The description of the method is preceded by some account of the steps by which the author acquired his present skill in the division of instruments, and by observations on the comparative merits of the respective methods employed by Bird, by the late Mr. John Troughton, and by other artists; after which Mr. Troughton proceeds to the ac- count of his own, which, he says, was first suggested by the action of the perambulator. In the first place, the circle to be divided is to be turned on its inner and outer edges, to correct circles, in the most exact and careful manner. A roller is then adapted to its edge, hav- ing its diameter, as nearly as possible, one sixteenth that of the circle; and since perfect equality could not be directly obtained, the exterior Surface of the roller is rendered slightly conical, by a difference of «filo-17th of an inch in the diameters of its upper and under surface; so that by a small motion in the direction of its axis, some one part of its surface may be found perfectly adapted to its purpose. The roller itself being next divided into sixteen parts, each of these will correspond with Tg—gth of the whole circle; a number chosen on account of its being capable of continual bisection, although these divisions will coincide with a very small number of the ultimate divisions of the circle.
By means of two microscopes, one over the circle, and the other over the roller, the correct adaptation of the circle and roller to each other is first ascertained, or duly adjusted by raising or depressing the roller. An instrument for making dots, with uniformity, is next to be fixed at a due distance from the edge of the circle; and when one division of the roller is brought exactly under the wire of its microscope, the pointer being pressed down, makes the first dot at any point which may have been previously fixed upon. When the second division of the roller comes under its wire, a second dot is made in a similar manner, and so on till the whole 256 are com- pleted, at intervals that are nearly equal. But it is not really of any consequence _how erroneous they may be found by the very important process of examination which is next to follow, and which constitutes the intrinsic excellence of this method.
The dividing apparatus having next been removed, the circle is to be placed in the same position it is intended to have when employed for observation; and two microscopes are to be placed, at opposite sides, for the examination of the point of 180°. The dot at zero, and that at 180°, being first bisected, the circle is turned half round; and if when the zero point is bisected, that at 180° is found not to be bisected, the apparent error of its position is measured by the micro-
