carefuly computed all the eclipses of the sun and moon that had happened since the christian æra, which were printed in the work, entitled "L'Art de verifier les Dates," &c. Paris, 1750, in 4to. He also compiled a volume of astronomical ephemerides for the years 1745 to 1755; another for the years 1755 to 1765; and a third for the years 1765 to 1775; as also the most correct solar tables of any; and an excellent work, entitled "Astronomia Fundamenta novissimis Solis et Steliarum Observationibus stabilita."

Having gone through a seven year's series of astronomical observations in his own observatory in the Mazarine College, he formed the project of going to observe the southern stars at the Cape of Good Hope; being countenanced by the court, he set out upon this expedition in 1750, and in the space of two years he observed there the places of about 10,000 stars in the southern hemisphere, that are not visible in our latitudes, as well as inany other important elements, viz. the paral. laxes of the sun, moon, and some of the planets, the obliquity of the ecliptic, the refractions, &c. Having thus executed the purpose of his voyage, and no present opportunity offering for his return, he thought of employing the vacant time in another arduous attempt; no less than that of taking the measure of the earth, as he had already done that of the heavens, whence he discovered, that the radi of the parallels in south latitude are not the same length as those of the corresponding parallels in north latitude. About the 23d degree of south latitude he found a degree on the meridian to contain 342222 Paris feet. The court of Versailles also sent him an order to go and fix the situaation of the isles of France and of Bourbon.

M. de la Caille returned to France in the autumn of 1754, after an absence of about four years; loaded, not indeed with the spoils of the East, but with those of the southern heavens, before then almost unknown to astronomers. Upon his return, he first drew up a reply to some strictures which the celebrated Euler had published relative to the meridian; after which he settled the results of the comparison of his observations for the parallaxes, with those of other astronomers: that of the sun be fixed at 9"; of the moon at 56′ 56"; of Mars in his opposition, 36"; of Venus 38". He also settled the laws by which astronomical refractions are varied by the different density or rarity of the air, by heat or cold, and by dryness or

moisture. And, lastly, he shewed an easy and practicable method of finding the longitude at sea by means of the moon. His fame being now celebrated every where, M. de la Caille was soon elected a member of most of the academies and Societies of Europe, as London, Bologna, Petersburgh, Berlin, Stockholm, and Gottingen. He died in 1762, aged 49.

CAISSON, in the military art, a wooden chest, into which several bombs are put, and sometimes only filled with gunpowder; this is buried under some work, whereof the enemy intend to possess themselves, and when they are masters of it, is fired, in order to blow them up.

CAISSON is also used for a wooden frame, or chest, used in laying the foundations of the piers of a bridge.

The practice in building in caissons is a method sometimes adopted in laying the foundation of bridges in very deep or rapid rivers. There are large hollow vessels, framed of strong timbers, and made water tight, which being launched and floated to a proper position in the river, where the ground has been previously excavated and levelled, are there sunk. The piers of the bridge are then built within them, and carried up above, or nearly to the level of the water, when the sides of the caisson are detached from the bottom, and removed; the bottom, composed of a strong grating of timber, remaining and serving for a foundation to the pier. The most considerable work, where caissons have been used, was in the building of Westminsterbridge; of these, therefore, a particular account may be acceptable. Each of the caissons contained 150 loads of fir timber, and was of more tonnage than a man of war of 40 guns; their size was nearly 80 feet from point to point, and 30 feet in breadth; the sides, which were 10 feet in height, were formed of timbers laid horizontally over one another, pinned with oak trunnels, and framed together at all the corners, except the salient angles, where they were secured by proper iron-work, which, being unscrewed, would permit the sides of the caisson, had it been found necessary, to divide into two parts. These sides were planked across the timbers, inside and outside, with 3-inch planks, in a vertical position. The thickness of the sides was 18 inches at bottom, and 15 inches at top; and in order to strengthen them the more, every angle, except the two points, had three oaken knee timbers, properly bolted and secured. These sides, when finished, were fasten

ad to the bottom, or grating, by 28 pieces of timber on the outside, and 18 within, called straps, about 8 inches broad, and about 3 inches thick, reaching and lapping over the tops of the sides; the lower part of these straps were dove-tailed to the outer curb of the grating, and kept in their places by iron wedges. The purpose of these straps and wedges was, that when the pier was built up sufficiently high above low-water mark, to render the caisson no longer necessary for the masons to work in, the wedges being drawn up gave liberty to clear the straps from the mortices, in consequence of which the sides rose by their own buoy ancy, leaving the grating under the foundation of the pier. The pressure of the water upon the sides of the caisson was resisted by means of a ground timber or ribbon, 14 inches wide and 7 inches thick, pinned upon the upper row of tim bers of the grating; and the top of the sides was secured by a sufficient number of beams laid across, which also served to support a floor, on which the labourers stood to hoist the stones out of the lighters, and to lower them into the cais

son.

