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BALL, THOMAS (1819-1911), American sculptor (see 3.263), died at Montclair, N. J., Dec. n 1911.

BALLIN, ALBERT (1857-1918), German merchant and one of the most eminent representatives of German commercial interests, was born Aug. 15 1857 at Hamburg. After hav- ing completed his mercantile training he organized the 'tween-deck (emigrant) traffic of the Carr Line. He next undertook the management of the passenger traffic of the Hamburg-Amerika Line and became in 1886 director and soon afterwards director-general of that enterprise, the expansion of which was essentially his work. The share capital of the Hamburg-Amerika Line was increased tenfold during his manage- ment. The network of its service was extended over the whole world, largely by the acquisition of a number of other lines. Ballin succeeded, by means of agreements with other German shipping companies, in developing German shipping on a grand scale; he was likewise the author of the German-American ship- ping agreement of 1902. He was regarded as enjoying the special confidence of the Emperor William II., who employed his services as an expert in all matters of shipping and commerce. Ballin died suddenly heart-broken, it is said, by the military, political and commercial collapse of Germany at Hamburg on Nov. 9 1918. (C. K.)

BALLISTICS (see 3.276*). I. INTERIOR BALLISTICS. Interior Ballistics has as its province the behaviour of a projectile, its propellant, and the gun from which it is being fired between the moment of firing and the moment at which the shell leaves the muzzle of the gun. From its nature it is a subject in which the synthesis of experimental results into general laws is a matter of great difficulty, and, in its present stage of development, striking differences of opinion still exist on fundamental points. A review of the work published after 1910 illustrates some of these differ- ences.

In France the well-known system of Gen. P. Charbonnier, published in 1908, has been modified as well as elaborated by G. Sugot (Memorial de I'Arlillerie navale, 1913). Charbonnier, for French nitre-cellulose powder in long flat strips, assumes a rate of burning directly proportional to the pressure, and that the grains burn with a distinctly- decreasing surface, while Gen. Gossot and R. Liouville (the exponents of the other leading French system) assume, for the same propellant, a rate of burn- ing proportional to the pressure to the power of two-thirds, and a practically constant burning surface.

In Italy Madaschi's revision (published in 1914) of Bianchi's Nozioni Fondimentali di Balisticq Internet- sets forth a very com- prehensive system on different lines to that of Charbonnier, although it has some points in common such as the law of burn- ing and the treatment of the resistance of the driving band.

In the U.S. official Text Book of Ordnance and Gunnery (1917) Ingalls' system of Interior Ballistics has been replaced by that of Tschappat, who again has adopted the same law of burning and treatment of band resistance as Charbonnier, but then diverges entirely from his methods.

Published in England we may note Sir George Hadcock's " Internal Ballistics " (Proc. Royal Society, A, vol. 94, London 1918), in which the treatment of the resistance of the band is extended to include a separate phase while the band is actually being engraved.

The existence of such important divergencies between pub- lished systems would in any event make it difficult to present the subject in brief and definite form. But there is also a further obstacle in the fact that the connexion between Interior Ballistics and the design of artillery materiel is so intimate that much of the resulting work is still considered by the naval and military authorities of most countries, if not of all, as to a great extent confidential.

On the other hand the experiences of the World War em- phasized the importance of a due appreciation of the general principles of Interior Ballistics not only for purposes of design, but also for the intelligent and efficient employment of artillery materiel. To establish such an appreciation on a con- crete basis, working formulae are a necessity, as without them

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the magnitude of the effects cannot be studied, but the formulae should be comparatively simple, or from their cumbersome nature they will fail in their object. Formulae suitable for this purpose, although of a purely empirical nature, are available, and it is feasible to present and illustrate the leading principles with the aid of these simple formulae alone.

Monomial Formulae for Velocity and Pressure. Interior Ballistics is concerned with the circumstances attending the motion of the shell in the bore of the gun. Considering these circumstances in a general way, when the charge is ignited, gas is evolved from the burning surface, and this gas exerts a gradually increasing pressure on the base of the shell. When a certain pressure has been developed the shell starts to move and travels up the bore with continually increasing velocity until it leaves the muzzle of the gun with a certain muzzle velocity. During this travel up the bore the pressure at first increases comparatively rapidly until a certain pressure, the maximum pressure, is reached. The pressure then gradually decreases to the muzzle, the pressure when the shell leaves the muzzle being known as the muzzle pressure.

Modern propellants are for the most part colloids, and the grains composing the charge have some more or less definite geometrical shape. Typical velocity and pressure curves for such propellants will be found in the earlier article BALLISTICS (see 3.276-7). A charge made up in this way is in practice ignited in the chamber of the gun by means of a small additional charge of black powder, the igniter (which in turn has been ignited by the cap, primer, or tube), so that the whole of the surfaces of the grains are set alight or inflamed as nearly as possible simultaneously. For such colloid propellants the " Law of Burning by Parallel Layers " is well established. This law states that at any instant during the burning of the grain the thickness burnt through in the direction normal to the exposed surface is the same over the whole surface, or in other words, that the grain is diminished by an equal thickness in all directions.

The rate of burning of the propellant is a function of the pressure, and the greater the pressure, the quicker the grain will burn.

Consider now two charges of the same weight made up of (a) comparatively small and (b) comparatively large grains of the same geometrical shape.

For (a) the surface exposed when the charge is ignited (the " initial surface ") will be greater than for (b), and the emission of gas will be greater to start with. The pressure and the rate of burn- ing will increase comparatively rapidly, and the whole charge will be consumed sooner than in the case (b). In the case of (b) the total weight of gas emitted will be the same, but the mode of emission will be different. The initial surface is not so great, so that at the start the pressure will rise less rapidly and the combustion will be completed later. The maximum pressure will occur later and will be less than for (a), but will decrease more slowly.

Coming to the geometrical shape of the grain, the different forms employed may be divided into three main groups:

(i.) Those which burn with a continually decreasing surface. To this group belong all solid grains and short cylinders with an axial perforation.

(ii.) Those' which burn with a practically constant surface, such as long thin tubes.

(iii.) Those which burn with an increasing surface to a certain

stage, the grain then breaking up into other forms quite different from the original shape. An ex- ample of this type is a cylindrical grain pierced longitudinally by a num- ber of holes.

Cordite M.D.T. is an example of Group (ii.). The length of the tubes of circular section of which the charge is composed is so great compared with their thickness, that the burning of the ends may be neglected, and the surface of combustion is practi- cally constant throughout the burning, as the tubes burn both inside and out. The proportion of the

whole thickness burnt through at any time is the same as the pro- portion of the weight or volume of the whole tube consumed.

Cordite M.D., which is made up in long cords of circular section, is an example of Group (i.), and other forms frequently employed are long flat strips of rectangular section (such as the French B.N. powders), or square flat grains (such as ballistite). In all these forms the percentage of the thickness burnt through at any time of the burning is less than the percentage of the whole weight of the grain consumed.

FIG.

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