Encyclopaedia Britannica Volume 3, Part 1, Slice 2 Part 27

were all lovers of the ballet and performed various characters in them, and Richelieu used the ballet as an instrument for the expression of political purposes. Lully was the first to make an art of the composition of ballet music and he was the first to insist on the admission of women as ballet dancers, feminine characters having hitherto been a.s.sumed by men dressed as women. When Louis XIV. became too fat to dance, the ballet at court became unpopular and thus was ended the first stage of its development. It was then adopted in the colleges at prize distributions and other occasions, when the ballets of Lully and Quinault were commonly performed. The third period in the history of the ballet was marked by its appearance on the stage, where it has remained ever since. It should be added that up till the third period dramatic poems had accompanied the ballet and the dramatic meaning was helped out with speech and song; but with the advent of the third period speech disappeared and the purely pantomime performance, or _ballet d'action_, was inst.i.tuted.

The father of ballet dancing as we know it at the present day was Jean Georges Noverre (_q.v._). The _ballet d'action_ was really invented by him; in fact, the ballet has never advanced beyond the stage to which he brought it; it has rather gone back. The [v.03 p.0270] essence of Noverre's theory was that mere display was not enough to ensure interest and life for the ballet; and some years ago Sir Augustus Harris expressed a similar opinion when he was asked wherein lay the reason of the decadence of the modern ballet. Noverre brought to a high degree of perfection the art of presenting a story by means of pantomime, and he never allowed dancing which was not the direct expression of a particular att.i.tude of mind. Apart from Noverre, the greatest ballet-master was undoubtedly Gaetano Apolline Balthazare Vestris (_q.v._), who modestly called himself _le dieu de la danse_, and was, indeed, the finest male dancer that Europe ever produced.

Gluck composed _Iphigenie en Aulide_ in conjunction with Vestris. In 1750 the two greatest dancers of the day performed together in Paris in a ballet-opera called _Leandre et Hero_; the dancers were Vestris and Madame Camargo (_q.v._), who introduced short skirts in the ballet.

The word "balette" was first used in the English language by Dryden in 1667, and the first descriptive ballet seen in London was _The Tavern Bilkers_, which was played at Drury Lane in 1702. Since then the ballet in England has been purely exotic and has merely followed on the lines of French developments. The palmy days of the ballet in England were in the first half of the 19th century, when a royal revenue was spent on the maintenance of this fashionable attraction. Some famous dancers of this period were Carlotta Grisi, Mdlle Taglioni (who is said to have turned the heads of an entire generation), f.a.n.n.y Elssler, Mdlle Cerito, Miss P.

Horton, Miss Lucile Grahn and Mdlle Carolina Rosati. In later years Kate Vaughan was a remarkably graceful dancer of a new type in England, and, in Sir Augustus Harris's opinion, she did much to elevate the modern art. She was the first to make skirt-dancing popular, although that achievement will not be regarded as an unmixed benefit by every student of the art.

Skirt-dancing, in itself a beautiful exhibition, is a departure from true dancing in the sense that the steps are of little importance in it; and we have seen its development extend to a mere exhibition of whirling draperies under many-coloured lime-lights. The best known of Miss Vaughan's disciples and imitators (each of whom has contributed something to the art on her own account) were Miss Sylvia Grey and Miss Letty Lind. Of the older and cla.s.sical school of ballet-dancing Adeline Genee became in London the finest exponent. But ballet-dancing, affected by a tendency in modern entertainment to make less and less demands on the intelligence and intellectual appreciation of the public, and more and more demands on the eye--the sense most easily affected--has gradually developed into a spectacle, the chief interest of which is quite independent of dancing.

Thousands of pounds are spent on dressing a small army of women who do little but march about the stage and group themselves in accordance with some design of colour and ma.s.s; and no more is asked of the intelligence than to believe that a ballet dressed, for example, in military uniform is a compliment to or glorification of the army. Only a few out of hundreds of members of the _corps de ballet_ are really dancers and they perform against a background of colour afforded by the majority. It seems unlikely that we shall see any revival of the best period and styles of dancing until a higher standard of grace and manners becomes fashionable in society. With the constantly increasing abolition of ceremony, courtliness of manner is bound to diminish; and only in an atmosphere of ceremony, courtesy and chivalry can the dance maintain itself in perfection.

