equation finally obtained. Instead of the actual increments of the flowing or variable quantities, Newton introduced the furions of those quantities; meaning, by fluxions, quantities which had to one another the same ratio which the increments had in their ultimate or evanescent state. The fluxions of Newton corresponded with the differentials of Leibnitz; and the fluents of the former with the integrals of the latter. The fluxionary and the differential calculus are therefore two modifications of one general method. The problems which relate to the maxima and minima, or the greatest and least values of variable quantities, are among the most interesting in mathematics. When any function becomes either the greatest or the least, it does so by the velocity of its increase or decrease becoming equal to nothing: in this case, the fluxion which is proportional to that velocity must become nothing. By taking the fluxion of the given function, and supposing it equal to nothing, an equation may be obtained in finite terms, expressing the relation of the quantities when the function assigned is the greatest or least possible. The new analysis is peculiarly adapted to physical researches. The momentary increments represent precisely the forces by which the changes in nature are produced; so that this doctrine seemed created to penetrate into the interior of things, and take cognizance of those powers which elude the ordinary methods of geometrical investigation. It alone affords the means of measuring forces, when each acts separately and instantaneously, under conditions that can be accurately ascertained. In comparing the effects of continued action, the variety of time and circumstance, and the continuance of effects after their causes have ceased, introduce uncertainty, and render the conclusions vague and unsatisfactory. The analysis of infinites here goes to the point; it measures the intensity or instantaneous effort of the force, and removes all those causes of uncertainty. It is by effects, taken in their nascent or evanescent state, that the true proportion of causes must be ascertained. CALCULUS. Little stones, anciently used for computation, voting, &c., were called calculi. The Thracians used to mark lucky days by white, and unlucky by black pebbles; and the Roman judges, at an early period, voted for the acquittal of the accused by a white, and for condemnation by a black calculus: hence, niger or albus calculus, a favorable or unfavorable vote. Sometimes the ballots were

marked with characters, and then were made of wood. Calculi lusorii or latrones were counters used in a game, something like backgammon. Calculus Minerva was an expression employed to signify that the accused escaped by an equal division of the votes of the judges. He was said to be acquitted calculo Minerva (by the vote of Minerva), because Orestes was acquitted by the vote of that goddess when the judges were equally divided.

CALCULUS, or STONE, is the name given to all hard concretions, not bony, formed in the bodies of animals. Calculi may be divided into two classes, according as they are found in the gall-bladder or in the urinary bladder. The first are called biliary calculi, the second urinary calculi.-Biliary calculi are of a lamellated structure, and are composed of a substance which is considered, by M. Chevreul, as a peculiar principle, which he has named cholesterine (from xon, bile, and repcos, solid). It is described as a white, crystalline substance, with much lustre, insipid and inodorous, much resembling spermaceti, but differing in being less fusible, and in not forming a soap with alkalies. It is also converted, by the action of nitric acid, into a peculiar acid, called cholesteric acid. This is slightly soluble in water, and forms soluble salts with the alkalies. Cholesterine consists of carbon 85.095, oxygen 3.025, and hydrogen 11.88. It has lately been detected in the bile itself, both in that of animals and of man. Besides cholesterine, biliary concretions contain a portion of inspissated bile, and the yellow coloring matter of the bile in a concentrated state, which, from the beauty of its hue, and its permanence, is much valued as a pigment.Urinary calculi are of very variable characters and composition. The following substances enter principally into their composition: uric acid, urate of ammonia, phosphate of lime, phosphate of ammonia and magnesia, oxalate of lime, silex, sometimes oxyde of iron and animal matter-these being more or less pure or mixed, and being often diversified by mechanical structure, so as to render it difficult to constitute well-defined species. The six following species embrace the principal varieties of urinary calculi:-1. that composed chiefly of uric acid; 2. that consisting chiefly of the triple phosphate of ammonia and magnesia; 3. the bone-earth calculus, formed, almost entirely, of phosphate of lime; 4. the fusible calculus, composed of the two preceding intermixed; 5. the mulberry cal