The caisson was also provided with a sluice, to admit the water. The method of working was as follows: A pit being dug, and levelled in the proper situation for the pier of the same shape of the caisson, and about five feet wider all round, the caisson was brought to its position, a few of the lower courses of the pier built in it, and sunk once or twice, to prove the level of the foundation; then, being finally fixed, the masons worked in the usual methods of tide-work. About two hours before low water, the sluice of the caisson, kept open till then, lest the water, flowing to the height of many more feet on the outside than the inside, should float the caisson and all the stonework out of its true place, was shut down, and the water pumped low enough, without waiting for the lowest ebb of the tide, for the masons to set and cramp the stonework of the succeeding courses. Then, when the tide had risen to a considerable height, the sluice was opened again, and the water admitted; and as the caisson was purposely built but 16 feet high, to save useless expence, the high tides flowed some feet above the sides, but without any damage or incon. venience to the works. In this manner the work proceeded till the pier rose to the surface of the caisson, when the sides were floated away, to serve the same purpose at another pier.

CAKILE, in botany, sea-rocket, a genus of the Tetrandria Siliculosa class and order. Silicle lanceolate, somewhat four-sided, consisting of two deciduous joints, without valves, and each containing a single seed: the lower joint with a tooth on each side at the tip. There are two species, viz. C. maritima, found on the sea-coast of England; C. Ægyptiaca, a native of Italy and Egypt.

CALAGUALA root, brought from America for medicinal purposes, and has acquired considerable reputation on the continent. It is supposed to be obtained from a species of polypodium. Its colour is brown, and partly covered with scales, like the roots of fern, and is hard and difficult to reduce to powder. It is asserted by Vauquelin that it contains

The mode of analysis may be thus described. Alcohol dissolves the resin and sugar. By evaporating the solution to dryness, and treating the residue with water, the sugar is separated, and the resin left. Water dissolved the gum and the muriate of potash, which were obtained by evaporation. Diluted nitric acid dissolved the starch and colouring matter, and let fall the former, when mixed with four times its bulk of alcohol. The woody fibre remained, which, when incinerated, left carbonate of lime, muriate of potash, and a little silica. As the decoction reddened vegetable blues, it is possible that the lime was in combination with malic acid.

CALAMANCO, a sort of woollen stuff manufactured in England and in Brabant. It has a fine gloss, and is chequered in the warp, whence the checks appear only quite plain, others have broad stripes on the right side. Some calamancoes are adorned with flowers; some with plain broad stripes, some with narrow stripes, and others watered.

CALAMARIÆ, in botany, the name of a third order in Linnæus's "Fragments of a Natural Method." This order will be easily distinguished from the family of grasses, by recollecting, 1. That the base of the leaf, which embraces the stalk like a glove, has no longitudinal aperture in plants of this order, but is perfectly entire: 2. The stalk is generally triangular,

and without knots or joints: 3. The flow ers have no petals.

CALAMIÑARIS, or lapis calaminaris, a mineral containing zinc, united with iron and other substances. It is heavy, hard, and brittle, or of a consistence between stone and earth. The colour is whitish or grey, sometimes inclining to yellow, and sometimes to black. It is found in great plenty in many parts of Europe; but the best is obtained in this country. It seldom lies deep, and in many parts it is found mixed with lead ores. Calamine is the only true ore from which zinc is obtained by calcination. See ZINC.

CALAMUS, in botany, a genus of the Hexandria Monogynia class and order. Natural order Tripetaloideæ. Palma, Jussieu. Essential character: calyx sixleaved; corolla none; berry dried, oneseeded, imbricate backwards. According to Martyn, there is but one species, though Loureiro has discriminated six; iz. C. rotang, rattan, has a perennial stem, quite simple or unbranched, with out any tendrils: leaves alternate, sublanceolate, quite entire, scarcely a foot long: flowers commonly hermaphrodite, almost terminating on one spadix or more. The rattan seems to form the connecting link between the palms and the gramine ous plants, having the flower of the former, but the habit of the latter. The palm called raphia has the embryo placed in the same manner, namely, on a lateral cavity of the horny albumen; in the fruit and spadix it agrees nearly with this in form, only they are much larger: the flowers differ but little, except that they are monoecous, as the flowers of the rat tan probably are.

CALCAR, corolla, in botany, the spur of the corolla. The nectarium, so called, which terminates the corolla behind, like a cock's spur, in valerian, orchis, violet, balsam, larkspur, &c.

