which they more readily furnish; namely, the number of the revolutions of the wing, the greater or less regularity of these movements, and the equality or inequality of each of them.

Confining the question within these limits, experiment shows that the strokes of the bird's wing differ in amplitude and in frequency from one moment to another as they fly. When they first start, the strokes are rather fewer, but much more energetic; they reach, after two or three strokes of the wing, a rhythm almost regular, which they lose again when they are about to settle (fig. 96).

TRAJECTORY OF THE WING OF THE
BIRD DURING FLIGHT.

We have seen, when treating of the mechanism of insect flight, that the fundamental experiment was that which revealed to us the course of the point of the wing throughout each of its revolutions. Our knowledge of the mechanism of flight naturally flowed, if we may so say, from this first notion.

The same determination is equally necessary for the flight of birds; but the optical method is unsuitable for this purpose. In fact, the movement of the bird's wing, although too rapid to be appreciable by the eye, is not sufficiently so to furnish such a persistent impression on the retina as to show its whole course.

obtained on a cylinder whose rotation was not very rapid, which allowed us to collect a great number of movements in a small FIG. 96.-Showing the differences of amplitude and frequency of the strokes of a pigeon's wing, during a flight of 15 metres in length. To the left of the figure, we see great movements which mark the beginning of its flight. This tracing has been

space.

The graphic method, with its transmission of signals, which we have hitherto employed, only furnishes the expression of movements which take place in a straight line, such as the contraction or lengthening of a muscle, the vertical and horizontal oscillations of the body during the act of walking, &c. It is only by combining this rectilinear movement with the uniform advance of the smoked surface that receives the tracing, that we obtain the expression of the velocity with which the movement at each instant is effected.

The action of the wing during flight does not consist merely of alternate elevations and depressions. We have only to look at a bird as it flies over our head to ascertain that the wing is carried also forward and backward at each stroke. From this double action must result a curve which it is necessary to describe.

It can be geometrically shown that every plane figure, that is to say, every figure susceptible of being described upon a plane surface, can be produced by the rectangular combination of two rectilinear movements. The tracings obtained by Koenig by arming with a style Wheatstone's vibrating rods, and the luminous figures of musical chords which Lissajous produced by the reflection of a pencil of light upon two mirrors vibrating perpendicularly to each other, are wellknown examples of the formation of a plane figure by means of two rectilinear movements at right angles to each other.

Thus, if we can transmit at the same time the movements of elevation and depression executed by the wing of the bird, as well as those which the organ makes forwards and backwards; then, supposing that a tracing point can receive simultaneously the impulse of these two movements at right angles to each other, this point will describe on the paper the exact tracing of the movements of the bird's wing.

We have endeavoured first to construct an instrument which would thus transmit to a distance any movement whatever, and register it on a plane surface, without attending to the method by which this machine, which may be more or less heavy, might be adapted to the body of the bird. Fig. 97 represents our first experimental instrument, the description of which is indispensable in order to enable our readers to

understand the construction of the machine which we finally employed.

On two solid feet carrying vertical supports, we placed two horizontal arms parallel to each other. These were two aluminium levers, which, by means of the apparatus we are about to describe, will both execute the same movements. Each of these levers is mounted on a Cardan joint, that is to say, a universal joint which allows every kind of movement; so that each lever can be carried upwards, downwards, to the right or the left; it can describe with its point the base of a cone of which the Cardan forms the apex; in fact it will execute any kind of movement which the experimenter may please to give it.

It was requisite to effect the transmission of the movements of one of these levers to the other, and that at a distance of ten or fifteen metres. This is done by a method with which the reader is already acquainted-the employment of air-drums and tubes.

The lever, which in fig. 97 is seen to the left hand, is fastened by a vertical metallic wire to the membrane of a drum placed underneath it. In the vertical movements of the lever, the membrane of the drum, alternately depressed and raised, will produce a current of air, which will be transmitted by a long air-tube to the membrane of a similar drum belonging to the apparatus on the right hand. The second drum, placed above the lever which corresponds with it, and is fastened to it, will faithfully transmit all the vertical movements which have been given to drum No. 1 (that on the left). The motion of the two levers will be in the same direction, on account of the inversion of the position of the drums.

Let us suppose that we lower the lever No. 1; we compress the membrane of the drum beneath it; a current of air is produced which raises the membrane of the second drum, and consequently lowers lever No. 2. On the contrary, the elevation of lever No. 1 will produce an inward current of air, which will raise the membrane and the lever of No. 2.

Proceeding in the same manner for the transmission of movements in the horizontal plane, we place to the right of

FIG. 97.-Apparatus intended to transmit to a registering lever at a distance all the movements that are given to another lever.

one of the levers and to the left of the others, a drum whose membrane, situated in the vertical plane, acts in a lateral direction; the transmission of these movements is made by a special tube, as in the case of the vertical movements.

The apparatus having been thus constructed, if we take in our fingers the extremity of one of the levers, and give it any motion whatever, we shall see the other lever repeat it with perfect fidelity.

All the difference consists in a slight diminution of the amplitude of the movements in the second lever. This is because the air contained in each of the systems of tubes and drums is slightly compressed, and consequently does not transmit completely the movement which it receives. It would be easy to remedy this inconvenience, if it were found to be one, by giving to the receiving apparatus a greater sensibility, which might be effected by placing the Cardan joint a little nearer the point where the movement is transmitted to the lever of the second instrument. But it is better not to seek to amplify the movements too much when we wish to register them by tracings, since we then augment the friction, and diminish the force by which it must be overcome.

After having ascertained that the transmission of any movement whatever is effected in a satisfactory manner by this apparatus, we sought for a means of tracing this movement on a plane surface. The difficulty which occurred in the application of the graphic method to the study of the movement of the insect's wing, again presents itself here; but in this case there are no means of avoiding it by taking only partial tracings.

The point of the lever No. 2 describes in space a spherical figure incapable of becoming tangential, except in a single point, to the smoked surface which is to receive the tracing. Consequently, it has been necessary to register the projection of this figure on a plane surface, and to arrange the lever in such a manner that it may lengthen or shorten itself as required, in order to keep always in contact with the smoked glass. This result was obtained by means of a spring which served as a writing point.

Fig. 98 shows the spring in question, at the extremity of a lever. It is wide at the base, in order to resist any tendency