The speculum was held in a circular frame, which was free to turn round in another ring or frame; this frame was moved backwards and forwards by a vibrating lever to which it was attached by rods, carrying the speculum over the polisher. This motion he designates the stroke. Besides this there was the _side motion_ produced by a rod attached to the side of the frame opposite to that to which the rods giving it the stroke were attached and at right angles to the direction of stroke: this rod was in connection, by means of intermediate levers, with a pin on a rachet wheel, which was turned a tooth at a time by a rod in connection with the lever giving the _stroke_ motion, so that the rod giving the _side motion_ was pushed and pulled back by the pin on the rachet wheel every time it turned round, which it did every twenty or thirty strokes. There were also teeth on the ring fastened round the edge at the back of the speculum, into which claws worked which were attached by rods to a point on the lever a little distance from the attachment of the rod giving the stroke, so that the claws had a less motion than the speculum and its ring, and consequently pulled the ring, and with it the speculum, round a tooth or more at each stroke. The polisher was also turned round in the same manner in a contrary direction to the motion of the speculum. The speculum had therefore three motions, a revolving one on its centre, a stroke, and a side motion, making its centre describe a number of parallel lines over the polisher on each side of its centre. Sir W. Herschel gives as a good working length of stroke, 0·29, and 0·19 side motion measured from side to side, the diameter of the speculum being 1. To produce a seven-inch mirror with this instrument he would work continuously for sixteen hours, his sister “putting the victuals by bits into his mouth.” [Illustration: FIG. 65*.—Section of Lord Rosse’s polishing machine. ] Lord Rosse adopted a similar arrangement; the polisher, K L, Fig. 65, was worked over the speculum in straight strokes with side motion, the requisite straight motion being given by a crank-pin and rod and the side motion by the continuation of this latter rod on the other side of the polisher working in a guide on another crank-pin, which threw it from side to side as the wheel carrying the pin revolved. The trough E F carrying the speculum also revolved slowly, and the requisite motions were given by pulleys and straps of various sizes under the table on which the machine rested; the weight of the polisher was in a great measure counterpoised by strings from its upper surface to a weighted lever M above. The polisher was free to turn in its ring, which it did once in about twenty strokes, and for the six feet speculum the velocity of working was about eight strokes a minute, the length of stroke being one-third of the diameter of the speculum, and that of the side motion one-fifth.