culus, consisting of oxalate of lime; and, 6. a rare species, the cystic oxyde calculus. Two others, still more rare, are, the xanthic oxyde and fibrinous calculus, discovered by doctor Marcet; and, lastly, calculi have been met with formed of carbonate of lime. In all these calculi, besides the saline matter, there is present a portion of animal matter, which is conceived to be the mucus of the bladder. This seems to give them color and induration. It is found even in those which are white and crystalline. In the mulberry calculus it is present in a larger proportion than in the others. The ingredients of calculi are often, also, diversified by intermixture in layers. These must, of course, be various, and, as their production is, in some measure, accidental, irregularly arranged. Those which have been the most frequently observed are alternations of uric acid with phosphate of magnesia and ammonia, or phosphate of lime; or of oxalate of lime with uric acid, or with either or both of these phosphates.

CALCUTTA, the capital of Bengal, and of the whole British East Indies, is situated on the west branch of the Hoogly, an arm of the Ganges, on which the largest East Indiamen may come quite up to the city. The navigation, however, on account of several sandbanks, which are continually changing their size and position, is very dangerous. This place, formerly the insignificant village of Govindpour, rose, in the last century, to the size of a great city. The climate, when the English first made a settlement here, in 1690, was as unhealthy as that of Batavia; but it has been gradually becoming less fatal to settlers, partly by the removal of a forest near the city, partly by greater attention, in the settlers themselves, to their mode of living. Notwithstanding the unhealthiness of the place, it continued steadily to increase, quickly recovered from its losses in 1756, and is now one of the most magnificent cities in the world. In 1802, the population was computed at 600,000; a few years after (including the suburbs), at 1,000,000, of which about one half may be given to the city. The population of the surrounding districts, within a space of 20 miles, was estimated, in the same year, at 2,225,000 inhabitants. The houses of the English, who occupy a separate quarter of the city, are of brick, elegantly built, and many of them like palaces. On account of the heat of the climate, they are not joined together, but stand at some distance from

each other, have high and airy apartments, flat roofs, and are surrounded with verandahs. With this part of the city, "the black town," so called (the Pelta), which is the quarter occupied by the natives, forms a striking contrast. It has extremely narrow and crooked streets, interspersed with gardens and innumerable tanks. Some of the streets are paved. The houses, which are some of brick, some of mud, but mostly of bamboo er straw mats, present a motley appearance. Fort William, not far from the city, was begun by lord Clive, in 1757, and is a magnificent work, in the form of an octagon, but on too extensive a scale for the purposes of defence. It has bomb-proof barracks, large enough for 10,000 men, and would require 600 pieces of cannon for the works. It commands the river. A trench is drawn round the whole, which may be filled, in case of need, with water from the Hoogly, to the depth of eight feet. Between fort William and the city there is a plain, which forms & favorite promenade of the inhabitants. Hindoos, blacks, Europeans, equipages of all sorts, and palanquins, are here seen mixed together in a motley crowd. On the western side stands the new palace, built by the marquis of Wellesley, at an expense of a million pounds sterling, and reminding one, by its grandeur, of the fabled palaces of Arabian story. The old fort is now a custom-house, and the infamous "black hole" has been turned into a ware-house. An obelisk, 50 feet high, at the entrance, contains the names of the unfortunate captives, who, in 1756, when the city was taken and plundered by Suraja Dowla, fell victims to the most inhuman cruelty. Amongst the other public buildings are the court-house, an Armenian and an English church. In the middle of the city is a large tank, for the purpose of supplying the inhabitants during the hot season, when the river-water becomes offensive. Here is the residence of the governor-general of India, and the seat of the supreme court of justice, which decides causes according to the English law, without regard to rank, station or country. Smaller offences are tried by the superintendent of police and justices of the peace. Order is maintained by several companies of seapoys, who make regular patrols through the city. C. is the great emporium of Bengal, and the channel through which the treasures of the interior provinces are conveyed to Europe. The port is filled with ships of all nations. Mercantile en

