BALLISTIC PKNDULfM. 



BALLIUM. 



and Psyche,' , speaking at what he uU the dance, meaning the 

 mimetic put of it, " Being in ite origin used in the service of religion, 

 it thereby aamirwt a dignity which in modern time* it never possessed. 

 The mo*t end mysteries of heatlu-uuun were thus accompanied. 

 A|H>Uo, in a passage of Pindar, U called the Dancer (i^tn<rri>i) ; and 

 there U a Greek line extant which represent* Jupiter himself in the 

 very act of dancing. Even at Rome, where the danoe wai on the whole 

 much less respected, the priecU of Man, to whom the care of the sacred 

 wa* committed, were, from their customary and solemn dances, 

 Salii (from *dio). Of the imitative dance, both Plato and 



and p must be measured in the same unit of weight, and //. i, f, r. in 

 he lame unit of length. Then will the velocity of the ball at the 

 moment of striking, in fed, be 



Xeoophon, in the person of their master, Socrates, apeak very favour- 

 ably ; and ArutoJe ranks it with the art of poetry. Plutarch, in the 

 last book of ' Symposiac Questions,' considered it worthy of distinct 

 dkcusston. And Lucian, an author certainly not deficient in genius 

 or sagacity, has left an express eulogium, in which he scruples not to 

 prefer the arrJutHe to the speaking dramas. 'The Greek*,' says 

 Athencus, ' had brought their dance to such perfection, in the art of 

 imitating the passions, that the most eminent sculptors thought their 

 time not ill-employed in studying and designing the attitudes of the 

 public dancers ; and to this study (he adds) they owed, undoubtedly, 

 some of the transcendent beauties of their works.' " 



The ballet has been essentially a product of the European courts, 

 and a fashionable amusement In the beginning of the 16th century, 

 Aglio, count of Savoy, himself prepared and acted ballets with the 

 princes and princesses of his court. Baltagerini, the music director of 

 Catherine de' Medici, introduced it into France, where it became so 

 great a favourite that Louis XIII., and even Louis XIV. in his youth, 

 danced in ballet* ; they were however generally allegorical, and suffi- 

 ciently tasteless. Quinault first elevated it, and interwove it with 

 some of his operas. In 1697 A. H. de la Hotte still further improved 

 it, particularly in its action and dramatic interest. But, appealing 

 almost entirely to the eye, it is continually lowering iU character by 

 being forced to adapt itself to the caprices of individual dancers ; while 

 for its general effect it depends much on a lavish adornment in scenery, 

 dresses, and decoration. About 1750, however, M. Noverre operated a 

 great change in the ballet, and restored it- to nearly the dignity, con- 

 sidered as a public amusement, which it supported among the ancients. 

 We have already quoted his opinions on the ballet, and he very success- 

 fully applied them in his productions. His ' Mode*,' his ' Deserteur,' 

 and his ' Psyche 1 ,' still preserve a high reputation. The influence of 

 these works lasted many years ; but at length fashion, almost always 

 opposed to good sense and good taste, would view with favouring eyes 

 nothing but that which passes under the name of dancing ; and what 

 ought to be the ballet, is too frequently reduced to a divertissement in 

 which even good grouping is generally neglected. Some successful efforts 

 liave however been made in recent years to improve the character . >f the 

 ballet, and the introduction of the national ballets of other countries 

 has assisted in effecting this. Still, there is too much of mere conven- 

 tionality, and too much sacrifice of grace, sentiment, and the develop- 

 ment of feeling, to exhibitions of mere agility and tour* de farce, often 

 more surprising than pleasing. 



BALLISTIC PENDULUM, a heavy wooden pendulum, in section 

 like a gardener's spade : the lower part consisting of a heavy cubical 

 block of wood, plated with iron at the back. It was invented and 

 used by Mr. Robins, the celebrated writer on gunnery, for the purpose 

 of measuring the velocity of cannon-balls and musket-balls. It must 

 be of such a weight that the ball fired into it may not cause a vibra- 

 tion of very great extent. It U described at great length in Koliin.-.'s 

 ' Principles of Gunnery (we recommend Button's edition, London, 

 1805), prop, viii, and in Mutton's 'Mathematical Tracts,' vol. ii. 

 tract. 34. Those who attempt any experiments with such an instru 

 inent should particularly attend to the cautions given by Mr. Robins, 

 who learnt them at the risk of his life. 



The principle is as follows : The pendulum in its state of rest all 

 but touches with its lower end a horizontal bar. To the lower end of 

 the pendulum is attached a ribbon, which passes through an orifice in 

 the bar, moving almost freely. When, therefore, the pendulum is 

 raised, a quantity of ribbon U drawn out, which, if the radius be the 

 whole length of the pendulum, in the chord of the angle through which 

 the pendulum U inclined by the shock. When a shot is fired into the 

 pendulum, DO more ribbon is disengaged, during the oscillations which 

 follow, than was drawn out by the first rise of the pendulum ; because 

 friction and the resistance of the air will continually diminish the 

 extent of the oscillation. The extent of the first oscillation is greater 

 or less, according as the momentum of the shot is greater or less ; and 

 the mechanical problem to be solved is as follows : Given the v riclit 

 of the shot, the place at which it strikes, the weight, form, 4c., of the 

 pendulum, and the effect produced upon it by the shot ; required the 

 Telocity of the shot. The formula which answers this question is as 

 follows: 



* is the weight of the ball. 



f that of the whole pendulum. 



j distance from the pivot of the centre of gravity of the whok 



(after the 1*1 1). 



i distance fn.m tl,,- pivot to the point struck. 

 c length of nl.l-.n (Unengaged. 

 r ilintance from the pivot to the riblion. 

 the number of vibrations in a minute after receiving the shot. 