LITERATURE.--One of the most complete books on the ballet is by the Jesuit, Claude Francois Menestrier, _Des ballets anciens et modernes_, 12mo (1682).

He was the inventor of a ballet for Louis XIV. in 1658; and in his book he a.n.a.lyses about fifty of the early Italian and French ballets. See also Noverre, _Lettres sur la danse_ (1760; new ed. 1804); Castel-Blaze, _La Danse et les ballets_ (1832), and _Les Origines de l'opera_ (1869).

BALL-FLOWER, an architectural ornament in the form of a ball inserted in the cup of a flower, which came into use in the latter part of the 13th, and was in great vogue in the early part of the 14th century. It is generally placed in rows at equal distances in the hollow of a moulding, frequently by the sides of mullions. The earliest known is said to be in the west part of Salisbury cathedral, where it is mixed with the tooth ornament. It seems to have been used more and more frequently, till at Gloucester cathedral, in the south side, it is in profusion.

BALLIA, a town and district of British India, in the Benares division of the United Provinces. The town is situated on the left bank of the Ganges, below the confluence of the lesser Sarju. It is really an aggregation of rural villages. Pop. (1901) 15,278.

The district of Ballia, const.i.tuted in 1879, occupies an angle at the junction of the Gogra with the Ganges, being bordered by two districts of Behar. It contains an area of 1245 sq. m. Owing to the great pressure on the soil from the density of the population, to the reluctance to part with land characteristic of small proprietors, to the generally great productiveness of land and to the very light a.s.sessment of government revenue, land in Ballia, for agricultural purposes merely, has a market value higher than in almost any other district. It commonly brings in Rs.

200 per bigha, or 20 per acre, and sometimes double that figure. In 1901 the population was 987,768, showing a decrease of 5% in the decade. The princ.i.p.al crops are rice, barley, other food-grains, pulse, sugar-cane and opium. There are practically no manufactures, except that of sugar. Trade is carried on largely by way of the two bordering rivers.

BALLINA, a seaport and market-town of county Mayo, Ireland, in the north parliamentary division, on the left bank of the river Moy, with a station on the Killala branch of the Midland Great Western railway. Pop. of urban district (1901) 4505. Across the river, and therefore in county Sligo, is the suburb of Ardnaree, connected with Ballina by two bridges. In Ardnaree is the Roman Catholic cathedral (diocese of Killala), with an east window of Munich gla.s.s, and the ruins of an Augustinian abbey (1427) adjoining.

There is a Roman Catholic diocesan college and the Protestant parish church is also in Ardnaree. A convent was erected in 1867. In trade and population Ballina is the first town in the county. The salmon-fishery and fish-curing are important branches of its trade; and it has also breweries and flour-mills and manufactures snuff and coa.r.s.e linen. On the 25th of August 1798, Ballina was entered by the French under General Humbert, marching from their landing-place at Killala. In the neighbourhood there is the interesting cromlech of the four Maels, which, if actually erected over the criminals whose name it bears, is proved by the early annals of Ireland to belong to the 7th century A.D. Their story relates that these men, foster-brothers of Cellach, bishop of Kilmore-Moy, murdered him at the instigation of Guaire Aidhne, king of Connaught, but were themselves executed at Ardnare (_Ard-na-riaghadh_, the hill of the executions) by the bishop's brother. The Moy is a notable salmon river for rod-fishing and its tributaries and the neighbouring lakes contain trout.

