer to them. I would also direct attention to the writings of Langer, Henke, Meissner, and the late Professor Goodsir. Langer, Henke, and Meissner succeeded in demonstrating the “screw configuration” of the articular surfaces of the elbow, ankle, and calcaneo-astragaloid joints, and Goodsir showed that the articular surfaces of the knee-joint consist of “a double conical screw combination.” The last-named observer also expressed his belief, “that articular combinations, with opposite windings on opposite sides of the body, similar to those in the knee-joint, exist in the ankle and tarsal, and in the elbow and carpal joints; and that the hip and shoulder joints consist of single-threaded couples, but also with opposite windings on opposite sides of the body.” The following are the views of Langer as interpreted by Goodsir :—(Proc. Roy. Soc. Edin., Jan. 18, 1858, and Anatomical Memoirs, vol. ii. p. 231.) “Langer, acting on the happy idea of prolonging the screw by uniting, in one direction, a number of plaster casts of the same articular surface, succeeded in forming continued screws from the upper articular surface of the astragalus in the horse, panther, and human subject. Langer concludes that the ‘go line’ (a line obtained from the scratch of a steel point fixed on one of the articular surfaces, and which, marks the opposite surface when the joint is moved) of the ankle-joint in all the mammalia is a portion of a helix, and that therefore the astragaloid surface is a segment of a cylindrical or conical male screw, while the tibio-fibular surface is a segment of the corresponding female screw. The right ankle-joint is a left-handed screw combination; the left ankle-joint a right-handed. When therefore the foot is conceived to be fixed, the leg, in passing from a position of extension to flexion, moves laterally outwards along the axis of rotation, and the sine of the angle of inclination of the thread—that is, in proportion to the extent of flexion and the rapidity of the screw.” Goodsir, in attempting by Langer's method to develop those articular screw-models, found that when two casts were united, an apparently satisfactory helix was produced; but in adding to the series, the spire diminished, and the helix closed upon itself; so that it appeared that not only the angle of inclination of the thread, but also the radius of rotation, diminished. He was, therefore, of opinion, that the tibio-astragaloid articular surfaces could not be regarded as segments of a cylindrical series, and thought it extremely probable that, abstracting the terminal facets, the acting areas on each surface consist each of a segment of a conical screw—the convex portions of these two screws being on the astragaloid, the concave on the tibial articular surface; the one screw coming into action in flexion, the other in extension. Goodsir's experiments on the knee and ankle-joints, conducted with extreme care, by the aid of fresh specimens, casts, and models, led him to conclude that both joints were ‘spiral in their nature’—that in fact they were ‘screwed structures,’ and that the movements of the knee-joint are combined gliding and rolling movements of conical screwed surfaces upon one another. The following are his own words :—“The general character of the curves observed, and the corresponding movements and structure of the joint (knee-joint) leave little doubt in my mind that the flexion and extension, combined gliding and rolling movements of the knee, are performed between two conical double-threaded acrew-combinations, an anterior and a posterior—the anterior being a left-handed screw, and the posterior a right-handed screw in the right knee-joint; the anterior a right-handed, and the posterior a left-handed screw in the left knee-joint. The movements which take place round these two combinations are alternate, those round the anterior completing extension and commencing flexion, those round the posterior completing flexion and commencing extension of the joint.’

^{page 325 note *} Op. cit., Diag. 2, page 204; Plate XV. fig. 76.

^{page 325 note †} Op. cit., page 233, Diag. 5; Plate XV. fig. 61.

^{page 325 note ‡} Op. cit., page 233, Diag. 6; Plate XV. fig. 59.

^{page 325 note §} Op. cit., pages 231, 232, 233, and 234.

^{page 325 note ∥} Op. cit., Plate XV. figs. 68, 69, and 70.

^{page 325 note ¶} Op. cit., Plate XV. figs. 58, 61, 73, and 74.

^{page 326 note *} Op. cit., pages 219, 220, 221, 222.

^{page 326 note †} For further experiments in this direction, see footnote to pages 361 and 362.

^{page 326 note ‡} Op. cit., Plate XV. figs. 68, 69, 70, 73, and 74.

^{page 326 note §} Op. cit., Plate XV. figs 61 and 62.

^{page 326 note ∥} Op. cit., page 253; Diagram 18 A, a′b′, d′e′f′.

^{page 327 note *} Op. cit., page 233, Diagram 5. Compare this diagram with figs. 59 and 61 of Plate XV.

^{page 327 note †} Op. cit., Plate XV. fig. 68.

^{page 327 note ‡} Op. cit., Plate XV. figs. 58 and 59 a a′. Compare with a a′ of fig. 52.

^{page 327 note §} Op. cit., Plate XV. figs. 73 and 75 b a c.

^{page 327 note ∥} Op. cit., Plate XV. fig. 52 a a′.

^{page 327 note ¶} Op. cit., Plate XV. figs. 58 and 59.

^{page 328 note *} Op. cit., page 233, Diagram. 6.

^{page 328 note ‡} Op. cit., Plate XV. fig. 73, e.

^{page 328 note ∥} Op. cit., Plate XV. fig. 73, c.

^{page 328 note †} Op. cit. Plate XV. figs. 70, 73, and 74.

^{page 328 note §} Op. cit., Plate XV. fig. 73, a, c.

