bodies of said creatures are fixed, describe figure-of-8 tracks in
space—the figure-of-8 tracks, when the bodies are released and
advancing as in rapid flight, being opened out and converted
into waved tracks.
It may be well to explain here that a claim has been set up by his admirers for the celebrated artist, architect and engineer, Leonardo da Vinci, to be regarded as the discoverer of the principles and practice of flight (see Theodore Andrea Cook, Spirals in Nature and Art, 1903). The claim is, however, unwarranted; Leonardo’s chief work on flight, bearing the title Codice sul Volo degli Uccelli e Varie Altre Materie, written in 1505, consists of a short manuscript of twenty-seven small quarto pages, with simple sketch illustrations interspersed in the text. In addition he makes occasional references to flight in his other manuscripts, which are also illustrated. In none of Leonardo’s manuscripts, however, and in none of his figures, is the slightest hint given of his having any knowledge of the spiral movements made by the wing in flight or of the spiral structure of the wing itself. It is claimed that Leonardo knew the direction of the stroke of the wing, as revealed by recent researches and proved by modern instantaneous photography. As a matter of fact, Leonardo gives a wholly inaccurate account of the direction of the stroke of the wing. He states that the wing during the down stroke strikes downwards and backwards, whereas in reality it strikes downwards and forwards. In speaking of artificial flight Leonardo says: “The wings have to row downwards and backwards to support the machine on high, so that it moves forward.” In speaking of natural flight he remarks: “If in its descent the bird rows backwards with its wings the bird will move rapidly; this happens because the wings strike the air which successively runs behind the bird to fill the void whence it comes.” There is nothing in Leonardo’s writings to show that he knew either the anatomy or physiology of the wing in the modern sense.
Pettigrew’s discovery of the figure-of-8 and waved movements made by the wing in stationary and progressive flight was confirmed some two years after it was made by Prof. E. J. Marey of Paris[1] by the aid of the “sphygmograph.”[2] The movements in question are now regarded as fundamental, from the fact that they are alike essential to natural and artificial flight.
The following is Pettigrew’s description of wings and wing movements published in 1867:—
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| Fig. 10.—Right Wing of the Beetle (Goliathus micans) when at rest; seen from above. |
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| Fig. 11.—Right Wing of the Beetle (Goliathus micans) when in motion; seen from behind. This figure shows how the wing twists and untwists when in action, and how it forms a true screw. |
“The wings of insects and birds are, as a rule, more or less triangular in shape, the base of the triangle being directed towards the body, its sides anteriorly and posteriorly. They are also conical on section from within outwards and from before backwards, this shape converting the pinions into delicately graduated instruments balanced with the utmost nicety to satisfy the requirements of the muscular system on the one hand and the resistance and resiliency of the air on the other. While all wings are graduated as explained, innumerable varieties occur as to their general contour, some being falcated or scythe-like, others oblong, others rounded or circular, some lanceolate and some linear. The wings of insects may consist either of one or two pairs—the anterior or upper pair, when two are present, being in some instances greatly modified and presenting a corneous condition. They are then known as elytra, from the Gr. ἔλυτρον, a sheath. Both pairs are composed of a duplicature of the integument, or investing membrane, and are strengthened in various directions by a system of hollow, horny tubes, known to entomologists as the neurae or nervures. These nervures taper towards the extremity of the wing, and are strongest towards its root and anterior margin, where they supply the place of the arm in birds and bats. The neurae are arranged at the axis of the wing after the manner of a fan or spiral stair—the anterior one occupying a higher position than that farther back, and so of the others. As this arrangement extends also to the margins, the wings are more or less twisted upon themselves and present a certain degree of convexity on their superior or upper surface, and a corresponding concavity on their inferior or under surface,—their free edges supplying those fine curves which act with such efficacy upon the air in obtaining the maximum of resistance and the minimum of displacement. As illustrative examples of the form of wings alluded to, those of the beetle, bee and fly may be cited—the pinions in those insects acting as helices, or twisted levers, and elevating weights much greater than the area of the wings would seem to warrant” (figs. 10 and 11).... “To confer on the wings the multiplicity of movements which they require, they are supplied with double hinge or compound joints, which enable them to move not only in an upward, downward, forward and backward direction, but also at various intermediate degrees of obliquity. An insect with wings thus hinged may, as far as steadiness of body is concerned, be not inaptly compared to a compass set upon gimbals, where the universality of motion in one direction ensures comparative fixedness in another.”