BALLINASLOE, a market town of county Galway, Ireland, in the east parliamentary division, 91 m. W. of Dublin, on the Midland Great Western main line. Pop. of urban district (1901) 4904. The river Suck, an affluent of the Shannon, divides it into two parts, of which the eastern was in county Roscommon until 1898. The town contains remains of a castle of Elizabethan date. Industries include brewing, flour-milling, tanning, hat-making and carriage-building. Trade is a.s.sisted by water-communication through the Grand ca.n.a.l to the Shannon. The town is widely celebrated for its great annual cattle-fair held in October, at which vast numbers of cattle and sheep are offered or sale. Adjoining the town is Garbally Castle, the seat of the earl of Clancarty, into the demesne of which the great fair extends from the town.

BALLISTICS (from the Gr. [Greek: ballein], to throw), the science of throwing warlike missiles or projectiles. It is now divided into two parts:--_Exterior Ballistics_, in which the motion of the projectile is considered after it has received its initial impulse, when the projectile is moving freely under the influence of gravity and the resistance of the air, and it is required to determine the circ.u.mstances so as to hit a certain object, with a view to its destruction or perforation; and _Interior Ballistics_, in which the pressure of the powder-gas is a.n.a.lysed in the bore [v.03 p.0271] of the gun, and the investigation is carried out of the requisite charge of powder to secure the initial velocity of the projectile without straining the gun unduly. The calculation of the stress in the various parts of the gun due to the powder pressure is dealt with in the article ORDNANCE.

I. EXTERIOR BALLISTICS.

In the ancient theory due to Galileo, the resistance of the air is ignored, and, as shown in the article on MECHANICS (-- 13), the trajectory is now a _parabola_. But this theory is very far from being of practical value for most purposes of gunnery; so that a first requirement is an accurate experimental knowledge of the resistance of the air to the projectiles employed, at all velocities useful in artillery. The theoretical a.s.sumptions of Newton and Euler (_hypotheses magis mathematicae quam naturales_) of a resistance varying as some simple power of the velocity, for instance, as the square or cube of the velocity (the quadratic or cubic law), lead to results of great a.n.a.lytical complexity, and are useful only for provisional extrapolation at high or low velocity, pending further experiment.

The foundation of our knowledge of the resistance of the air, as employed in the construction of ballistic tables, is the series of experiments carried out between 1864 and 1880 by the Rev. F. Bashforth, B.D. (_Report on the Experiments made with the Bashforth Chronograph_, &c., 1865-1870; _Final Report_, &c., 1878-1880; _The Bashforth Chronograph_, Cambridge, 1890). According to these experiments, the resistance of the air can be represented by no simple algebraical law over a large range of velocity.

Abandoning therefore all a priori theoretical a.s.sumption, Bashforth set to work to measure experimentally the velocity of shot and the resistance of the air by means of equidistant electric screens furnished with vertical threads or wire, and by a chronograph which measured the instants of time at which the screens were cut by a shot flying nearly horizontally.

Formulae of the calculus of finite differences enable us from the chronograph records to infer the velocity and r.e.t.a.r.dation of the shot, and thence the resistance of the air.

As a first result of experiment it was found that the resistance of similar shot was proportional, at the same velocity, to the surface or cross section, or square of the diameter. The resistance R can thus be divided into two factors, one of which is d^2, where d denotes the diameter of the shot in inches, and the other factor is denoted by p, where p is the resistance in pounds at the same velocity to a similar 1-in. projectile; thus R = d^2p, and the value of p, for velocity ranging from 1600 to 2150 ft. per second (f/s) is given in the second column of the extract from the abridged ballistic table below.

These values of p refer to a standard density of the air, of 534.22 grains per cubic foot, which is the density of dry air at sea-level in the lat.i.tude of Greenwich, at a temperature of 62 F. and a barometric height of 30 in.

But in consequence of the humidity of the climate of England it is better to suppose the air to be (on the average) two-thirds saturated with aqueous vapour, and then the standard temperature will be reduced to 60 F., so as to secure the same standard density; the density of the air being reduced perceptibly by the presence of the aqueous vapour.

It is further a.s.sumed, as the result of experiment, that the resistance is proportional to the density of the air; so that if the standard density changes from unity to any other relative density denoted by [tau], then R = [tau]d^2p, and [tau] is called the _coefficient of tenuity_.