^{page 329 note *} Op. cit., Plate XV. fig. 73, f.

^{page 329 note ‡} Op. cit., Plate XV. figs. 73, 74, 75.

^{page 329 note ∥} Op. cit., Plate XV. fig. 73, a, c.

^{page 329 note **} Op. cit., Plate XV. fig. 75, c.

^{page 329 note ‡‡} Op. cit., p. 249, Diagram 14.

^{page 329 note †} Op. cit., Plate XV. fig. 73, a, b, c.

^{page 329 note §} Op. cit., Plate XV. fig. 73, b.

^{page 329 note ¶} Op. cit., Plate XV. fig. 74, b, c.

^{page 329 note ††} Op. cit., Plate XV. fig. 75, a, b.

^{page 329 note §§} Op. tit, p. 249, Diagram 15.

^{page 329 note ∥∥} Similar movements occur in the body and tail of the fish in the act of swimming. “The double curve or spiral into which the fish throws itself when swimming may be conveniently divided into an upper or cephalic curve,* and a lower or caudal one.† When the concavity of the caudal curve is biting or laying hold of the water, and when the concave surface of the tail is being forced during extension with great violence in the direction of the axis of motion,‡ where the concave surface is suddenly converted into a convex one, the concavity of the cephalic curve, i.e., the concave surface of the upper half of the fish, is being urged, with less vigour, in the direction of the same line from the opposite side of it. As the caudal and cephalic curves are obliterated when the line in question is reached, there is, consequently, a period (momentary it must be), between the effective and non-effective strokes, in which the body of the fish is comparatively straight, and, consequently, in a position to advance almost without impediment.”§

^{page 329 note *} Op. cit., Diag. 2, d, p. 204.

^{page 329 note †} Op. cit., Diag. 2, c, p. 204.

^{page 329 note ‡} Op. cit., Ding. 2, a, b, p. 204

^{page 329 note §} Op. cit., p. 205.

^{page 330 note *} Handbook of Natural Phil. (vol. on Electricity, Magnetism, and Acoustics), by Dr Lardner (Lond. 1863), pp. 366-7.

^{page 330 note †} Op. cit., pp. 378, 379, 380.

^{page 331 note *} Les mouvements de l'aile chéz les insectes, p. 171, 13th Février 1869. Mécanisme du vol chez les insectes—comment se fait la propulsion, p. 252, 20th Mars 1869. Du vol des oiseaux, p. 578, 14 Aout 1869. Du vol des oiseaux (suite), p. 601, 21 Aout 1869. Du vol des oiseaux (suite), p. 646, 11 Septemhre 1869. Du vol des oiseaux (fin), p. 700, 2 October 1869.

^{page 331 note †} Determination expérimentale du mouvement des ailes des insectes pendant le vol. Par M. E. J. Marey. Tome LXVII. p. 1341, Tome LXVIII. p. 667.

^{page 332 note *} Revue des Cours Scientifiques de la France et de l'Etranger.

^{page 333 note *} Revue des Cours Scientifiques de la France et de l'Etranger, 13 Février 1869, page 175, figure 5. Professor Marey represents the wing of the wasp as fanning the air in a vertical direction. In reality, the wing of the wasp and of most insects is made to vibrate very obliquely, and in a more or less horizontal direction.

^{page 333 note †} Revue des Cours Scientifiques et de la France et de l'Etranger, 13 Février 1869, pages 173, 174, and 176.

^{page 333 note ‡} Trans. Linn. Society, Vol. XXVI, page 233, Diagrams 5 and 6; page 249, Diagrams 14, 15, and 16; Plate XV. figures 59 and 61. Vide, introduction to present memoir.

^{page 333 note §} Op. cit., pages 247, 248, 249, and 250.

^{page 333 note ∥} Op. cit., pages 248 and 249, Diagrams 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16.

^{page 334 note *} Méchanisme du vol des insectes—comment se fait la propulsion. Revue des Cours Scientifiques de la France et de l'Etranger, 20th March 1869.

^{page 334 note †} Fifth Annual Report of the Aëronautical Society of Great Britain for 1870, pages 42-47. Figures 1, 2; Diagrams 1–4.

^{page 334 note ‡} Artificial flight is described at page 402.

^{page 337 note *} The movements of the wing somewhat resemble those of a sailing ship. The wing and ship both tack upon the wind, and both change their tack or reverse abruptly. The changing of the tack is moreover always accompanied by a slowing or diminution of the speed.

^{page 338 note *} For specific differences between the screws formed by the wings and the propellors employed in navigation, see memoir by the author, Trans. Linn. Society, vol. xxvi. pages 228, 229, 230, and 231.

^{page 339 note *} A precisely similar difference is found to exist between the aërial or flying wing and the subaquatic or diving wing. In the gannet, cormorant, merganser, grebe, &c., which fly under the water, it is the upper or dorsal surface of the pinion which gives the effective stroke, whereas in aërial flight it is the under or ventral surface. This is proved by the fact that in the penguin and great auk, which are incapable of flying out of the water, and confine their efforts to diving or swimming under it, the wing is actually twisted round, so that the dorsal surface of the pinion occupies the position normally occupied by the ventral surfaces in all other birds. This is necessitated by the fact that a diving bird, seeing it is of lighter specific gravity than the water, must always fly downwards; in other words, it must counteract buoyancy as the flying bird counteracts gravity—buoyancy forcing the diving bird to the surface of the water in the same way that gravity drags the flying bird to the surface of the earth. Levity and weight are therefore separate forces, and act under diametrically opposite conditions, levity being quite as useful to the diving bird as weight to the flying one. The wings of diving birds are applied to the water precisely in the same manner as the flippers of the seal, sea bear, walrus, turtle, porpoise, whale, manatee, &c. All these animals are lighter than the water, and, as a consequence, their travelling surfaces to be effective must act from below as in the case of the scull. It is the reverse in the air, the travelling surfaces acting invariably from above. For further development of this view see footnote to page 371.

