an indefinite number of perpendicular lines, it follows that the artist may choose in the duration of any pace, in any kind of locomotion, an indefinite number of different attitudes. Suppose him to have made his choice, and that he wishes to represent in the kind of pace (fig. 68), the instant which is marked by the vertical line 7, the notation will show him that the right fore-foot has just been placed upon the ground, that the left fore-foot is therefore beginning to rise, that the right hind-foot is almost at the end of its pressure on the ground, and that the left hind-foot is near the end of its rise. All that is necessary, in order to represent the animal exactly, is to know the attitude of each limb at the different instants of its rise, fall, or pressure, which is a comparatively easy matter. But the artist, guided by this method, will thus inevitably avoid altogether those false attitudes which often cause representations of horses to be so utterly unnatural.

FIGURES ARRANGED TO SHOW THE PACES OF THE HORSE.

Mons. Mathias Duval has undertaken to make, in order to illustrate the locomotion of the horse, a series of pictures, which, seen by means of the zootrope, represent the animal as if in motion in the various kinds of paces. This ingenious physiologist formed the idea of reproducing in an animated form, as it were, that which notation has done for the rhythm of the movements. The following is the arrangement which he employed. He first drew a series of figures of the horse taken at different instants of an ambling pace. Sixteen successive figures enabled him to represent the series of positions which each limb successively assumes in a pace belonging to this kind of locomotion. This band of paper, when placed in the instrument, gives to the eye the appearance of an ambling horse in actual motion.

We have said that all the walking paces may be considered as derived from the amble, with a more or less anticipation of the action of the hind limbs. Mons. Duval has realised this

in his pictures in the following manner. Each plate, on which has been drawn the series of pictures of the ambling horse, is formed of two sheets of paper placed the one on the other. The upper one has in it a number of slits or openings,

N

sheet, and the other The hind quarters,

so that each horse is drawn half on this half on that which is placed beneath. for example, having been drawn on the upper sheet, the fore quarters are drawn on the under sheet, and are visible through the portion cut out of the upper sheet. Let us suppose that we cause the upper paper to slide as far as the interval which separates two figures of the horse, we shall have a series of images in which the fore limbs will fall back a certain distance towards the hind limbs. We shall thus represent, under the form of pictures, what is obtained under the form of notation, by slipping the two lower slides of the notation rule one degree. And as this displacement to the distance of one degree for each of the movements of the hinder limbs gives the notation of the broken amble, we shall obtain, in the figures thus drawn, the series of the successive positions of the paces of the broken amble. If the paper be made to slip a greater number of degrees, we shall have the series of attitudes of the horse at his walking pace. A still greater displacement will give the attitudes of the trot.

In all these cases, these figures, when placed in the instrument, make the illusion complete, and show us a horse which ambles, walks, or trots, as the case may be. Then, if we regulate the swiftness of the rotation given to the instrument, we render the movements which the animal seems to execute more or less rapid, which will permit the inexperienced observer to follow the series of positions of each kind of pace, and soon enable him to distinguish with the eye a series of movements in the living animal which appear at first sight to be in absolute confusion.

We hope that these plates, though still somewhat defective, will soon be sufficiently perfect to be of real use to those who are engaged in the artistic representation of the horse.

After these studies of terrestrial locomotion, we ought to explain the mechanism of aquatic locomotion. Some recent experiments of Mons. Ciotti have thrown great light on the propulsive action of the tails of fishes; not that they have overthrown the theory held ever since the time of Borelli, concerning the mechanism of swimming, but they have approached the question in another manner, that of the synthetic

reproduction of this phenomenon. This method will certainly permit us to determine, with a precision hitherto unknown, both the motive work and resistant work in aquatic locomotion. It will, therefore, be advisable to wait for the results of experiments which are now being made, and which will be of equal service both to mechanicians and to physiologists.

BOOK THE THIRD.

AERIAL LOCOMOTION.

CHAPTER I.

OF THE FLIGHT OF INSECTS.

Frequency of the strokes of the wing of insects during flight; acoustic determination; graphic determination-Influences which modify the frequency of the movements of the wing-Synchronism of the action of the two wings-Optical determination of the movements of the wing; its trajectory; changes in the plane of the wing; direction of the movement of the wing.

IN terrestrial locomotion we have been able to measure by experiment the pressure of the feet on the ground, and hence we have deduced the intensity of the re-actions on the body of the animal. These two forces were easily ascertained by direct measurement. In the problem which is now to occupy us, the conditions are very different. The air gives a certain resistance to the wings which strike upon it, but it is a resistance every instant yielding, for it is only in proportion to the rapidity with which it is displaced, that the air resists the impulse of the wing. When we study the phenomena of flight, it is therefore necessary to know the movement of the wing in all the phases of its speed, in order to estimate the resistance which the air presents to that organ. We will propound in the following order the questions which must be resolved. 1. What is the frequency of the movements of the wing of insects ?

2. What are the successive positions which the wing occupies during its complete revolution?

3. How is the motive force which sustains and transports the body of the animal developed ?

1. Frequency of the movements of the wing of insects.—The frequency of the movements of the wing varies according to species. The ear perceives an acute sound during the flight of mosquitos and certain flies; there is a graver sound during the flight of the bee and the drone fly; still deeper in the macroglossa and the sphingidæ. As to the other lepidoptera, they have, in general, a silent flight on account of the few strokes which they give with their wings.

Many naturalists have endeavoured to determine the frequency of the strokes of the wing by the musical note produced by the animal as it flies. But in order that this determination should be thoroughly reliable, it must be clearly established that the sound produced by the wing depends exclusively on the frequency of its movements, in the same manner as the sound of a tuning-fork results from the frequency of its vibrations. But opinions differ on this subject; certain writers have thought that during flight there is a movement of the air through the spiracles of insects, and that the sound which is heard depends on these alternate movements.

Without giving our adherence to this opinion, which seems to be contradicted by many facts, we think that the acoustic method is insufficient to furnish an estimate of the frequency with which the wing moves. The reason which would induce us not to employ this method, is that the musical note produced by the flying insect is varied by other influences besides the changes in the strokes of the wing.

When we observe the buzzing of an insect flying with a uniform rapidity, we perceive that the tone does not continue constantly the same. As the insect approaches the ear, the tone rises; it sinks as it goes farther from us. Something of an analogous kind happens when we cause a vibrating tuning-fork to pass before the ear; the note at first becomes more shrill and then more grave, and the difference may attain to a quarter or even to half a tone. We must, therefore, take care that the insect on which we experiment should be always at the same distance from the observer. This disturbing phenomenon, however, presents no real difficulty of