terprise is nowhere more active than here. There are some houses which trade, annually, to the amount of 4 or 5 million pounds sterling. The trade in sugar, opium, silk, muslin, &c. is very considerable. Large quantities of salt are exported to Assam, and gold, silver, ivory, musk, and a peculiar kind of silky cotton, are brought back in exchange. Cowries, a kind of small shells, passing as coin, are received in exchange for rice from the Maldives. The trade with Pegu, Siam, and the Malay isles, formerly so profitable, has very much declined. The British merchants are, as might be expected, the most numerous; and many of them have acquired fortunes which enable them to live in a style of great splendor Next to them, in number and respectability, as well as in outward show, are the Armenians. They are peaceable and industrious merchants. Many of them have large capitals, and carry on an extensive trade to China and the ports to the west, as far as the Persian gulf. The Mongols, however, are the wealthiest ; and, as they lend only at an enormous interest, their profits, from this source, are three times as great as a capital commonly gives. The Hindoos remain fixed, however rich they may become, in their narrow views, and their accustomed frugality. Their houses and shops are mean, and it is only on occasion of their nuptials and religious festivals, that they indulge in any extraordinary expense. Then they assemble under magnificent, illuminated canopies, distribute rose-water and other perfumes in profusion, and regale themselves with confectionary from golden vessels, while they are entertained by the voices of singing girls, or the exhibition of a pantomime. The petty trade of C. is mostly in the hands of the Banyans and Sarkars, who are constantly on the watch for cheap purchases, and make use of the lowest artifices to impose on their customers. This kind of deception is so far from being in disrepute among their countrymen, that they honor the adepts in it with the title of pucka adme, which signifies a man of great talent.-Notwithstanding the high price of all the necessaries of life, and the enormous expenditures of the English merchants, we find a multitude of institutions for the relief of the indigent. Of this kind are, an hospital for those natives who are in want of medical aid, two schools for orphans whose fathers were in the service of the company, a free school, &c. The college of fort William, founded by the marquis of

Wellesley, has been changed, in part, from its original plan, which was, not only to instruct the youth in the service of the company in the languages, and other branches of study necessary for their profession, but also to watch over their behaviour, and to guard them from the dangers to which they were exposed by their inexperience. The latter part of the plan is now given up. The Asiatic society, founded by sir William Jones, in 1784, is devoted to the study and explanation of the literature, history, antiquities, arts and sciences of Asia. The papers already published are, generally, of great value. There is a botanical garden belonging to the society on the beautiful island of Garden Reach, the summer residence of the rich English.

CALDARA, Polidoro, called Caravaggio, born in 1495, at Caravaggio, in the Milanese, went to Rome in his youth, carried bricks, at first, for the masons who worked in the Vatican, and felt a great desire to become a painter, from seeing Giovanni da Udina and the other painters who were occupied in the Vatican. He formed a close friendship with Maturin of Florence, who assisted him with his advice. C. soon surpassed him, and exerted himself to introduce improvements in drawing, having always in view the antiques. Raphael employed him in the galleries of the Vatican, where he painted, under his direction, several excellent friezes. At Messina, he executed an oilpainting, which represents Christ bearing the cross, contains a number of beautiful figures, and proves his ability to treat the most elevated subjects. He has approached, more than any one, to the style and the manner of the ancients, particu larly in imitating their basso-relievos. His figures are correct, well-distributed and arranged; the positions are natural, the heads full of expression and character. It is evident that he would have acquired great celebrity if he had undertaken greater works. He applied himself to the chiaro-oscuro, particularly to that kind of it which is called sgraffiato. He showed, also, much talent in his landscapes. At the sack of Rome, in 1527, he fled to Naples, and, on his return from that place to Rome, in 1543, he was murdered by his domestic.

CALDARA, a celebrated composer of the 18th century, was born at Venice, 1714, and died 1763. His church compositions are still in repute.

CALDAS DE MONBUY; a small town in Catalonia, Spain, about 20 miles north

of Barcelona. It contains hot mineral springs, of such a temperature that the inhabitants bring eggs, vegetables, &c., to boil them in the water. When cooled, it is drunk in scrofulous and rheumatic complaints.