^{page 343 note *} On the Mechanism of Flight, by the Author, Trans. Linn. Society, vol. xxvi. pages 214, 255, and 256.

^{page 349 note *} It happens occasionally in insects that the posterior margin of the wing is on a higher level than the anterior one towards the termination of the up stroke as shown at a (dotted line) of fig. 16. In such cases the posterior margin is suddenly rotated in a downward and forward direction at the beginning of the down stroke—the downward and forward rotation securing additional elevating power for the wing. The posterior margin of the wing in bats and birds, unless they are flying downwards, never rises above the anterior one, either during the up or down stroke.

^{page 352 note *} When a bird rises from the ground it runs for a short distance, or throws its body into the air by a sudden leap, the wings being simultaneously elevated. When the body is fairly off the ground, the wings are made to descend with great vigour, and by their action to continue the upward impulse secured by the preliminary run or leap. The body then falls in a curve downwards and forwards, the wings, partly by the fall of the body, partly by the reaction of the air, on their under surface, and partly by the contraction of the elevator muscles and elastic ligaments being placed above, and to some extent behind the bird—in other words, elevated. The second down stroke is now given, and the wings again elevated as explained, and so on “ad infinitum,” the body falling when the wings are being elevated, and vice versa, as shown at fig. 14, p. 344. When a long-winged oceanic bird rises from the sea, it uses the tips of its wings as levers for forcing the body up, the points of the pinions suffering no injury from being brought violently in contact with the water. A bird cannot be said to be flying until the trunk is swinging forward in space and taking part in the movement. The hawk, when fixed in the air over its quarry, is simply supporting itself. To fly, in the proper acceptation of the term, implies to support and propel. This constitutes the difference between a bird and a balloon. The bird can elevate and carry itself forward, the balloon can simply elevate itself, and must rise and fall in a straight line in the absence of currents. When the gannet throws itself from a cliff the inertia of the trunk at once comes into play, and relieves the bird from those herculean exertions required to raise it from the water when it is once fairly settled thereon. A swallow dropping from the eaves of a house, or a bat from a tower, afford illustrations of the same principle. Many insects launch themselves into space prior to flight. Some, however, do not. Thus the blow-fly can rise from a level surface when its legs are removed. This is accounted for by the greater amplitude and more horizontal play of the insect's wing as compared with that of the bat and bird, and likewise by the remarkable reciprocating power which it possesses when the body of the insect is not moving forwards. (Vide figs. 3, 4, 5, and 6, page 338). When a beetle attempts to fly from the hand it extends its front legs and flexes the back ones, and tilts its head and thorax upwards so as exactly to resemble a horse in the act of rising from the ground. This preliminary over, whirr go its wings with immense velocity, and in an almost horizontal direction, the body being inclined more or less vertically. The insect rises very slowly, and often requires to make several attempts before it succeeds in launching itself into the air. I could never detect any pressure communicated to the hand when the insect was leaving it, from which I infer that it does not leap into the air. The bees, I am disposed to believe, also rise without anything in the form of a leap or spring. I have often watched them leaving the petals of flowers, and they always appeared to me to elevate themselves by the steady play of their wings, which was the more necessary, as the surface from which they rose was in many cases a yielding surface. The falling forward of the body during flight was indicated in my Memoir “On the Mechanism of Flight,” Trans. Linn. Society, vol. xxvi. p. 226.

^{page 356 note *} The importance to be attached to weight in flight is variously explained in my Memoir on the subject, Trans. Linn. Society, vol. xxvi. pages 218, 219, 246, 260, and 261.

^{page 357 note *} Mémoires du Muséum d'Histoire Naturelle. Tome septiéme. Paris, 1821. Essai sur le vol des Insectes, par I. Chabrier, p. 297. Plates x. xi. and xii.

^{page 361 note *} The wing area in insects is usually greatly in excess of what is absolutely required for flight, as the following experiments made, with the common white and brown butterfly and dragon-fly will show :—

1. Removed posterior halves of first pair of wings of white butterfly. Flight perfect.

2. 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.

3. 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.

4. Removed the posterior wings of the brown butterfly. Flight unimpaired.

5. 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.

6. 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.

7. 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.

8. 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 be cut away from the posterior or thin margin, the insect can still fly, but with effort.

Experiment 8 shows that the posterior or thin flexible margin of the wing may be dispensed with in flight. It is more especially engaged in propelling.

9. 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.

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

10. When the front edges of the first and second pair of wings are notched, or when they are removed, flight is completely destroyed.

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 edge of the wing that the pressure falls in flight, and by this edge the major portion of the wing is attached to the body. The principal movements of the wing are in addition communicated to this edge.

