To this list of Hartings we will add another which we have prepared by the same method (p. 225). All the experiments have been made on birds killed by the gun, and a few instants after death. We have taken the surface of the two wings instead of only one, as Hartings had done; this modification, which appeared necessary, is the principal cause of the difference which the reader will find between our numbers and those of the Dutch physiologist. To compare the two tables, it will be necessary to multiply by 2 the number obtained by Va Hartings as the expression of the ratio

i/p

The variations that we find in the ratio of the weight of the body to the surface of the wings in different species of birds, depends in a great degree on the form of the wings. In fact, it is not immaterial whether the surface which strikes the air has its maximum near the body or near the extremity; these two points have very different velocities. For an equal extent of surface the resistance will be greater at the point of the wing than at its base. It follows from this, that two birds of unequal surface of wing may find in the air an equal resistance, provided that these surfaces are differently arranged.

The weight of the pectoral muscles is, on the contrary, in a simple ratio to the total weight of the bird, and notwith

standing variations which correspond with the different aptitudes for flight with which each species is endowed, we find that it is about one-sixth of the whole weight in the greater number of birds.

In conclusion, each animal which sustains itself in the air must develop work proportionate to its weight; it ought, for this purpose, to possess muscular mass in proportion to this weight; for, as we have already seen, if the actions performed by the muscles of birds are always of the same nature, these actions and the work which they perform will be in proportion to the mass of the muscles.

But how is it that wings whose surfaces vary as to the square of their linear dimensions are sufficient to move the weights of birds which vary in the ratio of the cubes of these dimensions?

It can be proved that, if the strokes of the wing were as frequent in large as in small birds, each stroke would have a velocity whose value would increase with the size of the bird; and as the resistance of the air increases for each element of the surface of the wing, according to the square of the velocity of that organ, a considerable advantage would result to the bird of large size, as to the work produced upon the air.

Hence it follows, that it would not be necessary for large birds to give such frequent strokes of the wing in order to sustain themselves as would be required for those of smaller size.

Observers have not, hitherto, been able to determine very accurately the number of the strokes of the wing, in order to ascertain whether their frequency is in an exact inverse ratio to the size of birds; but it is easy to see that the number of strokes varies in birds of different size in a proportion of this kind.

CHAPTER IV.

OF THE MOVEMENTS OF THE WING OF THE BIRD
DURING FLIGHT.

Frequency of the movements of the wing-Relative durations of its rise and fall-Electrical determination-Myographical determination. Trajectory of the bird's wing during flight-Construction of the instru

ments which register this movement-Experiment-Elliptical figure of the trajectory of the point of the wing.

In the general remarks on the form of the bird, and on the deductions to be drawn from it, the reader must have seen that many hypotheses await experimental demonstration. For this reason, we have been anxious to apply to the flights of

the bird the method which has enabled us to analyse the other modes of locomotion.

Frequency of the strokes of the wing.-The graphic method which enabled us so easily to determine the frequency of the strokes of the insect's wing cannot be employed under the same conditions when we experiment on the bird. It will be necessary to transmit signals between the bird as it flies and the registering apparatus. We have here to deal with a problem similar to that which we solved with respect to terrestrial locomotion, when we registered the number and the relative duration of the pressures of the feet upon the ground. We must now estimate the duration of the impacts of the wing upon the air, and the time which it occupies in its rising motion.

Electrical method.-We made use at first of the electric telegraph. The experiments consist in placing on the extremity of the wing a kind of apparatus which breaks or closes an electric circuit at each of the alternate movements which it is induced to make. In this circuit is placed an electromagnetic arrangement which writes upon a revolving cylinder. Figure 94 shows this mode of telegraphy applied to the study of a pigeon's flight, simultaneously with the transmission of signals of another kind, to be hereafter described. In this figure the two conducting wires are separated from each other.

The writing point will trace a wavy line, the elevations and depressions of which will correspond with each change in the direction of the movement of the wing. In order that the bird may fly as freely as possible, a thin flexible cable, containing two conducting wires, establishes a communication between the bird and the telegraphic tracing point. The two ends of the wires are fastened to a very small light instrument which acts like a valve under the influence of the resistance of the air. When the wing rises, the valve opens, the current is broken, and the line of the telegraphic tracing rises. When the wing descends, the valve closes, the current closes at the same time, and the tracing made by the telegraph is lowered. This instrument, when applied to different kinds of birds, enables us to ascertain the frequency peculiar to the movements of each. The number of species which we have been

able to study is very small as yet; the following are the results obtained :

The frequency of the strokes of the wing varies also, according as the bird is first starting, in full flight, or at the end of its flight. Some birds, as we know, keep their wings perfectly still for a time; they glide upon the air, making use of the velocity already acquired.

Relative duration of the depression and elevation of the wing.— Contrary to the opinion entertained by some writers, the duration of the depression of the wing is usually longer than that of its rise. The inequality of these two periods is more distinctly seen in birds whose wings have a large surface, and which beat slowly. Thus, while the durations are almost equal in the duck, whose wings are very narrow, they are unequal in the pigeon, and still more so in the buzzard. The following are the results of our experiments:

It is more difficult than would have been expected, to determine the precise instant when the direction of the line traced by the telegraph changes. The periods during which the soft iron is first attracted and then set free, have an appreciable duration when the blackened cylinder turns with sufficient rapidity to enable us to measure the rapid movements which are the subjects of this inquiry. The inflections of the line traced by the telegraph then become curves, the precise commencement