GRADUATION, among mathematical instrument-makers, is the process of dividing the arcs of quadrants, theodolites, circular instruments, measures, &c., into degrees, fractions of a degree, &c. Accuracy in this operation is of the utmost importance in practical astronomy and surveying, and no small amount of practical skill is requisite to insure its successful execution. There are two methods employed in the dividing of instruments—the ordinary one consisting in making a copy of a system of divisions already existing; the other and more delicate process is that of original dividing. Straight scales and rules, such as are used in drawing, are divided by placing the particular instrument and the original pattern side by side, then passing a straight edge (with a shoulder fixed at right angles to serve as a guide) along the original, and pausing at each division, when a corresponding line is made on the copy by the dividing knife. Segments of circles may be graduated by making the straight edge revolve on the centre of a divided circle, and marking off the divisions as
in the straight scale. This method, which in skilful hands admits of considerable accuracy, was applied to the division of theodolites and common circular instruments until superseded by Ramsden's Dividing Engine. For the invention of this ingenious machine the author received from the Board of Longitude a premium of £300, and £315 for the machine itself, which he was permitted during pleasure to retain in his own possession, on condition of his dividing sextants and octants for other instrument-makers at fixed rates. A description of Ramsden's dividing engine would require a diagram to render it perfectly intelligible; but perhaps some general idea of its mode of action may be formed from the following brief explanation:—A horizontal circle, four feet in diameter, turns upon a vertical axis, and is moved by an endless screw, one revolution of which carries forward the circle ten minutes, or one sixth of a degree; the screw is moved forward by depressing a treadle, at each descent of which the screw, by a series of ingenious mechanical appliances, may be turned through any portion of its revolution; and when the pressure is removed, the position of the several parts is restored without communicating any return motion to the screw. The circle to be graduated is fixed upon the dividing-plate of the machine, and concentric with it, and the lines are cut after each depression of the treadle.
Some idea of the extreme delicacy required for original dividing may be derived from the fact that Ramsden, in laying down the original divisions on his dividing engine, divided his circle first into five parts, and each of these into three; these parts were then bisected four times, but being apprehensive lest some error might arise from quinquisection and trisection, in order to test the accuracy of the divisions he described another circle th inch within the former by continual bisections, when the two sets of divisions were found to exhibit no sensible difference. It was by means of this machine that Ramsden graduated his great theodolite, constructed under the inspection of General Roy for the trigonometrical survey of Great Britain. A description of this fine theodolite, with illustrative plates, may be found in the Philosophical Transactions, Lond., vol. lxxx.
Ramsden's dividing machine is the prototype after which various similar ones (with some alterations and improvements) have been constructed by Troughton, Adie of Edinburgh, and various other artists. The dividing machines of Reichenbach, Gambey, and other continental inventors, differ somewhat from those above mentioned. The German method of division, which admits of the greatest accuracy under skilful management, is performed by copying from a large circle originally divided with extreme precision. Upon this the copy is fixed concentrically; and by the aid of the micrometer-microscope fixed independently over the divided circle, the degrees and their fractional parts are cut in the copy.
Ample details of the different methods employed for graduation are to be found in various published works which treat of this particular subject, such as those of Bird, Ramsden, Troughton, de Chaulnes, &c., &c.