Note.—Some of my readers will probably infer from the foregoing experiments, that the figure of 8 curves formed along the anterior and posterior margins of the pinion are not necessary to flight, since the tip and posterior margin of the wing may be removed without destroying it. To such I reply, that the wing is flexible, elastic, and composed of a congeries of curved surfaces, and that so long as a portion of it remains, it forms, or tends to form, figure of 8 curves in every direction.

^{page 362 note *} Figures 39, 40, 41, 42, and 43 slow the double curves which occur on the anterior (b a c) and posterior (d e f) margins of the wing of the bat and bird.

^{page 363 note *} On the Mechanical Appliances by which Flight is attained in the Animel Kingdom, Trans. Linn. Society, vol. xxvi. pages 200, 201, and 262.

^{page 364 note *} “General Observations on the Anatomy of the Thorax in Insects, and on its Functions during Flight.” By E. T. Bennett, F.L.S., &c. (Extracted chiefly from the “Essai sur le vol des Insectes,” par Chabrier, J., Mém. du Muséum d'Histoire Naturelle. Zool. Journal, vol. i. art. xlvi. 1825Google Scholar.)

^{page 366 note *} The beetles have also their wings jointed.

^{page 370 note *} The alternate ascent and descent of the wings and body during the down and up strokes are well seen in the butterfly and in all animals whose wings are large for their bodies.

^{page 371 note *} Weight necessary to Flying Animals as at present constructed—Weight and Levity relatively considered with regard to Aërial and Subaquatic Flight (Diving).—Captain W. F. Hutton, in a recent pamphlet (On the Sailing Flight of the Albatros, Phil. Mag., August 1869), contends, that whereas a bird lighter than the water can fly in it, so, in like manner, a bird lighter than the air could fly in this medium, and that therefore weight is not necessary to aërial flight. Captain Hutton, however, forgets that a bird destined to fly above the water is provided with travelling surfaces so fashioned and so applied (they strike from above downwards and forwards), that if it was lighter than the air, they would carry it off into space without the possibility of a return; in other words, the action of the wings would carry the bird obliquely upwards, and render it quite incapable of flying either in a horizontal or downward direction. In the same way a bird destined to fly under the water (auk and penguin), if it was not lighter than the water, such is the configuration and mode of applying its travelling surfaces (they strike from below upwards and backwards), they would carry it in the direction of the bottom without any chance of return to the surface. In aërial flight, weight is the power which nature has placed at the disposal of the bird for regulating its altitude and horizontal flight, a cessation of the play of its wings, aided by the inertia of its trunk, enabling the bird to approach the earth. In subaquatic flight, levity is a power furnished for a similar but opposite purpose; this, combined with the partial slowing or stopping of the wings and feet, enabling the diving bird to regain the surface at any moment. Levity and weight are auxiliary forces, but they are necessary forces when the habits of the animals, and the form and mode of applying their travelling surfaces are taken into account. If the aerial flying bird was lighter than the air, its wings would requite to be twisted round to resemble the diving wings of the penguin and auk. If, on the other hand, the diving bird (penguin or auk) was heavier than water, its wings would require to resemble aërial wings, and they would require to strike in an opposite direction to that in which they strike normally. From this it follows that weight is necessary to the bird (as at present constructed) destined to navigate the air, and levity to that destined to navigate the water. If a bird was made very large and very light, it is obvious that the diving force at its disposal would be inadequate to submerge it. If, again, it was made very small and very heavy, it is equally plain that it could not fly. Mature, however, has struck the just balance; she has made the diving bird, which flies under the water, relatively much heavier than the bird which flies in the air, and has curtailed the travelling surfaces of the former, while she has increased those of the latter. For the same reason, she has furnished the diving bird with a certain degree of buoyancy, and the flying bird with a certain amount of weight—levity tending to bring the one to the surface of the water, weight the other to the surface of the earth, which is the normal position of rest for both. The action of the subaquatic or diving wing of the king penguin is well seen in the annexed woodcut (Fig. 44).

At A, the penguin is in the act of diving, and it will be observed that the anterior or thick margin of the wing is directed downwards and forwards, while the posterior margin is directed upwards and backwards. This has the effect of directing the under or ventral concave surface of the wing upwards and backwards, the effective stroke being delivered in this direction. The efficacy of the wing in counteracting levity is thus obvious. At B, the penguin is in the act of regaining the surface of the water, and in this case the wing is maintained in one position, or made to strike downwards and forwards like the aërial wing, the margins and under surface of the pinion being reversed for this purpose. The object now is not to depress but to elevate the body. Those movements are facilitated by the alternate play of the feet. What strikes one in the present woodcut is the comparatively small size of the diving or swimming wing, which resembles the flipper of the turtle, seal, sea bear, and walrus. At Plate XIII. figure 15, the aërial wing, as seen in the gull, is represented, and the large size of the flying pinion, as compared with the diving subaquatic one, is at once apparent. Here the anterior margin (x s t v w) of the wing is directed upwards and forwards, the posterior one (o p q) downwards and backwards. This causes the under or ventral concave surface of the pinion to look downwards and forwards, the direction in which the effective or down stroke is delivered. The aérial wing, like the subaquatic wing, is twisted upon itself. It strikes downwards and forwards, because this is the direction in which a body in motion would naturally fall.

^{page 376 note *} The valve action, as explained, is called more or less into play according to circumstances.