CALDER, or CAWDOR; a village and parish in Nairnshire, Scotland, in which are seen the remains of a castle, once the residence of Macbeth, destroyed by Malcolm; 4 miles south of Nairn.

CALDERARI (coppersmiths). This name was assumed by one of the many secret societies which have sprung up in Italy, from the political agitation of the times. Of late years, they have been most numerous at Naples, and, indeed, more so in the provinces than in the capital, where they were once united, for a long time, with the Carbonari, but were afterwards opposed to them. All these societies, so far as they have any definite political object, appear to have in view the political union of Italy, and its liberation from foreign dominion, but differ from each other so widely, in regard to the means and the results, that a decided hostility has been the consequence. Of the true character of each of these societies, among which the Calderari and the Carbonari have been the most famous and extensive, it is as difficult to give any certain information, as it is to ascertain their history; for, though they have both, and particularly the Carbonari, published their statutes and proceedings since 1817, yet these sources of information have not all reached us, nor are they entirely to be depended on. Of the Calderari, we are told by count Orloff (Memoires sur le Royaume de Naples, vol. ii. 286), that they sprung from the Carbonari, towards the end of the year 1813. It appears that a change was then made in the form of the society, which had become too large, and a great number of its former members were excluded in consequence. These united themselves into a new society, under the name of the Calderari, and became the most bitter opponents of their former brethren. After the return of king Ferdinand to Naples, prince Canosa, minister of police, favored the Calderari, that he might more effectually put down the Carbonari, who were objects of his suspicion. For this purpose, he organized them anew, divided them into wards, appointed a central ward in each province to oversee the rest, and gave them the name of Calderari del contrapeso (Calderari of the counterpoise). He distributed 20,000 muskets among them; but,

when the king was apprized of this hazardous undertaking, which had been begun without his knowledge, a stop was put to any further proceedings by Canosa's dismissal and banishment; but the association was not then abolished. This account has been contradicted from other quarters. Canosa was turned out of his office, which he had held but six months, June 27, 1816; and, three months after his banishment, a royal decree was issued, renewing the prohibitions and penalties against all secret societies, not excepting the Calderari, and commanding their prosecution, although they had lately manifested their attachment to the king and to good order. Canosa himself, in an anonymous work (I Pifferi di Montagna, Dublin, 1820), has contradicted the statements of count Orloff with regard to him and the Calderari. According to his account, they sprang up, not in Naples, but in Palermo, when lord Bentinck abolished the companies of tradesmen. This measure excited great dissatisfaction. The 'coppersmiths' or Calderari, in particular, declared to the queen their readiness to take up arms against the British, and disturbances ensued, in which the Neapolitan fugitives took a conspicuous part. Lord Bentinck had them sent to Naples, where they became active in the secret associations against Murat; and, on this occasion, one of the old societies, which had hitherto borne the name of Trinitarians, assumed that of Calderari. When it was proposed, in the ministry of 1816, to take strong measures against them, as the remains of the party of 1799, prince Canosa was for upholding the party, not for any selfish reason, but from the belief that they were a necessary counterpoise to the more numerous and formidable Carbonari. The society, however, has never adopted the name of Calderari of the counterpoise; and the story of the distribution of muskets is contradicted by prince Canosa, in the publication abovementioned. The Calderari, who, according to the above accounts, appear to be a continuation of the body got together by cardinal Ruffo, in 1799, are composed, almost entirely, of the lower classes, and, hence, not so much has been published by them, as by the Carbonari. A single unimportant publication, by the jurist Pasqu Tonelli (Breve Idea della Carbonaria, a Origine nel Regno di Napoli, suo Scopo, sua Persecuzione e Causa che fe' nascere la Setta de' Calderari, Naples, 1820), has a notice of them.

