CAL 



GAL 



Genus III. 



11 



12 



It becomes a question of great import- 

 ance 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 un- 

 questionably the most abundant, it is no 

 doubt from the chemical action they ex- 

 ert 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 ener- 

 gy than an alkaline solution of similar 

 strength, in destroying the aggregation 

 of urinary concretion. Mr. Murray bears 

 his testimony to the same fact : " I ob- 

 served," 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 dissolv- 

 ed, the liquor, after a short time, giving 

 a copious white precipitate with muriatic 

 acid ; but the remaining calculus preserv- 

 ed its aggregation, apparently without 

 much alteration, the external layer hav- 

 ing been merely removed ; while a cal- 

 culus 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 pene- 

 trated ; its cohesion was subverted ; it 

 presented a kind of loose scaly appear- 

 ance, and the least touch marie 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 di- 

 rected to this operation than to the ef- 

 fect 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 unquestion- 

 ably are, it would appear from these ob- 

 servations to be superior to them as a 

 solvent.*' 



CALCULUS denotes a method of com- 

 putation, 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. 

 C uric acid, urate of ammonia, earthy phos 

 2 phates, and si lex. 



CALCULUS specialist or literalis. See AL- 



GEBHA. 



CALCULUS, differ 'entialis, 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 infinite- 

 ly small quantity, or infinitesimal, is a 

 portion of a quantity less than any assign- 

 able one ; it is therefore accounted as no- 

 thing; and hence two quantities, only dif- 

 fering by an infinitesimal, are reputed 

 equal. The word infinitesimal is merely 

 respective, and implies a relation to ano- 

 ther quantity ; for example, in astronomy 

 the diameter of the earth is an infinitesi- 

 mal in respect to the distance of the fix- 

 ed stars. Infinitesimals are likewise call- 

 ed differentials, or differential quantities, 

 when they are considered as the differ- 

 ence of two quantities. Sir Isaac New- 

 ton 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 sur- 

 face. The calculus differentialis, there- 

 fore, and the doctrine of fluxions, are the 

 same thing, under different names, the 

 latter given by Sir laac Newton, and the 

 former by Mr. Leibnitz, who disputes 

 with Sir Isaac the honour of the discove- 

 ry. There is, however, one difference 

 between them, which consists in the man- 

 ner of expressing the differentials of 

 quantities : Mr. Leibnitz, and most fo- 

 reigners, express them by the same let- 

 ters as variable ones, prefixing only the 

 letter d : thus the differential of x is call- 

 ed d x, and the differential of y,dy: and 

 dx is a positive quantity, if x continually 

 increase ; and a negative quantity, if x de- 

 crease. We, on the other hand, follow- 

 ing Sir Isaac Newton, instead of dx vvrite 

 x', (with a dot over it,) and instead ofdy, 

 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 ex- 

 ponential quantities, and summing up the 

 differentials of exponential quantities. 

 IJy an exponential quantity is meant, a 