^{page 380 note *} In some cases, as for instance in the more rounded form of wing shown in fig. 20, Plate XIV., the 4th, 5th, and 6th primaries are longer and stronger, and overlap more than the 1st, 2d, and 3d.

^{page 382 note *} The same happens in the wings of all birds, and in the wing of the bat and insect. The outward and upward inclination of the tip of the wing is well seen in the beetle. This portion of the wing acts as a true kite, when the wing is being extended or thrust away from the body towards the termination of the up stroke. The under surface of the tip of the wing consequently contributes to flight during the up stroke.

^{page 386 note *} The grebes among birds and the beetles among insects furnish examples where small wings, made to vibrate at high speeds, are capable of elevating great weights.

^{page 386 note †} “On the Mechanism of Flight,” by the Author, Trans. Linn. Soc., vol. xxvi. page 219.

^{page 386 note ‡} Vide page 326 and foot-note to pages 361 and 362 of the present memoir, and pages 219, 220, 221, and 222 of my memoir “On the Mechanical Appliances by which Flight is Attained in the Animal Kingdom,” Trans. Linn. Society, vol. xxviGoogle Scholar.

^{page 387 note *} “On the Flight of Birds, of Bats, and of Insects, in reference to the subject of Aërial Locomotion,” by de Lucy, M., ParisGoogle Scholar.

^{page 388 note *} Compare with mechanical experiment described at pages 355 and 356.

^{page 388 note †} The swallow and crane, which dart along at a very high speed, tilt their bodies in turning; but, in addition, flap their wings and fly round the curve they wish to describe.

^{page 389 note *} In the dragon-fly the anterior pair of wings make a smaller angle with the horizon than the posterior pair. The first pair of wings are, consequently, more actively engaged as propellors—the second pair as elevators.

^{page 390 note *} “Experiments practically demonstrating the laws by which birds fly,” by Dr W. Smyth. Second Annual Report of the Aeronautical Society of Great Britain for 1867.

^{page 392 note *} I have frequently timed the heats of the wings of the common heron (Ardea cinerea) at Warren Point (Ireland). In March 1869 I was placed under unusually favourable circumstances for obtaining reliable results. I timed one bird high up over a lake for fifty seconds, and found that in that period it made fifty down and fifty up strokes; i.e., one down and one up stroke per second. I timed another one in a heronry belonging to Major Hall. It was snowing at the time (March 1869), but the birds, notwithstanding the inclemency of the weather and the early time of the year, were actively engaged in hatching, and required to be driven from their nests on the top of the larch trees by knocking against the trunks thereof with large sticks. One unusually anxious mother refused to leave the immediate neighbourhood of the tree containing her tender charge, and circled round and round it right overhead. I timed this bird for ten seconds, and found that she made ten down and ten up strokes; i.e., one down and one up stroke per second precisely as before. I have therefore no hesitation in affirming that the heron, in ordinary flight, makes exactly sixty down and sixty up strokes per minute. The heron, however, like all other birds when pursued or agitated, has the power of greatly augmenting the number of its beats.

^{page 392 note †} The above observation was made at Carlow on the Barrow in October 1867, and the account of it is abstracted from my note-book.

^{page 395 note *} C. J. L. Krarup, a Danish author, gives it as his opinion that the wing is elevated by a vital force, viz., by the contraction of the pectoralis minor; this muscle, according to him, acting with th the intensity of the pectoralis major (the depressor of the wing). He bases his statement upon the fact that in the pigeon the pectoralis minor or elevator of the wing weighs ⅛th of an ounce, whereas the pectoralis major or depressor of the wing weighs ⅞ths of an ounce. It ought, however, to be borne in mind that the volume of a muscle does not necessarily determine the precise influence exerted by its action; for the tendon of one muscle may be made to act upon a long lever, and, under favourable conditions, for developing its powers, while that of another muscle may be made to act upon a short lever, and, consequently, under unfavourable conditions.—On the Flight of Birds, p. 30. Copenhagen, 1869.

^{page 397 note *} A careful account of the musculo-elastic structures occurring in the wing of the pigeon is given by Mr Macgillivray in his admirable “History of British Birds,” pages 37 and 38. Lond. 1837.

^{page 399 note *} In this diagram I have represented the wing by a straight rigid rod. The natural wing, however, is curved, flexible, and elastic. It likewise moves in curves, the curves being most marked towards the end of the down and up strokes, as shown at m, n, o, p. The curves, which are double figure of 8 curves, are obliterated towards the middle of the strokes (r, a). This remark holds true of all natural wings, and of all artificial wings properly constructed. The curves and the reversal thereof are necessary to give continuity of motion to the wing during its vibrations, and what is not less important, to enable the wing alternately to seize and dismiss the air.

^{page 404 note *} On Aërial Locomotion, by Wenham, F. H., Esq., World of Science for June, 1867Google Scholar.

^{page 404 note †} Flying Machines, by Breary, F. W., Esq., Popular Science Review for January, 1869Google Scholar.

^{page 405 note *} Mr Stringfellow stated that his machine occasionally left the wire, and was sustained by its superimposed planes alone.

^{page 405 note †} Mr Henson designed his aërostat in 1843.

^{page 405 note ‡} Astra Castra, by Turner, Hatton, Esq. London, 1865, pages 311 and 312Google Scholar.

