GRADUAL (Med. Lat. gradualis, of or belonging to steps or degrees; gradus, step), advancing or taking place by degrees or step by step; hence used of a slow progress or a gentle declivity or slope, opposed to steep or precipitous. As a substantive, “gradual” (Med. Lat. graduale or gradale) is used of a service book or antiphonal of the Roman Catholic Church containing certain antiphons, called “graduals,” sung at the service of the Mass after the reading or singing of the Epistle. This antiphon received the name either because it was sung on the steps of the altar or while the deacon was mounting the steps of the ambo for the reading or singing of the Gospel. For the so-called Gradual Psalms, cxx.-cxxxiv., the “songs of degrees,” LXX. ᾠδὴ ἀνὰ βαθμῶν, see [Psalms, Book of].
GRADUATE (Med. Lat. graduare, to admit to an academical degree, gradus), in Great Britain a verb now only used in the academical sense intransitively, i.e. “to take or proceed to a university degree,” and figuratively of acquiring knowledge of, or proficiency in, anything. The original transitive sense of “to confer or admit to a degree” is, however, still preserved in America, where the word is, moreover, not strictly confined to university degrees, but is used also of those successfully completing a course of study at any educational establishment. As a substantive, a “graduate” (Med. Lat. graduatus) is one who has taken a degree in a university. Those who have matriculated at a university, but not yet taken a degree, are known as “undergraduates.” The word “student,” used of undergraduates e.g. in Scottish universities, is never applied generally to those of the English and Irish universities. At Oxford the only “students” are the “senior students” (i.e. fellows) and “junior students” (i.e. undergraduates on the foundation, or “scholars”) of Christ Church. The verb “to graduate” is also used of dividing anything into degrees or parts in accordance with a given scale. For the scientific application see [Graduation] below. It may also mean “to arrange in gradations” or “to adjust or apportion according to a given scale.” Thus by “a graduated income-tax” is meant the system by which the percentage paid differs according to the amount of income on a pre-arranged scale.
GRADUATION (see also [Graduate]), the art of dividing straight scales, circular arcs or whole circumferences into any required number of equal parts. It is the most important and difficult part of the work of the mathematical instrument maker, and is required in the construction of most physical, astronomical, nautical and surveying instruments.
The art was first practised by clockmakers for cutting the teeth of their wheels at regular intervals; but so long as it was confined to them no particular delicacy or accurate nicety in its performance was required. This only arose when astronomy began to be seriously studied, and the exact position of the heavenly bodies to be determined, which created the necessity for strictly accurate means of measuring linear and angular magnitudes. Then it was seen that graduation was an art which required special talents and training, and the best artists gave great attention to the perfecting of astronomical instruments. Of these may be named Abraham Sharp (1651-1742), John Bird (1709-1776), John Smeaton (1724-1792), Jesse Ramsden (1735-1800), John Troughton, Edward Troughton (1753-1835), William Simms (1793-1860) and Andrew Ross.
The first graduated instrument must have been done by the hand and eye alone, whether it was in the form of a straight-edge with equal divisions, or a screw or a divided plate; but, once in the possession of one such divided instrument, it was a comparatively easy matter to employ it as a standard. Hence graduation divides itself into two distinct branches, original graduation and copying, which latter may be done either by the hand or by a machine called a dividing engine. Graduation may therefore be treated under the three heads of original graduation, copying and machine graduation.
Original Graduation.—In regard to the graduation of straight scales elementary geometry provides the means of dividing a straight line into any number of equal parts by the method of continual bisection; but the practical realization of the geometrical construction is so difficult as to render the method untrustworthy. This method, which employs the common diagonal scale, was used in dividing a quadrant of 3 ft. radius, which belonged to Napier of Merchiston, and which only read to minutes—a result, according to Thomson and Tait (Nat. Phil.), “giving no greater accuracy than is now attainable by the pocket sextants of Troughton and Simms, the radius of whose arc is little more than an inch.”