when flying towards the tail with a horizontal motion like that of oars, but always bend them downwards, and so describe circles raised perpendicularly to the horizon.1

Besides, in boats the horizontal motion of the oars is easily made, and a perpendicular stroke on the water would be perfectly useless, inasmuch as their descent would be impeded by the density of the water. But in birds, such a horizontal motion (which indeed would rather hinder flight) would be absurd, since it would cause the ponderous bird to fall headlong to the earth; whereas it can only be suspended in the air by constant vibration of the wings perpendicular to the horizon. Nature was thus forced to show her marvellous skill in producing a motion which, by one and the same action, should suspend the bird in the air, and carry it forward in a horizontal direction. This is effected by striking the air below perpendicularly to the horizon, but with oblique strokes an action which is rendered possible only by the flexibility of the feathers, for the fans of the wings in the act of striking acquire the form of a wedge, by the forcing out of which the bird is necessarily moved forwards in a horizontal direction."

The points which Borelli endeavours to establish are these:

First, That the action of the wing is a wedge action.

Second, That the wing consists of two portions-a rigid anterior portion, and a non-rigid flexible portion. The rigid portion he represents in his artificial bird (fig. 113, p. 220) as consisting of a rod (er), the yielding portion of feathers (a o).

Third, That if the air strikes the under surface of the wing perpendicularly in a direction from below upwards, the flexible portion of the wing will yield in an upward direction, and form a wedge with its neighbour.

Fourth, Similarly and conversely, if the wing strikes the

1 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, and forwards as well as upwards during the up stroke. These points, as well as the twisting and untwisting figure-of-8 action of the wing, were first described by the author. Borelli seems to have been equally ignorant of the fact that the wings of insects vibrate in a more or less horizontal direction.

air perpendicularly from above, the posterior and flexible portion of the wing will yield and be forced in an upward direction.

Fifth, That this upward yielding of the posterior or flexible margin of the wing results in and necessitates a horizontal transference of the body of the bird.

Sixth, That to sustain a bird in the air the wings must strike vertically downwards, as this is the direction in which a heavy body, if left to itself, would fall.

Seventh, That to propel the bird in a horizontal direction, the wings must descend in a perpendicular direction, and the posterior or flexible portions of the wings yield in an upward direction, and in such a manner as virtually to communicate an oblique action to them.

Eighth, That the feathers of the wing are bent in an upward direction when the wing descends, the upward bending of the elastic feathers contributing to the horizontal travel of the body of the bird.

I have been careful to expound Borelli's views for several

reasons:

1st, Because the purely mechanical theory of the wing's action is clearly to be traced to him.

2d, Because his doctrines have remained unquestioned for nearly two centuries, and have been adopted by all the writers since his time, without, I regret to say in the majority of cases, any acknowledgment whatever.

3d, Because his views have been revived by the modern French school; and

4th, Because, in commenting upon and differing from Borelli, I will necessarily comment upon and differ from all his successors.

As to the Direction of the Stroke, yielding of the Wing, etc.The Duke of Argyll1 agrees with Borelli in believing that the wing invariably strikes perpendicularly downwards. His words are—“ Except for the purpose of arresting their flight birds can never strike except directly downwards; that is, against the opposing force of gravity." Professor Owen in his Comparative Anatomy, Mr. Macgillivray in his British Birds, Mr. Bishop in his article "Motion" in the Cyclopedia of Anatomy "Reign of Law"-Good Words, 1865.

and Physiology, and M. Liais "On the Flight of Birds and Insects" in the Annals of Natural History, all assert that the stroke is delivered downwards and more or less backwards.

To obtain an upward recoil, one would naturally suppose all that is required is a downward stroke, and to obtain an upward and forward recoil, one would naturally conclude a downward and backward stroke alone is requisite. Such, however, is not the case.

In the first place, a natural wing, or a properly constructed artificial one, cannot be depressed either vertically downwards, or downwards and backwards. It will of necessity descend downwards and forwards in a curve. This arises from its being flexible and elastic throughout, and in especial from its being carefully graduated as regards thickness, the tip being thinner and more elastic than the root, and the posterior margin than the anterior margin.

In the second place, there is only one direction in which the wing could strike so at once to support and carry the bird forward. The bird, when flying, is a body in motion. It has therefore acquired momentum. If a grouse is shot on the wing it does not fall vertically downwards, as Borelli and his successors assume, but downwards and forwards. The flat surfaces of the wings are consequently made to strike downwards and forwards, as they in this manner act as kites to the falling body, which they bear, or tend to bear, upwards and forwards.

