Graduation , the art of dividing astronomical, geodetical, and other mathematical instruments. It was formerly done by hand with ordinary dividing instruments, and so few makers possessed the requisite skill that it was very difficult to procure good instruments for the ordinary purposes of navigation; but now the operation is performed with great exactness by machines called dividing engines. Jesse Ramsden, a cloth pressor, who subsequently turned his attention to engraving, being brought in contact with mathematical instrument makers, was led to construct the engine which for many years was called by his name. At that time it was considered so valuable that the English commissioners of longitude entered into a contract with him (1775) to instruct a certain number of persons, not exceeding ten, in the method of making and using it, and to divide sextants and octants at certain prices as long as the engine remained in his possession, they becoming the purchasers for the sum of £315, and giving £300 in addition for the invention.

Perfect as the instrument was then considered, it has since been greatly improved, so that it is now automatic, the whole operation of dividing a circle, after it has been placed on the engine, being performed by a motion given by the descent of a weight, or by a crank turned by hand. The engine consists of a large wheel of bell metal, the circumference being ratched into 720, 1,080, 1,440, 2,160, or 4,320 teeth, or any number which, divided by 2, 3, 4, 6, or 12, will give 300. These teeth are cut with great accuracy, and the wheel is turned on its centre by an endless screw, by which it may be moved any number of degrees or parts desired. The dividing point is fixed in a frame which admits of a free and easy motion to and from the centre. In England, Troughton, Simms, Thomas, Jones, Ross, and a few others, have been successful in making these engines, while many others have failed. On the continent of Europe they were first made automatic, and other improvements were also made in them. Gambey of Paris has so arranged his as to divide an instrument without any eccentricity, even when placed in a slightly eccentric position on the engine.

Oertling of Berlin has an arrangement for correcting any original errors in the teeth while dividing, and other mechanists of celebrity have constructed them to suit their own views, and for their own use. In the United States there is a large one belonging to the coast survey, made by Simms of London, and afterward made automatic by Saxton; also one in Philadelphia made by Young, and one in New York by the Messrs. Blunt, both of which are automatic. There is no branch of the mechanic arts which requires more skill in the use of tools, more geometrical knowledge, and greater patience, than the construction of a circular dividing engine. The large astronomical instruments are divided in a different manner, and, unless placed on a large engine from which the divisions may be in a manner copied, are original divisions. Troughton, Simms, and Jones of London have used movable microscopes with micrometers; while others on the continent of Europe have availed themselves of the feeling lever, a powerful instrument for that purpose invented by the astronomer Bessel. Straight line divisions for scales, etc, are made by means of a screw, a milled roller, or a wedge which is employed to move a platform sliding freely beneath a cutting frame, and carrying the scale to be divided.

In the use of the screw much depends on its accuracy, and, with regard to the roller or wedge, on the working or manner of applying them. When great accuracy is required, the divisions are tested by means of two microscopes, and an error can be detected of 1/30,000 of an inch. The ruling machines used by engravers in this country are well calculated for this purpose.