By endowing the cavalry with mobility and rapidity, and placing it ia the hands of a competent commander, it becomes indeed a formidable arm, of the utmost importance in the field of battle. In the twinkling of an eye, cavalry has frequently changed a desperate conflict into glorious victory. Strokes of power, strokes of audacity, strokes of genius, are the special and peculiar exploits of cavalry, says Guibert; and General Marbot reminds us that it is often at the very moment in battle when all seems lost, that a brave cavalry finds its best opportunity for winning distinction, by boldly rushing upon the enemy at a moment when he can be easily conquered, precisely for the reason that he already thinks himself victorious. Thus, at Marengo, 500 horemen, led by Kellermann, pouring down furiously on the Austrians at the moment of their greatest success, utterly stunned them by the vigour of the attack, pierced them on several points, and contributed by this brilliant charge to snatch from them a victory of which they had believed themselves assured.

Such, then, are the views and considerations which have directed the recent improvements in the French cavalry, whose results have been most satisfactorily demonstrated at the camp of Châlons.

Colonel the Baron d'Azemar completely expresses the opinion of the generals of his country in the following averment: "Were it permitted to raise for a moment the veil that hides the future of the cavalry, we are persuaded that we shall see its destinies enlarged. Yes, that is our conviction. Henceforth the only part that the cavalry will play in the field of battle will be to strike decisive blows, to fulminate, to annihilate the enemy. In battle, cavalry will appear like lightning; its action will be as terrible as it will be unforeseen and unexpected; it will warrant more than ever that ancient and poetical qualification of the Bible-a horse-storm: procella equestris."

The French have got the start of us-as in everything else—in their cavalry improvements. It remains to be seen whether we shall "take action" in this most imperative want and preparation, without waiting for the stern and cruel lesson of our habitual and proverbial teacherDISASTER.

which we should avoid as much as possible in the infantry, must be familiar to the cavalry, which has frequently to form with the rapidity of lightning on the flanks and forward, whether it be right or left in front. It would lose all its advantages if the inconveniences of the inverted order could fetter its movements. If, for instance, on debouching from the defile it had only room to deploy on the right of the infantry, it should-in order to form as rapidly as possible-execute the manoeuvre by inversion on the left into line, supposing it came up right in front; but, if it be not accustomed to this movement, it would be dangerous to perform it for the first time under fire. Consequently the commander would have to continue his march until his whole column is unmasked and form to the left in line; and, if he has a battery or the enemy's cavalry on his flank, it is probable that he will not execute the manœuvre without disorder: at all events he will have lost time, which is always disastrous. It is, therefore, very essential that the cavalry should be practised in forming line in the inverted as well as in the natu ral order. Many troops have received notable checks by not being able to fight in the inverted order; the Seven Years' War gives several examples.* Decidedly our infantry should be practised in these inversions, as they may be needed. The new French battalion drill insists upon their importance. See "Ecole de Bataillon," pp. 117 and 84. * General Dufour, ubi suprà.

Monday, May 20th, 1861.

COLONEL P. J. YORKE, F.R.S. in the Chair.

ON A MODEL ILLUSTRATING THE PARABOLIC THEORY OF PROJECTION FOR RANGES IN VACUQ.

By LIEUT.-COL. A. LANE FOX, Gren. Gds.

The idea of illustrating the parabolic theory by means of a model occurred to me in 1853, when the School of Musketry was established at Hythe. It was part of my business as chief instructor to give lectures to the non-commissioned officers and men sent there for instruction upon the theory of projectiles, with a view of rendering them familiar with the use of their sights at all distances. It was, of course, desirable that such lectures should be as simple as possible, and the object of the model was to enable them to take in the subject quickly by the eye, without perplexing them with mathematical terms and problems, to which they were unaccustomed. The parabolic curve, as all those acquainted with the principles of gunnery are aware, differs materially from the true curve described by a projectile in the air. But in explaining the principles of gunnery, the parabolic theory is a necessary preliminary to be gone through, for the true curve is simply a modification of the parabolic curve caused by the presence of another force, viz., the resistance of the air, which is not included in the parabolic theory.

It is, I fear, somewhat a threadbare subject; but, at the risk of appearing tedious, I will briefly remind you of the history of these theories.

For some time during the use of the early cannon which were employed only to blow open barriers, or against troops at a very short range, it was supposed that the bullet flew for some distance in a straight line, and then dropped suddenly, and it is not improbable that the large rings at the muzzles of the early cannon may partly have originated with a view of rendering the line of sight parallel to the axis of the piece, and thereby of enabling the gunners to aim, as they supposed, more accurately at the mark to be hit.

In 1537, Tartaglia, an Italian mathematician, was the first to point out that no part of the track described by a bullet was in a straight line, but he considered that the curvature was in some cases so small that it need not be attended to, comparing it to the surface of the sea, which, "though

and marking the intersection of the line of beads upon the plane drawn with a white line upon the board; the number of beads above the plane denoting the time of flight. For instance, if the index is set to 221 elevation, the intersection of the beads with the horizontal plane will be at 760 yards, the time of flight 8 seconds. At 45° it will register 1,068 yards and 14 seconds; at 67° the range will be again reduced to 760 yards, but the time of flight will be increased to 18 seconds. It is, therefore, shown that the greatest range upon a level plane is at an angle of 45° elevation. In this case the angle of descents will be seen to equal the angle of ascent; the vertex or highest point of the trajectory will be situated in the centre of the range, and its greatest height will be equal to one-fourth the range, or to one-half the impetus or height to which the ball would ascend if fired vertically; consequently the impetus is equal to one-half the range when fired at an angle of 45°.

Upon every plane, whether of elevation or depression, the greatest range is at an angle equal to half the angle formed by that plane and the perpendicular: thus, on the level it is 45°; and on a plane depressed 45° below the horizon, the greatest range is at 22° elevation, or an angle of 674° with the plane. It may also be shown, that on every plane there are two angles which register the same range; the two together equalling the total angle formed by the plane and the perpendicular. Thus, on the level plane; 221 and 67° give the same range: and on a plane depressed 45° below the horizon; 673° elevation gives the same range as 223° depression: also, upon the same plane; 45° of elevation gives the same range as a shot fired at 0°, or the level. If the index is set to 674° elevation, or an angle of 22° with the perpendicular; it will be found that the curve thus produced will cut any given plane at the same spot as if set to 221° with that plane; showing that with a given angle of elevation the range increases in proportion as the plane departs from the zenith and approaches the nadir.

All the problems connected with the parabolic theory may, I believe, be shown on the model, but there is an arrangement specially adapted for showing how the range on any plane may be obtained from the impetus. The impetus BX, as I before said, is the height to which the ball would ascend if fired vertically. From the point B on the perpendicular BG set off a space B V equal to four times the impetus; then to obtain the range upon any plane at any angle of elevation, mark off from the point V, with the line V B, an angle equal to the elevation, produce the line till it touches the "line of fire," let fall a vertical line upon the plane, and the intersection will be the range upon that plane. For instance, to obtain the range upon a plane BK depressed 45° below the horizon at an elevation of 90° with the plane, BE will be the "line of fire" from the point V: set off V W at an angle of 90°, and from W let fall a vertical line to P, then BP will be the range on the plane B K, at an elevation of 90° with the plane. The lines VW-WP are shown on the model by a thread with a weight suspended. A protractor is fixed at V, and a moveable arm is used to hold the thread at W or any other point upon the surface of the board.

It only remains to be said that, although the parabolic curve gives no approximation to the range of shot fired in the air with great velocities,