So much for the direction of the stroke during the descent of the wing.

Let us now consider to what extent the posterior margin of the wing yields in an upward direction when the wing descends. Borelli does not state the exact amount. The Duke of Argyll, who believes with Borelli that the posterior margin of the wing is elevated during the down stroke, avers that, "whereas the air compressed in the hollow of the wing cannot pass through the wing owing to the closing upwards of the feathers against each other, or escape forwards because of the rigidity of the bones and of the quills in this direction, it passes backwards, and in so doing lifts by its force the elastic ends of the feathers. In passing backwards it communicates

to the whole line of both wings a corresponding push forwards to the body of the bird. The same volume of air is thus made, in accordance with the law of action and reaction, to sustain the bird and carry it forward."1 Mr. Macgillivray observes that "to progress in a horizontul direction it is necessary that the downward stroke should be modified by the ele vation in a certain degree of the free extremities of the quills.'

3

Marey's Views.-Professor Marey states that during the down stroke the posterior or flexible margin of the wing yields in an upward direction to such an extent as to cause the under surface of the wing to look backwards, and make a backward angle with the horizon of 45° plus or minus according to circumstances. That the posterior margin of the wing yields in a slightly upward direction during the down stroke, I admit. By doing so it prevents shock, confers continuity of motion, and contributes in some measure to the elevation of the wing. The amount of yielding, however, is in all cases very slight, and the little upward movement there is, is in part the result of the posterior margin of the wing rotating around the anterior margin as an axis. That the posterior margin of the wing never yields in an upward direction until the under surface of the pinion makes a backward angle of 45° with the horizon, as Marey remarks, is a matter of absolute certainty. This statement admits of direct proof. If any one watches the horizontal or upward flight of a large bird, he will observe that the posterior or flexible margin of the wing never rises during the down stroke to a perceptible extent, so that the under surface of the wing on no occasion looks backwards, as stated by Marey. On the contrary, he will find that the under surface of the wing (during the down stroke) invariably looks forwards the posterior margin of the wing being inclined downwards and backwards; as shown at figs. 82 and 83, p. 158; fig. 103, p. 186; fig. 85 (abc), p. 160; and fig. 88 (cdefg), p. 166.

The under surface of the wing, as will be seen from this

1 "Reign of Law"-Good Words, February 1865, p. 128.

2 History of British Birds. Lond. 1837, p. 43.

3" 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.

account, not only always looks forwards, but it forms a true kite with the horizon, the angles made by the kite varying at every part of the down stroke, as shown more particularly at d, e, f, g; j, k, l, m of fig. 88, p. 166. I am therefore opposed to Borelli, Macgillivray, Owen, Bishop, M. Liais, the Duke of Argyll, and Marey as to the direction and nature of the down stroke. I differ also as to the direction and nature of the up stroke.

Professor Marey states that not only does the posterior margin of the wing yield in an upward direction during the down stroke until the under surface of the pinion makes a backward angle of 45° with the horizon, but that during the up stroke it yields to the same extent in an opposite direction. The posterior flexible margin of the wing, according to Marey, passes through a space of 90° every time the wing reverses its course, this space being dedicated to the mere adjusting of the planes of the wing for the purposes of flight. The planes, moreover, he asserts, are adjusted not by vital and vito-mechanical acts but by the action of the air alone; this operating on the under surface of the wing and forcing its posterior margin upwards during the down stroke; the air during the up stroke acting upon the posterior margin of the upper surface of the wing, and forcing it downwards. This is a mere repetition of Borelli's view. Marey delegates to the air the difficult and delicate task of arranging the details of flight. The time, power, and space occupied in reversing the wing alone, according to this theory, are such as to render flight impossible. That the wing does not act as stated by Borelli, Marey, and others may be readily proved by experiment. It may also be demonstrated mathematically, as a reference to figs. 114 and 115, p. 228, will show.

Let ab of fig. 114 represent the horizon; m n the line of vibration; xc the wing inclined at an upward backward angle of 45° in the act of making the down stroke, and ad the wing inclined at a downward backward angle of 45° and in the act of making the up stroke. When the wing xc descends it will tend to dive downwards in the direction f giving very little of any horizontal support (ab); when the wing ad ascends it will endeavour to rise in the direction g, as it darts up like a kite (the body bearing it being in motion)