784 



VAR VARIATIONS OF THE MOON. 



to a temperature considerably above that of the 

 atmosphere, and the body is suffered to remain for 

 some time in this heated air, the common effect of 

 which is, to increase its temperature, and to ac- 

 celerate the circulation of the blood. After some 

 time, the steam is admitted, when the former 

 symptoms are removed, and a profuse perspiration 

 is produced. This is usually promoted by friction, 

 and removal to a warm bed. The general effect of 

 this process is to relax the body, remove obstruc- 

 tions of the skin, alleviate pain and spasmodic con- 

 tractions, and promote sleep. In the vapour bath, 

 the stimulant power of heat is modified and tem- 

 pered by the moisture diffused through the air; 

 and, as the elastic vapour, like air, is a less power- 

 ful conductor of heat than a watery fluid, the effect 

 of vapour in raising the temperature of the body is 

 much less than that of the hot bath. Its heating 

 effect is also further diminished by the copious per- 

 spiration that ensues ; so that, on all accounts, the 

 vapour bath is safer, and, in most cases, more effec- 

 tual, than the hot water bath. See Bath. 

 VAR. See Departments. 

 VARANGIANS, OR VARAGIANS (i. e. hunt- 

 era, or corsairs) ; a Scandinavian race, who seem to 

 have received this name in Russia, where they estab- 

 lished several principalities. Some of them after- 

 wards entered the service of the Byzantine em- 

 perors, and performed the duty of imperial guards 

 at Constantinople. Here they were recruited, ac- 

 cording to the Byzantine writers, by bands of their 

 countrymen from Thule ; i. e. by Saxons and Danes, 

 who fled from England to escape the Norman yoke. 

 They continued to speak the Saxon or Danish lan- 

 guage till the overthrow of the empire. The pe- 

 culiar weapon of these Varangian guards, to whom 

 the keys of the palace and the capital were entrust- 

 ed, was the two-edged battle-axe. 



VARCHI, BENEDETTO, an eminent man of let- 

 ters, born at Florence, in 1502, was educated at 

 the university of Padua, where he made a great pro- 

 gress in the belles-lettres, but was designed for the 

 law, which he studied during the life of his father, 

 and was even admitted a notary. When the decease 

 of his parents left him at liberty to pursue his own 

 inclinations, he forsook the law, and devoted him- 

 self entirely to literature. He accordingly studied 

 the Greek language and philosophy, until driven 

 from Florence by his attachment to the Strozzi: he 

 then returned to Padua, where he read public lec- 

 tures on morals and literature. The grand duke oi 

 Tuscany, Cosmo I., invited him back to Florence, 

 although he had opposed the Medici, and assigned 

 to him the office of writing a history of the late 

 revolution. Whilst thus employed, he was attack- 

 ed, at night, by some persons who feared that his 

 strictures might be unfavourable to them, and stab- 

 bed in several places. He, however, recovered 

 and had either the prudence or the lenity not to 

 name the parties, although he knew them. He was 

 carried off by an apoplexy, in 1565, at the age o 

 sixty-three. Varchi was a man of indefatigable in 

 dustry, and there is scarcely a branch of literature 

 which he did not cultivate. His Storia ftorentina 

 comprising only the period of eleven years, is very 

 voluminous, and written in a diffuse, languid man 

 ner. It is also charged with adulation to the house 

 of Medici. Varchi likewise wrote poems and a 

 comedy, and, as a grammarian, obtained reputation 

 by his dialogue entitled L'Ercolano, on the Tuscan 

 language. His Lezioni lette nella Academia Fioren 

 tine display a multifarious erudition. 



VARENNES; a petty town in the north-east 

 of France, 150 miles north-east of Paris, and eigh- 

 teen north-west of Verdun. It has about 1300 in- 

 :iabitants, with manufactures of leather and paper ; 

 but is chiefly remarkable as the place where Louis 

 XVI. was stopped in his imprudent flight from 

 Paris, in June, 1791. See Louis XVI. 



VARIABLE QUANTITIES, in geometry and 

 analytics, denote such as are either continually in- 

 creasing or diminishing, in opposition to those 

 which are constant, remaining always the s:ime. 

 Thus the abscisses and ordinates of an ellipsis, or 

 other curve line, are variable quantities, because 

 they vary or change their magnitudes together. 

 Some quantities may be variable by themselves 

 alone, while those connected with them are con- 

 stant ; as the abscisses of a parallelogram, whose 

 ordinates may be considered as all equal, and there- 

 fore constant. The diameter of a circle, and the 

 parameter of a conic section, are constant, while 

 their abscisses are variable. Variable quantities 

 are usually denoted by the last letters of the al- 

 phabet, z, y, x, while the constant ones are denoted 

 by the first letters, a, b, c. 



VARIATION, in music, is the different manner 

 of singing or playing the same air, tune or song, 

 either by subdividing the notes into several others 

 of less value, or by adding graces, in such a manner, 

 however, that the tune itself may still be discovered, 

 through all its embellishments. These repetitions 

 or variations were formerly called doubles. Mozart's 

 variations for the piano, and those of Rode for the 

 violin, are particularly excellent. Generally speak- 

 ing, variations are more suited to instrumental than 

 vocal music. The latter sort are chiefly intended 

 for practice, or to show the splendid talents of the 

 singer ; e. g. those sung by madame Catalan! . 

 There are also variations in poetry, called glosses, 

 used in Spanish and Portuguese poetry. See G/oss. 



VARIATION OF CURVATURE, in geome- 

 try, is used for that inequality or change which hap- 

 pens in the curvature of all curves except the circle ; 

 and this variation, or inequality, constitutes the 

 quality of the curvature of any line. 



VARIATION OF THE MAGNETIC NEE- 

 DLE. See Magnetism. 



VARIATIONS, CALCULUS or ; that branch of 

 the differential calculus (see Calculus') in which 

 the mathematician ascends from the theory of the 

 maximum and minimum to the more important and 

 difficult investigation of that curve, or those, among 

 all possible curves, to which belong certain given 

 qualities in the highest or .lowest degree. If, for 

 instance, the question is, to find the brachystochr- 

 ones (i. e. those among all curves of equal length, 

 which a body, moved by given powers, passes 

 through in the shortest time), the analytical answer 

 to this and similar questions leads to the calculus 

 of variations, which, therefore, appears as an ex- 

 tended theory of the maximum and minimum, and, 

 instead of confining itself to differentiation, rather 

 requires us to deduce from a derived equation al- 

 ready found the primitive one possessing the re- 

 quired quality. The method of variations, which 

 owes it origin to John Bernoulli's proposing the 

 above-mentioned problem of the brachystochrones, 

 in 1693, crowns the admirable fabric of modern 

 geometry See Dicksen's Analytische Darstellung 

 der Variationsrechnung (Berlin, 1826, 4to.). 



VARIATIONS OF THE MOON; inequalities 

 in the revolution of the moon, known only since 

 the time of Tycho Brahe. 