... “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 when the sudden or effective stroke is being given, and gradually decreasing in an opposite direction during flexion, or when the wing is being more slowly recovered preparatory to making a second stroke. The effective stroke in insects, and this holds true also of birds, is therefore delivered downwards and forwards, and not, as the majority of writers believe, vertically, or even slightly backwards.... The wing in the insect is more flattened than in the bird; and advantage is taken on some occasions of this circumstance, particularly in heavy-bodied, small-winged, quick-flying insects, to reverse the pinion more or less completely during the down and up strokes.”... “This is effected in the following manner. The posterior margin of the wing is made to rotate, during the down stroke, in a direction from above downwards and from behind forwards—the anterior margin travelling in an opposite direction and reciprocating. The wing may thus be said to attack the air by a screwing movement from above. During the up or return stroke, on the other hand, the posterior margin rotates in a direction from below upwards and from before backwards, so that by a similar but reverse screwing motion the pinion attacks the air from beneath.”... “A figure-of-8, compressed laterally and placed obliquely with its long axis running from left to right of the spectator, represents the movements in question. The down and up strokes, as will be seen from this account, cross each other, the wing smiting the air during its descent from above, as in the bird and bat, and during its ascent from below as in the flying fish and boy’s kite” (fig. 12).
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| Fig. 12 shows the figure-of-8 made by the margins of the wing in extension (continuous line), and flexion (dotted line). As the tip of the wing is mid-way between its margins, a line between the continuous and dotted lines gives the figure-of-8 made by the tip. The arrows indicate the reversal of the planes of the wing, and show how the down and up strokes cross each other. |
... “The figure-of-8 action of the wing explains how an insect 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. Although the figure-of-8 represents with considerable fidelity the twisting of the wing upon its axis during extension and flexion, when the insect is playing its wings before an object, or still better when it is artificially fixed, it is otherwise when the down stroke is added and the insect is fairly on the wing and progressing rapidly. In this case the wing, in virtue of its being carried forward by the body in motion, describes an undulating or spiral course, as shown in fig. 13.”
... “The down and up strokes are compound movements—the termination of the down stroke embracing the beginning of the up stroke, and the termination of the up stroke including the beginning of the down stroke. This is necessary in order that the down and up strokes may glide into each other in such a manner as to prevent jerking and unnecessary retardation.”[3]...
- ↑ Revue des cours scientifiques de la France et de l’Étranger, 1869.
- ↑ The sphygmograph, as its name indicates, is a recording instrument. It consists of a smoked cylinder revolving by means of clock-work at a known speed, and a style or pen which inscribes its surface by scratching or brushing away the lampblack. The movements to be registered are transferred to the style or pen by one or more levers, and the pen in turn transfers them to the cylinder, where they appear as legible tracings. In registering the movements of the wings the tips and margins of the pinions were, by an ingenious modification, employed as the styles or pens. By this arrangement the different parts of the wings were made actually to record their own movements. As will be seen from this account, the figure-of-8 or wave theory of stationary and progressive flight has been made the subject of a rigorous experimentum crucis.
- ↑ This continuity of the down into the up stroke and the converse is greatly facilitated by the elastic ligaments at the root and in the substance of the wing. These assist in elevating, and, when necessary, in flexing and elevating it. They counteract in some measure what may be regarded as the dead weight of the wing, and are especially useful in giving it continuous play.
