CALCULUS. 



firft, in which one of the variable quantities is regarded as a 

 fiindion of the other, we fhall employ, after the manner of 

 La Grange, the cliarafterillic J ; and we fhall fiippofe, with 

 him, that, when_y changes only hy virtue of the change of 

 ,v which becomes .\- -J- dx, its difftreiitial is dy : but that, 

 when the relation of y and x varies, thefe two ouantities 

 become refpeiStivcly x-^lx, y-\riy ; and we note by the name 

 of variations, the ip.cremcnts ^.v and dy. 



" Hence it follows that, as dit =: — .I'x + dy, 



dx dy 



u being a fimflion of .v and_)', 



nx oy 



" In applying this to the example •^' „e mua regard 



dx 



dy 



-T as a fundion of x and y ; vvh-.Mice it refiilts that 

 'dx dxSv . / dx 



and . 



dy - dy' ^ [ dy ) 



(4) = 



dyldx 



(Ixoiit 



-Jxdiy 



dy' dy' 



for idx =: dox, ady r: d'Sy. — ." 



M. La Croix then proves idx = dlx. Sec. After the 

 methods for finding the variations of any fundtion whatever, 

 is given the application of the calculus to the problems of 

 maxima and minima. 



Calculus Ideralis, or Hi eral C.M-cvhvs,, is the fame with 

 fpecions arithmetic, or algebra, fo called, from its ufing the 

 letters of the alphabet : in contradillinttion to nnmeraj 

 arithmetic, which ufes figures. 



In the literal calculus, given quantities are exprcffed by 

 the firft letters, a,b,c,d; and quantities fought by the lail 

 z,y, X, &c. Equal quantities arc denoted by the fame letters. 

 See Algebra. 



Calculus, in Mcd'ic'me, the difeafe of the ftone in the 

 bladder or kidneys. The calculus in the bladder is called 

 lilh'iiifis ; and in the kidneys, uephritis. See Stohe. 



Calculus, Bdiary. Small, hard, roundifh, concrete 

 fublfances are often found in the gall bladder, or in the 

 dufts leading from the liver and gall-bladder to the intelHne, 

 which occafion in their paffage moll acute pain to man, and 

 probably other animals, and have attrafted fomc attention 

 from chemifts. 



Bihary calculi [or galljlones, as they are alfo termed) vary 

 both in external appearance, and in chemical propertie-i 

 The colour is generally green or yellowiOi-brown, fometimes* 

 though rarely, vvlute ; in ihape they are molUy oblonp-, often 

 tuberculated. When cut through, they moll frequently 

 confift of a radiated femi-cryftalline mafs, internally often re- 

 fembhng fpcrmaceti, coated with fevrral concentric lamina 

 1 he radiated part is reoilly white and tallelefs ; the lami- 

 sated i-i fometimes bitter. 



Gall-ftones arc diftinguifhed for their lightncfs and irflam- 

 mabihty, few of them being fo heavy as to fink in water- 

 and when put to a lighted candle, moft of them melt like 

 wax, and burn with a very bright flame, and very httle am- 

 momacal fmell. From the infinite minute varieties in eall- 

 ^ones, no natural arrangement is indicated, but themoft im- 

 portant differences, (hewn by chemical analyfis, rell upon the 

 proportion of the radiated, cryflallized, central part, and the 

 general lightnefs and inflammability. 



The radiated gall-ftones are largely foluble in oil of tur- 

 pentine, and in all the effential oils by heat. Alcohol when 

 cold has but httle aflion, but when boiling it dilTolves almoft 

 all the inflammable part of the calculus, leaving an eajthy 



refidue behind. On cooling, this folutfon depofits very co. 

 pious fpecular cryflals, ilrongly refembling thofe of fperma. 

 ceti treated in this way, and this fingular fubftance forms by 

 far the mofl curious part of theie morbid concretions. 

