Page:Cyclopaedia, Chambers - Volume 1.djvu/291

 C A L

CALATRAVA, a Military Order, infti tilted in u j8, by Sancho III. King of Caflile, on the following Occafion: The jWoon going to attack the little City Calatrava, and the Templers, who held it, furrendering it up to the King,, on a Sufpicion of their Inability to defend it, 2)icgo Felafquez, a Ciftercian Monk, but a Man of Quality, perfuaded Rai- tnond Abbat of Fitera, a Monaftery of Cijlercians, to beg Calatrava of the King. He obtain'd it ; and Rmmoiid and 2)iego put themselves in it 5 being follow'd by a great number of People, who join'd 'em out of Zeal, for the De- fence of Calatrava. The Moors abandoning the Enterprize, many of thofe who came to the Defence of the City, en- tered the Order of the Cijlercians 5 and that under a Habit more fit for Military than Monaftic Exercifes. According- ly, they began to make Excursions on the Moors $ which was the Rife of the Order of Calatrava. The firft Grand Matter was Garcias ; under whofe Government the Order was confirm 'd by Alexander III. in 1164. In 1489, Ferdinand, and Isabella, with the Confent of Pope Innocent VIII. re- mitted the Grand- M alter fhip of Calatrava to the Spanijb Crown : So that the Kings of Spain are now become per- petual Administrators thereof. The Knights bear a Crofs Gules, fleurdeliz'd with Green, &c. Their Rule and Ha- bit was originally that of the Cijlercians ; but their Drefs was a little Jhorten'd on account of their Exercifes 5 and in procefs of Time they were permitted a fecular Habit.

CALCANEUS, in Anatomy, the fame as Os Calcis r or the Heel-Bone : It lies under the Afhragallts, to which it is articulated by Ginglimus ; behind it is a large Protuberance, which makes the Heel, and into which the Tendo AchilllS is inferred.

CALCANTHUM, is Vitriol Rubify'd. Some maintain Calcanthum and Colcotbar to be the fame Thing : but to- met is of another Sentiment, and takes Calcanthum to be nothing clfe but Vitriol. See Vitriol, and Chalcitis.

CALCINATION, the Action of calcining any Matter ; i. e. of reducing it into a Calx, or a very fubtile Pouder, or even only into Afhes, by Fire ; Ibmetimes alfo termed Chymical *Ptrtverifation. Calcination is the next degree of the Power of Fire beyond that oKFufion : For when Fufion is longer continu'd, not only the more fubtile Particles of the Body it felf fly off, but the Particles of Fire likewife do infinuate themfelves in fuch Multitude, and are fo difperfed and blended throughout its whole Subftance, that the Fluidity which was firil caus'd by the Fire, can no longer fubfift : From this Union arifes a third kind of Body, which being very porous and brittle, is eafily redue'd to Pouder. For the Fire having penetrated every where into the Pores of the Body, the Particles are both hinder'd from mutual contact, and divided into minute Atoms 3 fo that they are eafily reducible into the fineft Pouder.

Obymifb, Goldfiniths, and Founders, diftinguifh two Kinds of Calcination ; the one call'd Actual, the other ^Potential. Actual Calcination, is that effected by actual Fire, of Wood, Coals, or other Fuel, rais'd to a certain Heat, according to the Nature of the Subftance to be cal- cind. Potential Calcination, is that procur'd by potential Fire, viz. by Waters, Drugs, ££r. which have, as it were, the Force of Fire 5 as Strong Waters, Corrofive Spirits, &c. Gold is calci?z'd in the Fire of a Reverberatory, with Mer- cury, and Sal Ammoniac. See Gold. Silver with common Salt and Alkali Salt. See Silver. Copper with Salt and Sulphur ; Iron with Sa] Ammoniac and Vinegar; Tin with Antimony, Lead and Sulphur ; Mercury with Aqua fortis : This laft, alfo, with moll other Minerals, calcines with tire alone, without any other Ingredient.

Calcination ^Philofopb/cal, is when Horns, Hoots, i$c. are hung over boiling Water, or other Liquor, rill they have loft their Mucilage, and are eafily reducible into Pouder.

CALCULATION, the Aft of computing feveral Sums, by adding, fubtracting, multiplying, or dividing. See A- rithmetic. An Error in Calculation is never protected or fecur'd by any Sentence, Decree, f$c. In Hating Ac- compts there is always underftood, falvo errore calculi. The Word Calculus is us'd in this Senfe, in alluiion to the Practice of the Ancients, who us'd Calculi, or little Stones, in making Computations, in taking Suffrages, and in keep- ing Accompts, &c. as we now ufe Counters, Figures, £5?c.

Calculation is particularly us'd to fignify the Compu- tations in Aftronomy and Geometry j for making Tables of Logarithms, Edipfes, Ephemerides, £?e. See Eclipse., £f?c. Calculation of Clock and Watch-Work. See Clock and Watch-work.

CALCULUS, in Medicine, the Difeafc of the Stone in the Bladder, or Kidneys 5 See Stone, Ijithotomv, £$?£. In the Bladder 'tis ufually call'd Litbiafis 5 and in the Kid- neys Nephritis; which fee. The Term is pureZtfriw, and fignifies, literally, a little Pebble, or Flint. Whence alfo, the Term Calculation. See Calculation.

