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LEFT CALCULTTS 287 CALCUTTA similar to it in general principles, though it varies from it in some points in the method adopted in its construc- tion. It was purchased by Mr. Rath- bone, of Albany, and presented by him to the Dudley Observatory in that city. More modern calculating machines are the slide-rule, adding machines, multi- plying and dividing machines, and cash registers, which are described in detail under their several names. CALCULUS, the medical term for what is popularly known as stone. Cal- culi vary in size from a pin's head to a pigeon's egg, and even larger, and weigh from a few grains to several ounces. They derive their special name and character as well from the organs of the body in which they are found as from the constituents of which they are composed. Thus, for example, a cal- culus found in the kidney or ureter is called renal, in the bladder vesical, and so on ; but, acording to its chemical com- position, it would also be called either (1) uric (lithic) acid calculus, or (2) oxalic (mulberry) calculus, or (3) phos- phatic calculus. Calculi derived from the bile are also found in the gall-blad- der, and in the biliary and intestinal ducts, where they receive the name of gall-stones, or biliary calculi. Those found in the salivary glands are called salivary calculi. CALCULUS, a branch of mathemat- ical science. The lower or common anal- ysis contains the rules necessary to calculate quantities of any definite mag- nitude whatever. But quantities are sometimes considered as varying in mag- nitude, or as having arrived at a given state of magnitude by successive varia- tions. This gives rise to the higher analysis, which is of the greatest use in the physico-mathematical sciences. Two objects are here proposed: First, to descend from quantities to their ele- ments. The method of effecting this is called the differential calculus. Second, to ascend from the elements of quanti- ties to the quantities themselves. This method is called the integral calculus. Both of these methods are included un- der the general name infinitesimal, or transcendental analysis. Those quanti- ties which retain the same value are called constant; those whose values are varying are called variable. When vari- able quantities are so connected that the value of one of them is determined by the ^ value ascribed to the others, that variable quantity is said to be a func- tion of the others. A quantity is infin- itely great or infinitely small, with re- gard to another, when it is not possible 6o assign any quantity sufficiently large or sufficiently small to express the ratio of the two. When we consider a variable quantity as increasing by infinitely small degrees, if we wish to know the value of those increments, the most natural mode is to determine the value of this quantity for any given period, as a second of time, and the value of the same for the period immediately following. This dif- ference is called the differential of the quantity. The integral calculus, as has been already stated, is the reverse of the differential calculus. There is no vari- able quantity expressed algebraically, of which we cannot find the differential; but there are differential quantities which we cannot integrate: some be- cause they could not have resulted from differentiation; others because means have not yet been discovered of inte- grating them. Newton was the first dis- coverer of the principles of the infinites- imal calculus, having pointed them out in a treatise written before 1669, but not published till many years after. Leib- nitz, meanwhile, made the same dis- covery, and published it before Newton, with a much better notation, which is now universally adopted. CALCUTTA, a city of Hindustan, capi- tal of the presidency of Bengal, until 1912 capital of the British dominions in the East and seat of the supreme gov- ernment, on the Hooghly river, an arm of the Ganges, about 100 miles N. of the Bay of Bengal. On approaching the city from the sea, it presents a mag- nificent appearance, with its elegant villas on each side of the river, the gov- ernment botanical gardens, its numer- ous spires of churches and temples, and the strong and regular citadel of Fort William. This city extends along the bank of the Ganges for 6 miles, and has an average breadth of 2 miles. A handsome quay, the Strand, about 40 feet above low-water mark, embanks the river for about 3 miles, and is furnished with about 30 principal ghauts, or land- ing-places. The river here is about a mile in width, and is crowded with ship- ping. The European residents live mostly in the Chowringhee suburb of the city, and at Garden Reach, in beau- tiful and detached villas. The citadel, or Fort William, is not only the strong- eslf and most complete fortress in India, but also in the British dominions. Cal- cutta is popularly denominated the "City of Palaces," and this is not an overdrawn appellation. It is certainly replete with magnificent buildings, but, nevertheless, like all Eastern cities, it contains quarters, inhabited by the na- tive people, which are dingy-looking and