 Pouletier and Fourcroy have both attended minutely to this 

 matter. The former dilcovered fimilar cryllalh'ne concre- 

 tions in a piece of liver long hung ;ip in a drv air. 



When the hot alcoholic folution of tiiis concrete is 

 dropped into a large quantity of water, a white fiacculent 

 prtcipitate is formed, which when dritd is found to be of a 

 refinous nature. The fupernatant liquor by faturation with 

 muriatic acid and evaporation gives murlat of foda, by which 

 it is evident that the foda of the bile remains in union with 

 its refin during its converfion into biliary calculus; but the 

 chemical nature of this converfion is very obfcure. 



Ether diffoives the fpermaccti-like concrete as well as oil 

 of turpentine, and depofits the greater part on cooling. 

 Hot nitric acid is decompofed on it, and nitrous gas is givfn 

 out^ and when cool, a white oil is found concreted on the 

 furnace of the acid, now no longer of a cryftalline texture, 

 but altered in its properties, bel'ng brittle and friable like I 

 refin, and when re-diffolved in alcohol it has loft its powr of 

 cryftalhzing by cooling. It is ftill, however, infoluble in 

 water. Ether diffoives this altered concrete as it did when 

 m Its natural ftate, but water now fepanites it in the form of 

 drops of oil. Saunders on the Bile. Fourcrov. Boftock i:» 

 Phil. Journ. vol. vi. 



Calculus Miner-v^r, among the yjndcnt Laiiyers, de- 

 noted the decifion of a caufe, wherein the judges were equally- 

 divided. The exprefiion is taken from the hiftory of Oref'les 

 reprcfented by ^fchylus and Euripides; at whofe trial' 

 before the Areopagites for the murder of his mother, the' 

 votes being equally dividtd for and againft him, Minerva 

 interpofed, and gave the cafling vote, or calculus, in his 

 behalf. 



M. Cramer, profeffor at Marpurg, has a difconrfe exprefs 

 " De Calculo Minerva: ;" wherein he maintains, that all the' 

 effect an entire equality of voices can have, is to leave the 

 caufe injiatu quo. 



Calculus Tihirt'mus, a fort of figured ftone, formed in 

 great plenty about the catarafts of the Anio, a-^d other rivers- 

 in Italy ; of a white colour, and in fiiapt oblong, round or 

 echinated. They are a fpechs of tl,e >>/* latide^, ^nd 

 generated hke them ; and fo hke fugar-plums in the whole , 

 that It IS a common jeft at Ro.r-e to deceive the unex- 

 perienced by ferving them up at deferts. 



Calculus, urinary. See Urinary calculi. 

 CALCUTTA, in Geography, a city of Hindooflan, and 

 capital of Bengal, and of all the Britifh poffefTions in India, 

 IS htuated on the river Hoogly, the weftern arm of the 

 Cjranges, atthediftanceofabout J oo miles from the fea - and 

 the river is navigable up to the town, for the largcft ihips that 

 .^l ,„ ^^^ "'^'^'^^ '^ P'^'^'^^ '" N. lat. 22° 3 3'. E Jong. 

 ^8' 27' 4_5". It is comparatively a modern city, having been 

 built towards the clofe of the 17th century on the fite of 

 the village called Govindpour. The Englifh fadory ob- 

 tamed leave to remove hither from Hoogly in the year ,68a 

 (fee BrNCAL), when Mr. Channock was agent in Benoal ■ 

 and who fixed upon this fpot for the Bntilh emporium 

 though from feveral circumllances it was at that time the 

 moft unhealthy he could have chofen. For 3 miles to the 

 north-eaft there was a falt-water lake, that overflowed in the 

 months of September and October; and in the two follow- 

 ing months, when thofe floods withdrew, prodigious quan- 

 tuies of fift, were left dry, the putrefaSion of which was 

 luppofed to affed the air; and this, together with the fetid 

 putrid exhalations from the ooze and flime, conveyed by the 

 north-eaft wind to Fort WUliam, occafioned a yearly morta- 



lity. 