'ENTKE or) : but if it be determine 

 the value of g after the shot is 



mechanical methods (GRAVITY, 

 as usual, before the shot, tli. n 



The ballistic pendulum, in the hands of Robins and Hutton, was 

 useful in supplying information respecting the velocity of cannon-balls, 

 and the resistance of the air to rapid motions. [AERO-DYNAMICS.] It 

 las also tested the correctness of the theory propounded on that subject 

 by Robins. [GumiKBT.] We give in the following table the results 

 of that set of experiments, in which the greatest difference was found 

 Between the prediction from theory and the experiment, omitting all 

 ie circumstances of each charge, as no connection can be traced 

 Between them and the discordances. In the fourth and fifth examples, 

 the barrel had previously lain by in a moist place. Considering the 

 very great difficulty and uncertainty of the subject, the accordance is 

 remarkable. The first two columns represent the length of ribbon dis- 

 engaged (in inches and tenths), the first from experiment, the second 

 irom theory ; the third is the difference between the two : 



Experiment. 



17-1 

 15-2 

 154 

 11-5 

 11-5 

 87 

 12-3 

 14-4 

 14-4 

 10-8 

 14-7 

 15-7 



Theory. 

 17-2 

 15-0 

 15-0 

 12-8 

 12-8 

 9-0 

 12-5 

 14-4 

 14-4 

 10-5 

 14-5 

 15-3 



Difference. 



+ 'I 



-2 



-4 

 + 1-8 

 + 1-3 

 + -3 

 -r -2 



o-o 



O'O 

 + -2 



..> 



-4 



Average discordance + -18 



When a heavier pendulum was used, the discordances were consider- 

 ably less. The friction of the pivots was not taken into account in the 

 theory. 



It has been proposed to make the gun itself a pendulum, by hanging 

 it as such, and observing by means of a ribbon, the arc of recoil. This 

 instrument was also used by Robins as on tprovxttte for gunpowili i i > 

 firing the same gun with successive charges of pow.l. r i .liil'. i. ML 

 qualities, and using no ball. By first measuring the recoil without. 

 the ball and afterwords with it, it is presumed that the additional 

 momentum given to the gun in one direction is also that given to the 

 boll in the other. This there appears no reason to dispute ; but the 

 comparison between the gun-pendulum and the ballistic-pendulum 

 cannot be very satisfactorily made, because between the two comes 

 another unknown quantity, namely, the effect of the air on the ball 

 between the instant of leaving the gun and striking the pendulum. 

 But various circumstances, particularly described by Dr. Hutton in the 

 tract alluded to, render the principle assumed in the use of the gun- 

 1 .1 M. IM IMIM very doubtful. 



BA'LLIUM; BAILLIE, or BAILEY. This term, according to 

 Dufresne, anciently meant on outer bulwark ; but was afterwards 

 adopted for the area or court-yard contained within one. It appears 

 clear from the word, and its original use, that it is a corrupted form of 

 the Latin Vallum. 



Grose (' Antiq. of Engl. and Wales,' vol. i. pref. p. 7) says, the ditch 

 of a royal castle was sometimes called the Ditch del Bayle, or of the 

 Balliuin, to distinguish it from the ditches of the interior works, 

 it was either a standing or draw bridge, leading to the Killiimi. Within 

 the ditch were the walls of the ballium, or outworks. In towns, the 

 appellation of ballium was given to a work fenced with palisades, and 

 some-times masonry, covering the suburbs ; but in castles it was the 

 space immediately within the outer wall. When there WMS> double 

 enclosure of walls, the areas next each wall were styled the nut, 

 inner ballia. The manner in which these are mentioned by Camden, 

 from the Chronicle of Dunstaple, in the siege of Bedford Castle, 

 A.D. 1224, sufficiently justifies this position. The castle was taken by 

 four assaults. In the first was taken the barbacan ; in the second, the 

 outer ballia ; in the third, the wall by the old tower was thrown down 

 by the miners, when with great danger they possessed themselves of 

 the inner ballia through a chink; at the fourth assault the miners 

 set fire to the tower, so that the smoke burst out, and the tower itaelf 

 was cloven, so as to show visibly some broad chinks, whereupon the 

 enemy surrendered. 



The wall of the ballium in castles was commonly high, flanked with 

 towers, and had a parapet, embattled, crenellated, or garrotted, for the 

 mounting of it. There were flights of steps at convenient distances, 



