CALCULUS, DIFFERENTIAL AND INTEGRAL, in mathematics, is the method by which we discuss the properties of continuously varying quantities.  The nature of the method and the necessity for it may be indicated by a simple example; e. g. the motion of a train in a track, or the motion of a planet in its orbit.  If we know the successive positions of the moving body at successive short intervals of time, the rules of the differential calculus enable us to calculate the speed, the change of speed, the change of direction of motion (i. e. the curvature of the path), and the effective force acting on the body.  Conversely, given the force at every point, and the initial position and velocity, the rules of the integral calculus assist us in calculating the position and velocity of the body at any future time.  Expressed somewhat crudely, the differential calculus has to do with the differentials (increments or decrements) of varying quantities; while the integral calculus is a process of summation or integration of these differentials.

CALCUTTA (900), on the left bank of the Hooghly, the largest and westernmost branch of the Ganges delta, about 80 m. from the sea; is the capital of Bengal and the Indian Empire, and the residence of the Governor-General; the Government buildings, Bishop’s College (now an engineering school) High Court, town hall, bank, museum, university, St. Paul’s cathedral, and many other English Buildings have earned for it the name “city of palaces”; but the native quarters, though being improved, are still squalid, the houses of mud or bamboo; an esplanade, numerous quays, an excellent water-supply, gas, and tramway services, add to the amenities; there are extensive dockyards, warehouses, iron-works, timber yards, and jute mills; extensive railway and steamboat communications make it the chief emporium of commerce in Asia; ships of 5000 tons enter the docks; founded in 1686, Calcutta was captured by Surajah Dowlah, and the “Black Hole” massacre perpetrated in 1756; became the capital of India in 1772, and has suffered frequently from cyclones; the population are two-thirds Hindus, less than a third Mohammedan, and 41/2 per cent.  Christian.

CALDECOTT, RANDOLPH, artist, born in Chester; exercised his art chiefly in book illustrations, which were full of life, and instinct with a kindly, graceful humour; though professionally untrained, his abilities as an artist were promptly and generously recognised by the Academy; he suffered from ill-health, and died in Florida, whither he had gone to recruit (1846-1886).

CALDER, SIR ROBERT, British naval officer; served bravely in several naval engagements; was tried by court-martial, and reprimanded for not following up a victory which he had gained, a sentence which was afterwards found to be unjust; attained afterwards the rank of admiral (1745-1818).

CALDERON DE LA BARCA, the great Spanish dramatist, born at Madrid; entered the army, and served in Italy and Flanders, producing the while dramas which were received with great enthusiasm; took holy orders, and became a canon of Toledo, but to the last continued to write poems and plays; he was a dramatist of the first order, and has been ranked by the more competent critics among the foremost of the class in both ancient and modern times (1600-1681).