^{page 407 note *} Report on the First Exhibition of the Aëronautical Society of Great Britain, held at the Crystal Palace, London, in June 1868, page 10.

^{page 407 note †} Mons. Nadar, in a paper written in 1863, enters very fully into the subject of artificial flight, as performed by the aid of the screw. Liberal extracts are given from Nadar's paper in “Astra Castra,” by CaptainTurner, Hatton. London, 1865, page 340Google Scholar. To Turner's handsome volume the reader is referred for much curious and interesting information on the subject of Aërostation.

^{page 409 note *} Borelli, . De Motu Animalium. Sm. 4to. 2 vols. Romæ 1680Google Scholar.

^{page 409 note †} “De Motu Animalium,” Lugduni Batavorum apud Petrum Vander. Anno MDCLXXXV. Tab. XIII. figure 2. (New edition.)Google Scholar

^{page 409 note ‡} Revue des Cours Scientifiques de la France et de l'Etranger. Mars 1869Google Scholar.

^{page 411 note *} It is clear from the above that Borelli did not know that the wings of birds strike forwards as well as downwards during the down stroke. He seems to have been equally ignorant of the fact that the wings of insects vibrate in a more or less horizontal direction.

^{page 413 note *} Reign of Law “Good Words,” February 1865, p. 128.

^{page 413 note †} History of British Birds. Lond. 1837, p. 43Google Scholar.

^{page 413 note ‡} Méchanisme du vol chez les insectes. Comment se fait la propulsion, by Professor E. J. Marey. Revue des Cours Scientifiques de la France et de l'Etranger for 20th March 1869, p. 254.

^{page 415 note *} Revue des Cours Scientifiques de la France et de l'Etranger. 8vo. March 20, 1869.

^{page 419 note *} Compare Marey's description with that of Borelli, a translation of which I subjoin. “Let a bird be suspended in the air with its wings expanded, and first let the under surfaces (of the wings) be struck by the air ascending perpendicularly to the horizon with such a force that the bird gliding down is prevented from falling : I say that it (the bird) will be impelled with a horizontal forward motion, because the two osseous rods of the wings are able, owing to the strength of the muscles, and because of their hardness, to resist the force of the air, and therefore to retain the same form (literally extent, expansion), but the total breadth of the fan of each wing yields to the impulse of the air when the flexible feathers are permitted to rotate around the “manubria” or osseous axis, and hence it is necessary that the extremities of the wings approximate each other : wherefore the wings acquire the form of a wedge whose point is directed towards the tail of the bird, but whose surfaces are compressed on either side by the ascending air in such a manner that it is driven out in the direction of its base. Since, however, the wedge formed by the wings cannot move forward unless it carry the body of the bird along with it, it is evident that it (the wedge) gives place to the air impelling it, and therefore the bird flies forward in a horizontal direction. But now let the substratum of still air be struck by the fans (feathers) of the wings with a motion perpendicular to the horizon. Since the fans and sails of the wings acquire the form of a wedge, the point of which is turned towards the tail (of the bird), and since they suffer the same force and compression from the air, whether the vibrating wings strike the undisturbed air beneath, or whether, on the other hand, the expanded wings (the osseous axis remaining rigid; receive the percussion of the ascending air; in either case the flexible feathers yield to the impulse, and hence approximate each other, and thus the bird moves in a forward direction.”—De Motu Animalium, pars prima, prop. 196, 1685.

^{page 421 note *} Fig. 57 represents a longitudinal section of bamboo reed 10 feet long, and 1 inch wide.

^{page 421 note †} Fig. 58. The appearance presented by the same reed when made to vibrate by the hand. The reed vibrates on either side of a given line (x x), and appears as if in two places at the same time, viz., c and f, g and d, e and h. It is thus during its vibration thrown into figures of 8 or opposite curves.

^{page 421 note ‡} Fig. 59. The appearance presented by the same reed when made to vibrate more rapidly. In this case the waves made by the reed are less in size, but more numerous than in fig. 58. The reed vibrates alternately on either side of the line x x, being now at i now at m, now at n now at j, now at k now at o, now at p now at l. This reed, when made to vibrate by the hand, has no dead points, a circumstance due to the fact that no two parts of it reverse or change their curves at precisely the same instant. It is because of this curious reciprocating motion that the wing can seize and disengage itself from the air with such rapidity.

^{page 421 note §} Fig. 60. The same reed with a flexible elastic curtain or fringe added to it. The curtain consists of tapering whalebone rods covered with a thin layer of india-rubber, a b anterior margin of wing. c d posterior ditto.

^{page 421 note ∥} Fig. 61 gives the appearance presented by the artificial wing (fig. 60) when made to vibrate by the hand. It is thrown into longitudinal and transverse waves. The longitudinal waves are represented by the arrows c d e, and the transverse by the arrows f g h. A wing constructed on this principle gives a continuous elevating and propelling power. It developes figure of 8 curves during its action in longitudinal, transverse, and oblique directions. It literally floats upon the air. It has no dead points—is vibrated with amazingly little power, and has apparently no slip. It can fly in an upward, downward, or horizontal direction by merely altering its angle of inclination to the horizon. It must be applied to the air by an irregular motion—the movement being most sudden and vigorous always at the beginning of the down stroke.

