Page:The American Cyclopædia (1879) Volume III.djvu/576

570 CALCULI ries and valves about the heart ; by the saliva in the mouth, in the substance of the cheek as well as upon the teeth ; and by the bile in the gall bladder. They are found in the tissue of the lungs and in the bronchial glands, and in gouty persons under the skin, about the joints of the fingers and toes, &c. But their most common occurrence is in the kidney, bladder, and urinary passages, left by decomposition of the complex fluid of these organs. Urinary calculi are variously composed, and may be classed as those which are soluble in caustic potash or soda, and those which are insoluble. ' One of the most common of the former class is the uric acid calculus. This ingredient in nrine, when secreted in undue proportion, forms minute red crystals and red sand, which are passed in a solid state. If retained, they increase in size and produce the disease called the stone. The acid, if greatly in excess, is deposited in successive layers, forming yellow- ish-colored stones of such size that they can be removed only by the operation either of lith- otomy, which is making an incision into the bladder and removing the stone by forceps, or of lithotrity, which is the introduction of an instrument into the urethra, by which the stone is broken, so that it may be removed by voiding it in fragments. If the uric acid is not in excess, the concretion once produced is liable to be covered with an incrustation of an ammonio-phosphate of magnesia or of a phos- phate of lime, and thus increase in size. These phosphates, when deposited alone, as is some- times the case, are included among the insoluble calculi, of which other varieties are produced in the form of oxalate of lime, called, from their resemblance to the mulberry, the mul- berry calculus, of a brown color and mamelon- ated form, which are sometimes nuclei for the uric acid calculus ; and again as carbonate of lime, which are of rare occurrence. Other calculi, which belong to the soluble class, are formed with uric acid in combination with ammonia ; others of cystic oxide or cystine, and of xanthic oxide or xanthine. These are distinguished from each other by their various shades of color, different degrees of hardness, and their peculiar reaction with different chemical agents. Concretions of uric acid are not uncommon with children, and recur in the same persons in advanced age. Those are most liable to them who suffer from dyspeptic and gouty tendencies. When this is observed, serious trouble may in most cases be obviated by particular attention to the diet, and by the use of proper medicines ; but if the concretions are allowed to increase till they are too large to be passed, there is then no recourse but an operation ; for, once formed, they are never afterward absorbed, nor has any solvent for them been discovered upon which dependence can be placed. Calculi deposited by the bile in the gall bladder, the liver, and its ducts, are known as biliary concretions and as gall stones. They are generally of a round or oval form, CALCULUS and of various colors, as white, yellow, brown, and dark green. Usually they are soft, and sometimes brittle and easily pulverized to an unctuous powder ; their size has in some cases reached that of a walnut. In man they gen- erally consist of cholesterine, more or less in- termixed with the mucus and coloring matter of the bile ; but some have been found consist- ing of carbonate of lime V2'7 per cent., phos- phate of lime 13-51, and mucus 10'81. In animals their composition is very variable, some consisting of the same ingredients as are found in those of men. In the stomachs of ruminating animals they are found in the form of balls of hair, earthy matter, and food, ce- mented around some hard central nucleus. CALCULUS, in mathematics, a mode of calcu- lating. In this broad signification we may speak of common arithmetic and algebra as forms of a calculus. Thus also trigonometry is called the calculus of sines, and the doctrine of chances is spoken of as the calculus of proba 1 bilities. The branches of mathematics to which the term is more especially applied are the dif- ferential calculus, integral calculus, calculus of variations, to which we may add the calculus of imaginaries, that of residuals, and that of quaternions. The IMAGINARY CALCULUS inves- tigates the nature of quantities which are re- quired to fulfil apparently impossible conditions. It has been discovered by means of this calcu- lus that every absurdity in geometry can be reduced to an attempt to measure a straight line in a direction different from that of its length ; and that every algebraic absurdity can be represented by one symbol, always capable of this one geometrical interpretation. This extensively useful calculus has been chiefly de- veloped by M. Cauchy. The RESIDUAL CAL- CULUS investigates cases of apparent impossibil- ity, arising from the attempt to measure a quan- tity which has become immeasurably great. Imaginaries and residuals are chiefly employed as subsidiary to the operations of the higher species of calculus. The DIFFERENTIAL CALCU- LUS, called by the English fluxions, is the most valuable of mathematical modes, from the great variety of subjects to which it is ap- plicable, and from the strength of its solvent power. Its discovery is justly assigned to the latter part of the 17th century, although there were doubtless some hints of it among earlier writers. Archimedes had demonstrated the area of a parabola to be two thirds of its circumscribing rectangle, and also the truth of his celebrated propositions concerning the sphere and the cylinder. Kepler, seizing the spirit of his method, introduced the words infinite and infinitesimal into geome- try. Cavalieri, Roberval, and Fermat en- larged the application of his mode. In the mean while Vieta, Cardan, Harriot, and others had improved algebra, and Descartes had ap- plied it to geometry by his invaluable system of variable coordinates. Thus the way was pre- pared for Leibnitz and Newton, who, iudepen-