The factor [tau] becomes of importance in long range high angle fire, where the shot reaches the higher attenuated strata of the atmosphere; on the other hand, we must take [tau] about 800 in a calculation of shooting under water.

The resistance of the air is reduced considerably in modern projectiles by giving them a greater length and a sharper point, and by the omission of projecting studs, a factor [kappa], called the _coefficient of shape_, being introduced to allow for this change.

For a projectile in which the ogival head is struck with a radius of 2 diameters, Bashforth puts [kappa] = 0.975; on the other hand, for a flat-headed projectile, as required at proof-b.u.t.ts, [kappa] = 1.8, say 2 on the average.

For spherical shot [kappa] is not constant, and a separate ballistic table must be constructed; but [kappa] may be taken as 1.7 on the average.

Lastly, to allow for the superior centering of the shot obtainable with the breech-loading system, Bashforth introduces a factor [sigma], called the _coefficient of steadiness_.

This steadiness may vary during the flight of the projectile, as the shot may be unsteady for some distance after leaving the muzzle, afterwards steadying down, like a spinning-top. Again, [sigma] may increase as the gun wears out, after firing a number of rounds.

Collecting all the coefficients, [tau], [kappa], [sigma], into one, we put

(1) R = nd^2p = nd^2f(v), where (2) n = [kappa] [sigma] [tau],

and n is called the _coefficient of reduction_.

By means of a well-chosen value of n, determined by a few experiments, it is possible, pending further experiment, with the most recent design, to utilize Bashforth's experimental results carried out with old-fashioned projectiles fired from muzzle-loading guns. For instance, n = 0.8 or even less is considered a good average for the modern rifle bullet.

Starting with the experimental values of p, for a standard projectile, fired under standard conditions in air of standard density, we proceed to the construction of the ballistic table. We first determine the time t in seconds required for the velocity of a shot, d inches in diameter and weighing w lb, to fall from any initial velocity V(f/s) to any final velocity v(f/s). The shot is supposed to move horizontally, and the curving effect of gravity is ignored.

If [Delta]t seconds is the time during which the resistance of the air, R lb, causes the velocity of the shot to fall [Delta]v (f/s), so that the velocity drops from v+[Delta]v to v-[Delta]v in pa.s.sing through the mean velocity v, then

(3) R[Delta]t = loss of momentum in second-pounds, = w(v+[Delta]v)/g - w(v-[Delta]v)/g = w[Delta]v/g

so that with the value of R in (1),

(4) [Delta]t = w[Delta]v/nd^2pg.

We put

(5) w/nd^2 = C,

and call C the ballistic coefficient (driving power) of the shot, so that

(6) [Delta]t = C[Delta]T, where (7) [Delta]T = [Delta]v/gp,

and [Delta]T is the time in seconds for the velocity to drop [Delta]v of the standard shot for which C=1, and for which the ballistic table is calculated.

Since p is determined experimentally and tabulated as a function of v, the velocity is taken as the argument of the ballistic table; and taking [Delta]v = 10, the average value of p in the interval is used to determine [Delta]T.

Denoting the value of T at any velocity v by T(v), then

(8) T(v) = sum of all the preceding values of [Delta]T plus an arbitrary constant, expressed by the notation (9) T(v) = [Sum]([Delta]v)/gp + a constant, or [Integral]dv/gp + a constant, in which p is supposed known as a function of v.

The constant may be any arbitrary number, as in using the table the difference only is required of two tabular values for an initial velocity V and final velocity v and thus

(10) T(V) - T(v) = [Sum,v:V][Delta]v/gp or [Integral,v:V]dv/gp;

and for a shot whose ballistic coefficient is C

(11) t = C[T(V) - T(v)].

To save the trouble of proportional parts the value of T(v) for unit increment of v is interpolated in a full-length extended ballistic table for T.

Next, if the shot advances a distance [Delta]s ft. in the time [Delta]t, during which the velocity falls from v+[Delta]v to v-[Delta]v, we have