^{page 423 note *} Fig. 62. Elastic spiral wing, which twists and untwists during its action, to form a mobile helix or screw. This wing is made to vibrate by a direct piston action, and by a slight adjustment can be propelled vertically, horizontally, or at any degree of obliquity.

a, b, Anterior margin of wing, to which the neuræ or ribs are affixed. c, d, Posterior margin of wing crossing anterior one. x, Ball and socket joint at root of wing, the wing being attached to the side of the cylinder by the socket. t, Cylinder. r, r, Piston, with cross heads (w, w) and piston head (s). o, o, Stuffing boxes, e, f, Driving chains. m, Superior elastic band, which assists in elevating the wing. n, Inferior elastic band, which antagonises m. The alternate stretching of the superior and inferior elastic bands contributes to the continuous play of the wing, by preventing dead points at the end of the down and up strokes.

^{page 424 note *} Fig. 63. Artificial Wing with Driving Apparatus.

a b, Strong elastic rod, which tapers towards the tip of the wing.

d, e, f, g, h, i, j, k, Tapering curved reeds, which ran obliquely from the anterior to the posterior margin of the wing, and when radiate towards the tip.

m, Similar curved reeds, which run still more obliquely.

a, n, o, p, q, Tapering curved reeds, which run from the anterior margin of the wing, and at right angles to it. These support the two sets of oblique reeds, and give additional strength to the anterior margin.

x, Ball and socket joint, by which the root of the wing is attached to the cylinder.

s, Steam cylinder.

r, Piston, with cross bar, with which driving gear (t) is connected by ball and socket joint (l), and by a hinge joint (m). The hinge joint is mounted on a tube, through which the root of the wing passes, and within which it can rotate in the direction of its length (long axis). The hinge joint and the tube on which it is mounted can be moved out and in upon the root of the wing, and fixed by the aid of pins. By this means the range of the wing, i.e., the length of the stroke, can be increased or diminished. The driving gear is arranged on a similar principle. Thus, by causing the portion marked u to move within the tube (t) in an upward direction, the wing vibrates on a higher level than natural. If, on the other hand, the portion marked u be moved in a downward direction, the wing vibrates on a lower level. The range of the wing and its are of vibration are thus easily regulated.

1, 2, Cross bar attached to steam chest (7) and to cylinder (s). To this anterior (v) and posterior (w) elastic bands are affixed. Those elastic bands (anterior and posterior) are bound to the anterior and posterior portions of the ring c; y, superior elastic band; 2, inferior ditto.

3, 4, Steel springs running at right angles to each other, and attached respectively to the cross bar and the root of the wing anteriorly. They come in contact when the wing descends, and prevent the anterior margin of the wing from dipping, i.e., from diving downwards during the down stroke. This result is also secured by inserting the superior elastic band (y) into the upper and anterior portion of the ring c. Indeed, by employing a cross bar or lever, similar to that marked 4, in place of the ring c, the amount of rotation of the posterior margin round the anterior one can be regulated both during the down and up strokes. If the superior elastic band (y) be moved towards the tip of the lever, the degree of rotation is increased; if it be moved towards the root of the lever, it is diminished.

5. Rod fixed to posterior of cylinder, and bearing cross bar (6), to which the superior elastic band (y) is attached.

Note.—In the present arrangement the steam chest (7) and valve occupy the centre of the cylinder posteriorly, the valve being opened and closed by the aid of an idle rod (furnished with two kickers), which passes through a loop projecting from the piston anteriorly. The idle rod and kickers move a small lever (9), which in turn moves the spindle (8), to which the steam valve is attached. The cylinder is fixed to the top of the boiler, and the ports for the admission of steam to the cylinder are unequal in size, the upper port being larger than the under one. Unequal quantities of steam are thus admitted to the top and bottom of the cylinder respectively, the greater quantity admitted to the top causing the wing to descend much more quickly than it ascends. From the above figure it will be seen that the movements of the wing are communicated directly from the piston, a great saving in weight and power being thus effected.

^{page 425 note *} Fig. 64. x, Ball and socket joint at root of wing, a, b, Anterior margin of wing, c, d, Posterior margin of wing. i, Portion of wing composed of one layer of flexible material. h, Portion of wing composed of two layers. g, Portion of wing composed of three layers. f, Portion of wing composed of four layers. e, Portion of wing composed of five layers.

^{page 425 note †} Fig. 65. Flexible valvular wing with India-rubber springs attached to its root.

a, b, Anterior margin of wing, tapering and elastic. c, d, Posterior margin of wing, elastic. f, f, f, Segments which open during the up stroke and close during the down, after the manner of valves. These are very narrow, and open and close instantly, g, g, g, The same segments magnified. x, Universal joint. m, Superior elastic band. n, Ditto inferior. o, Ditto anterior. p, g, Ditto oblique. r, Ring into which the elastic bands are fixed.

^{page 429 note *} Figures 67 and 68. Wing made to close or fold during the up stroke, and to open out or expand during the down stroke.

At fig. 67, the wing is represented as folded upon itself, x Universal joint at root of wing. a Proximal portion of wing. d Central portion of wing. g Distal portion of wing. b Joint uniting proximal and central portions of wing. e Joint uniting central and distal portions. h i, j k Sheet of elastic substance which when contracted as represented, tends to approximate the proximal (a), central (d), and distal (g), portions of wing. l, m, n A cord or wire fixed at f and running through an aperture at c. If this cord be rendered taught (provided the root of the wing (x) is fixed in its socket), it causes the proximal (a), central (d), and distal (g) portions of the wing suddenly to dart out and arrange themselves in a nearly straight line as shown at a, d, g of fig. 68.