C Hi j

CAL

, Calculus, or Methodus ZJiffcrentialis, in Mathema- Hcks,isa Method of differencing Quantities; or of finding an infinitely fmall Quantity, which being taken infinite times, mall be equal to a given Quantity : or, as others define it, the Arithmetic of infinitely fmall Differences between variable Quantities.

The Foundation, then, of this Calculus, is an infinitely, imall Quantity, or an Infinitefimal, which is a Portion of a Quantity, incomparable to that Quantity ; or that is lefs ?f n a "y aflignable one, and therefore accounted as nothing : the Error accruing by omitting it being lefs than any aflignable one, i. e. lefs than nothing. Hence two Quantities, only differing by an Infinitefimal, are equal. The better to con- ceive the Nature of an Infinitefimal, fuppofe, that in mea- furing the Height of a Mountain, while you are looking thro the Sights, the Wind blows off the fmalleft Grain of Duft ; the Height of the Mountain is, then, lefs by the Dia- meter of the Duft than befoK : But as the Mountain is ftill found the fame Height, whether the Duft be there or not, its Diameter has nothing to do in the prefent Cafe, and paffes for nothing, ;. e. is infinitely fmall. Thus, in Aftro- nomy, the Diameter of the Earth is an Infinitefimal, in refpect ot the Diftance of the Fix'd Stars : And the fame holds in abftraS Quantities. The Name Infinitefimal, therefore, is merely refpective, and involves a Relation tQ another Quantity ; not any real Ens or Being.

Now Infinitefimals are call'd 'Differentials, or differential Quantities, when they are confider'd as the Differences qf two Quantities. Sir jfaac Newton calls 'em Fluxions ; con- sidering them as the momentary Increments of Quantities 5 v. g. of a Line generated by the Flux of a Point ; or of » Surface by the Flux of a Line, &'c. The differential Cal- culus, therefore, and the Doctrine of Fluxions are the fame thing under different Names : The former, given by M. Leibnitz, and the latter by Sir Ifaac Newton ; each of whom lay claim to the Difcovery. See Fluxions. There is, indeed, a Difference in the manner of expreffing the Quantities, refulting from the different Views wherein the two Authors confider the Infinitefimals 5 the one as Incre- ments, the other as Differences : Leibnitz, and moll Fo- reigners, exprefs the Differentials of Quantities by the fame Letter as variable ones, only prefixing the Letter d ; thus the Differential of * is call'd dx ; and that of y, dy : Now dx is a pofitive Quantity, if a- continually increafe ; negative if it decreafe.

The Euglijh, with Sir Ifaac Newton, inftead of d x, write i (with a Dot over it) for dy, y, &c. which Fo- reigners object, againft, on account of that Confufion of Points, which they imagine arifes, when Differentials are again differene'd ; b.'fides, that the Printers are more apt to overlook a Point than a Letter.

Stable Quantities being always exprefs'd by the firft Let- ters of the Alphabet da = 0, db = 0, dc = o i wherefore d (x-\-y — a) =- dx 4- dy, and d(xy-\-a) dx — dy. So that the Differencing of Quantities is eafily perform 'd, by the Addition or Subtraction of their Compounds.

To difference Quantities that mutually multiply each other ; The .Rule is, firft, Multiply the Differentiafof one Factor into rhe other Factor, the Sum of the two Factors is the Differential fought: thus, the Quantities being xy, the Differenrkil viiWnex dy-\-y d x, i.e. d(xy) — xdy-\-ydx. Secondly, if there be three Quantities mutually multiply- ing each other, rhe Factum of the two muft then be mul- tiply'd into the Differential of the third : thus, fuppofe v xy, let vx = t, then v xy = t y ; conicquently dfvxy) == tdy+ydt: But dt = vdx-j- xdv. Thefe Values, therefore, being lubftituted in the antecedent Differential, t d y -\-y dt, the Refult is d (vx y) =v xd y -f- vy dx ~\- x y dv. Hence 'tis eafy to apprehend how to proceed, where the Quantities are more than three.

Ifone variable Quantity increafe, while the orher ydecrea- fes, 'tis evident ydx—xdy will be the Differential of x y.

To difference Quantities that mutually divide each other : The Rule is, firft, multiply the Differential of the Divifor into the Dividend, and, on the contrary, the Differential of the Dividend into the Divifor ; fubtract the laft Product from the firft, and divide the Remainder by the Square of the Divifor ; the Quotient is the Differential of the Quan- tities mutually dividing each other. See Fluxion.

Calculus Exponentialis, is a Method of differencing exponential Quantities, and fumming up the Differentials or Fluxions of Exponentials. By exponential Qiiantity, is here underftood a Power, whofe Exponent is variable; v.g, ,v v a*.

To difference an exponential Quantity : There is nothing requir'd but to reduce the exponential Quantities to Lo- garithmic ones ; which done, the differencing is manag'd as in Logarithmic Quantities : Thus, fuppofe the Differen- tial of the Exponential Quantity xy requir'd, let

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