CALCEOLARIA, in botany, a genus of the Diandria Monogynia class and order. Natural order of Corydales. Scrophulariz, Jussieu. Essential character: corolla ringent, inflated; capsule two-celled, twovalved; calyx four-parted, equal. There are seven species, of which C. pinnata, pinnated slipper-wort, has an annual root; stem erect, two feet high, round, brittle, with a thick down, and from sixteen to twenty joints; flowers from each top and stalk double; corollas yellow; upper-lip subglobular, inflated, emarginate in front, with a cleft for the prominent anthers; capsule thin, from a swelling base, dimin

ishing to a pyramidal top; seeds very small, almost cylindric, sreaked : native of Peru, in moist places.

CALCINATION, in chemistry. A substance is said to be calcined, when it has been exposed to heat of a sufficient intensity to drive off every thing volatile, but short of that by which it might be fused: a calyx, therefore, was formerly understood to be a pulverulent substance, no longer combustible, or capable of further alteration by fire than that of vitrification. As most metals were found to be reducible to such a form by the continuance of the melting heat, the term "calces of metals" was; long appropriated to them, and is still partially retained, though it has been chiefly supplanted by the more characteristic appellation of oxide, which expresses the peculiar change that occurs in metallic bodies by the absorption of oxygen Calcination expresses the mode, by which, in metals, this change is produced, and oxydation the circumstance of change. It is, however, improper to consider the term calcination as synonymous with oxydation, even in speaking of metals, since the former term implies the agency of fire; whereas oxydation may be produced as well by the action of acids, as by heat and air.

CALCITRAPA, in botany, a genus of the Tetrandria Monogynia class and or der; calyx four-cleft; corolla four-cleft; berry four-seeded. There are twelve species, found in both Indies, Cochin-China, and Japan.

CALCULATION, the act of comput ing several sums, by adding, substracting, multiplying, or dividing. See ARITH

METIC.

An error in calculation is never protected or secured by any sentence, decree, &c. for in stating accounts it is always understood that errors of calculation are excepted.

CALCULATION is more particularly used to signify the computations in astronomy and geometry, for making tables of logarithms, ephemerides, finding the time of eclipses, &c.

CALCULATION, in music: many eminent mathematicians suppose that a good ear, and strong hand on instruments, where the tone depends on the performer, are the musician's best guide, without having recourse to calculation. On this subject the celebrated D'Alembert says, "It is an achievement of no small im portance, to have deduced the principal facts to a system from one experiment,

viz. the harmonies of a single string. Calculation may, indeed, facilitate the intelligence of certain points of theory, such as the relation between the tones of the gamut and temperament; but the calculation necessary for treating these two points is so simple and trifling, that it merits no display. Let us not, therefore, imitate those musicians, who believe themselves geometricians, or those geometricians, who fancy themselves musicians, and in their writings heap figures on figures, imagining, perhaps, that this display is necessary to the art." See D'ALEMBERT.

CALCULI, biliary, in chemistry, are small stones found in the gall-bladder, and probably formed by the changes produced on the bile while it remains in that organ. These are not uniform in their appearance, but vary in colour, texture, and hardness. The most common are of a lamellated structure, resembling spermaceti, disposed in crystalline laminæ, which have a close resemblance in their properties to ADIPOCIRE, which see. Biliary calculi are soluble in oil of turpentine; but more completely in the fixed alkalies, by which they are reduced to a saponaceous state. Ammonia, unless in the boiling state, has little effect upon them. Nitric acid dissolves them, forming a liquid similar to the oil of camphor, which becomes concrete, and without any crystalline structure, and is more soluble in ether, and the alkalies, than the original matter. This substance is contained, in a greater or less degree, in nearly all the human biliary calculi: hence they partake of its properties: are fusible, inflammable, and more or less soluble in the re-agents which dissolve it. Other calculi are occasionally found in the gall-bladders of quadrupeds, which have been supposed to consist of inspissated bile; they are irregular, and of vaSpecies 1. Calculus of

Genus I.

2.

rious forms. Gall-stones in general are distinguished for their lightness and inflammability, few of them being so heavy as to sink in water, and when put to a lighted candle they usually melt like wax, and kindle with a bright flame, attended with an ammoniacal smell.

CALCULI, urinary, concretions formed in the kidney or bladder, and composed, in greater or smaller proportions, of the following substances, viz. uric acid, urate of ammonia, phosphate of lime, phosphate of ammonia and magnesia, oxalate of lime, silex, and animal albumen. These principles being more or less common, and in different proportions, give rise to numerous varieties.