At fig. 68 the wing is represented as fully extended or spread out. The lettering is the same as in fig. 67. o, p, q Ribs or stays of the wing which support the covering or curtain.

^{page 430 note *} Fig. 69. Wing which folds upon itself during the up stroke, and expands during the down one, made to vibrate by a direct piston action. At A the wing is fully expanded and in the act of commencing the down stroke. At B the wing is at mid stroke and very slightly folded. At C the wing is fully folded, and ready to begin the up stroke. It is thus that the wing acts as a long lever at the beginning of the down stroke, and a short one at the beginning of the up one. Compare with figs. 18 and 19, Plate XIV., and also with figs. 9, 10, and 11, Plate XII. The lettering of the wing in the present fig. is the same as in fig. 68, p. 429.

x Universal joint at root of wing received into cup-shaped cavity (v) of cylinder (t).

a Proximal, d central, and g distal portions of wing.

b, e, Joints which unite the three portions of the wing to each other.

f, q, Points to which the cord or wire of wing is fixed.

c, Aperture through which cord or wire of wing glides as the wing ascends and descends. When the piston ascends it elevates the wing by its gearing y z. It also renders the cord l n taught, the cord in its turn extending the wing (A) and the elastic substance h k. When the piston descends to mid stroke the wing is very slightly folded (B) and the cord l′ n′ somewhat relaxed. When the piston has quite descended the cord l″ n″ is very much relaxed, and as a consequence the elastic substance extending between the different portions of the wing has contracted, the wing being thereby folded upon itself (C). The elastic substance may be dispensed with, if a strong elastic cord be employed instead of the non-elastic one l, n. If two cords be fixed to two points on the cylinder as at p and q, and the one cord be passed on the upper surface of the wing, and the remaining one on the under surface, the wing will be under control during the whole of the down and up strokes, the one cord extending the wing, the other flexing it.

t, t, Cylinder. o, o, Stuffing boxes. r r, Piston. w, w, Cross heads for driving gear. y z Driving gear. s Piston head. v, Cup-shaped cavity for receiving root of wing.

^{page 432 note *} The human wrist is so formed that if a wing be held in the hand at an upward angle of 45°, the hand can apply it to the air in a vertical or horizontal direction without difficulty. This arises from the power which the hand has of moving in an upward and downward direction, and from side to side with equal facility. The hand can also rotate on its long axis, so that it virtually represents all the movements of the wing at its root.

^{page 435 note *} Fig. 70. Stroke of artificial wave wing from right to left. x, x′, Horizon. m, n, o, Wave track described by wing from right to left. p, Angle made by wing at beginning of stroke. q, Ditto, made at middle of stroke. b, Ditto, towards end of stroke. c, Wing in the act of reversing; at this stage the wing makes an angle of 90° with the horizon, and its speed is less than at any other part of its course. d, Wing reversed, and in the act of darting up to u, to begin the stroke from left to right (vide u of fig. 71).

^{page 435 note †} Fig. 71. Stroke of artificial wave wing from left to right. x, x′, Horizon. u, v, w, Wave track described by wing from left to right. t, Angle made by the wing with the horizon at beginning of stroke. y, Ditto, at middle of stroke. z, Ditto, towards end of stroke. r, Wing in the act of reversing; at this stage the wing makes an angle of 90° with the horizon, and its speed is less than at any other part of its course. s, Wing reversed, and in the act of darting up to m, to begin the stroke from right to left (vide m of fig. 70).

^{page 437 note *} The artificial currents produced by the wing during its descent may be readily seen by partially filling a chamber with, steam, smoke, or some impalpable white powder, and causing the wing to descend in its midst. By a little practice, the eye will not fail to detect the currents represented at d, e, f, g, h, i, l, m, n, o, p, q, r of fig. 72, p. 438.

^{page 440 note *} Fig. 72. Aerial wave screw whose blades are slightly twisted upon themselves (a b, c d; e f, g h), so that those portions nearest the root (d h) make a greater angle with the horizon than those parts nearer the tip (b f). The angle is thus adjusted to the speed attained by the different portions of the screw. The angle admits of further adjustment by means of the steel springs z, s, these exercising a restraining, and to a certain extent a regulating influence which effectually prevents shock.

It will be at once perceived from this figure that the portions of the screw marked m and n travel at a much lower speed than those portions marked o and p, and these again more slowly than those marked q and r. As however the angle which a wing or a portion of a wing, as I have pointed out, varies to accommodate itself to the speed attained by the wing, or a portion thereof, it follows, that to make the wave screw mechanically perfect, the angles made by its several portions must be accurately adapted to the travel of its several parts as indicated above.

x, Vertical tube for receiving driving shaft. v, w, Sockets in which the roots of the blades of the screw rotate, the degree of rotation being limited by steel springs z, s. a b, e f, Tapering elastic reeds forming anterior or thick margins of blades of screw. d e, h g, Posterior or thin elastic margins of blades of screw. m n, o p, q r, Radii formed by the different portions of the blades of the screw when in operation. The arrows indicate the direction of travel.