CALDERON. Don Pedro Calderon de

la Barca Henao y Riano, descended from an ancient family, was born at Madrid, Jan. 1, 1601, received his early education in the Jesuits' college of his native city, and studied at Salamanca, where he devoted himself chiefly to history, philosophy and jurisprudence. His poetical genius early discovered itself. Before his 14th year, he had written his first play, El Carro del Cielo (vol. 9 of his works). His talent for this species of poetry, which has brought his name down to posterity, and, perhaps, his powers of invention in the preparation of entertainments for festivals, soon gained him friends and patrous. When he left Salamanca, in 1625, to seek employment at the court of Madrid,many noblemen interested themselves in bringing forward the young poet. But, having an inclination for the military profession, he entered the service in 1625, and bore arms with distinction for 10 years in Milan and the Netherlands. In 1636, he was recalled by Philip IV, who gave him the direction of the court entertainments, and, in particular, the preparation of plays for the court theatre. The next year, he was made knight of the order of San Jago, and served in the campaign in Catalonia. The unexpected termination of the war restored him again to his peaceful occupation. The king now conferred on him a monthly pension of 30 escudos de oro; but he still employed his talents with unintermitted industry in composing for the theatre and the church. The king spared no cost in the representation of his theatrical pieces. Ten years after, in 1651, he procured permission from the order of San Jago to enter the clerical profession, and, in 1653, obtained a chaplain's office in the archiepiscopal church at Toledo, without quitting, however, his former occupation. But, as this situation removed him too far from court, he received, in 1663, another at the king's court-chapel (being still allowed to hold the former); and, at the same time, a pension was assigned him from the Sicilian revenue. His fame greatly increased his income, as he was solicited by the principal cities of Spain to compose their autos sacramentales, for which he was liberally paid. He bestowed particular pains on the composition of these pieces, and, in fact, eclipsed all that the Spanish literature, so rich in this department of fancy, had hitherto produced. These subjects were particularly suited to his religious turn of mind; and he set a peculiar value on his performances of this kind, so as even to disparage his other works, which

deserve no mean reputation. Religion is the ruling idea, the central point, of his poems. Whatever subject he handles, he exhibits true poetical genius. Even allowing that he is inferior in richness of invention to Lope de Vega, he certainly excels him in fineness of execution, elevation of feeling, and aptness of expres sion. If we find in him much that is foreign to our modes of thinking and feeling, to our accustomed views and manner of expression, we shall have occasion much oftener to admire his unrivalled genius. The Spanish nation esteem C. among the greatest poetical geniuses. Many faults in his writings are to be attributed to the age and circumstances of the author. Among his dramatic works are many pieces of intrigue, full of complicated plots, and rich in interesting incidents. There are, besides, heroic comedies and historical plays, some of which merit the name of tragedies. To this class belongs the Constant Prince, which deserves an honorable place among romantic tragedies of the first rank. Besides these, C. has left 95 autos sacramentales, 200 loas (preludes) and 100 saynetes (farces). He wrote his last play in the 81st year of his age. The smaller poems of C., his songs, sonnets, ballads, &c., notwithstanding the applause which they received from his contemporaries, are now forgotten; but his plays have maintained their place on the stage even more than those of Lope de Vega. The number of his collected plays amounts to 128. He wrote, however, many more, some of which were never published. The most complete edition of his works is that published by D. Juan de Vera Tassis y Villarroel (Madrid, 1685, 9 vols.). A. W. Schlegel and Gries have given masterly translations of his pieces into German, The former has published 5 plays in 2 vols. (Berlin, 1803-1806); the latter, 10 plays in 5 vols. (Berlin, 1815-1822). These were followed by the translations of baron Malsburg, of which 6 vols, (Leipsic, 1819-1825) have appeared, Göthe and Schlegel have the merit of having opened the German stage to the genius of C., as Schröder, before them, had done to that of Shakspeare. The Constant Prince shows, perhaps, in the highest degree, the skill of C. as a tragic poet. It turns on one of the most perplexing of all subjects, viz. the idea of destiny, managed in a truly poetical way, in a tragedy terminating happily. The great fertility of C.'s invention has heaped up an abundance of materials, from which foreign