The calculi most common are those composed of uric acid; they are generally of a brown or yellowish colour, smooth on the surface, and with a texture compact or radiated; they are perfectly soluble in alkaline solutions, and give a red colour when treated with nitric acid. Dr. Wollaston has arranged the urinary calculi under four species, viz. 1. The uric acid concretion: 2. The fusible calculus, or phosphate of ammonia and magnesia: 3. The mulberry calculus, or oxalate and phosphate of lime: And, 4. the bony earthy calculus, composed of phosphate of lime, which forms the basis of bone. Fourcroy and Vauquelin have given a different arrangement; they af firm that in all calculi there exists a quantity of animal matter, which appears to connect their particles; but independently of this, which is common to the whole, they compose three genera; the first contains three species, each formed of one ingredient; the second comprises seven species, formed of two ingredients each and in the third there are two species, consisting of three or four ingredients; this system is exhibited in the following table: uric acid.

It becomes a question of great importance and interest to mankind, how far the solution of calculi in the bladder may be practicable. From what has been said, it is evident, that, being of very different chemical composition, the same solvent cannot be applicable to all of them. Long experience has sufficiently established the advantage of alkaline remedies; and as the calculi composed of uric acid are unquestionably the most abundant, it is no doubt from the chemical action they exert upon it that the benefit is derived. Lime, under the form of lime-water, has been employed as a solvent: and from some experiments of Dr. Egan, it should seem that lime-water acts with more energy than an alkaline solution of similar strength, in destroying the aggregation of urinary concretion. Mr. Murray bears his testimony to the same fact: "I observed," says he, "this effect strikingly displayed in a comparative trial which these experiments led me to make. In a dilute solution of pure potassa, a calculus of the uric acid kind was in part dissolved, the liquor, after a short time, giving a copious white precipitate with muriatic acid; but the remaining calculus preserved its aggregation, apparently without much alteration, the external layer having been merely removed; while a calculus of a similar kind, and discharged from the person, immersed in lime-water, became in a few days white and spongy : it appeared at length to be entirely penetrated; its cohesion was subverted; it presented a kind of loose scaly appearance, and the least touch made it fall down. The lime probably operates more upon the albumen or animal matter, which appears to serve as the cement or connecting substance, than upon the uric acid; and in endeavouring to discover solvents for these concrections, our views ought perhaps rather to be directed to this operation than to the effect on the saline matter. If lime, when received into the stomach under the form of lime water, can be secreted by the kidneys, as the alkalies unquestionably are, it would appear from these observations to be superior to them as a solvent."

CALCULUS denotes a method of computation, so called from the calculi, or Counters, anciently used for this purpose. VOL. III.

uric acid, or urate of ammonia, earthy phosphates, and oxalate of lime.

uric acid, urate of ammonia, earthy phos. phates, and silex.

CALCULUS specialis, or literalis. See AL

GEBRA.

CALCULUS, differentialis, is a method of differencing quantities, that is, of finding an infinitely small quantity, which, being taken an infinitive number of times, shall be equal to a given quantity. An infinitely small quantity, or infinitesimal, is a portion of a quantity less than any assignable one; it is therefore accounted as nothing; and hence two quantities, only dif fering by an infinitesimal, are reputed equal. The word infinitesimal is merely respective, and implies a relation to another quantity; for example, in astronomy the diameter of the earth is an infinitesimal in respect to the distance of the fixed stars. Infinitesimals are likewise called differentials, or differential quantities, when they are considered as the difference of two quantities. Sir Isaac Newton calls them moments, considering them as momentary increments of quantities; for instance, of a line generated by the flux of a point, of a surface by the flux of a line, or of a solid by the flux of a surface. The calculus differentialis, therefore, and the doctrine of fluxions, are the same thing, under different names, the latter given by Sir Iaac Newton, and the former by Mr. Leibnitz, who disputes with Sir Isaac the honour of the discovery. There is, however, one difference between them, which consists in the manner of expressing the differentials of quantities: Mr. Leibnitz, and most foreigners, express them by the same letters as variable ones, prefixing only the letter d thus the differential of x is called d x, and the differential of y, dy: and da is a positive quantity, if x continually increase; and a negative quantity, if x decrease. We, on the other hand, following Sir Isaac Newton, instead of dx write

:

, (with a dot over it,) and instead of d y, y. But foreigners reckon this method not so commodious as the former, because, if differentials were to be differenced again, the dots would occasion great confusion; not to mention, that printers are more apt to overlook a point than a letter. See FLUXIONS.

CALCULUS exponentialis, among mathe. maticians, a method of differencing exponential quantities, and summing up the differentials of exponential quantities. By an exponential quantity is meant, a

F