The machine, which is a simplification of Lord Rosse’s, was intended to give spiral strokes. It differed from the original, however, in demanding a changeable stroke, and in the absence of the lateral motion. In another most essential feature it varied from both that and Mr. Lassell’s, _the mirror was always uppermost while polishing_, and being uncounterpoised escaped to as great an extent as possible from the effects of irregular pressure. To any one who has studied the deformations of a reflecting surface, and knows how troublesome it is to support a mirror properly, the advantage is apparent. [Illustration: Fig. 21. Polishing Machine.] [Illustration: Fig. 22. The Foot Power.] The construction is as follows: A stout vertical shaft, _a_, Fig. 21, carries at its top a circular table _b_, upon which the polisher _c_ is screwed. Below a band-wheel _d_ is fixed. Above the table, at a distance of four inches, a horizontal bar _e_ is arranged, so as to move back and forward in the direction of its length, and to carry with it by means of a screw _l_, the mirror _m_, and its iron back or chuck _n_. The bar is moved by a connecting rod _f_, attached to it at one end, and at the other to a pin _g_ moving a slot. This slot is in a crank _h_, carried by a vertical shaft _i_, near the former one _a_. The band-wheel _k_ is connected with the foot power, Fig. 22. The machine, except those parts liable to wear by friction, is made of wood. The ends _o o′_ of the horizontal bar _e_, are defended by brass tubes working in mahogany, and have even now but little shake, though many hundred thousands of reciprocations have been made. The foot power consists of an endless band with wooden treads _a a′_, passing at one end of the apparatus over iron wheels _b b′_, which carry the band-wheel c upon their axle. At the other end it goes over the rollers _d d′_. Two pairs of intermediate wheels _e e′_, serve to sustain the weight of the man or animal working in it. The treads are so arranged that they interlock, and form a platform, which will not yield downwards. Owing to its inclination when a weight is put on the platform _a′_, it immediately moves from _b_ toward _d_ and the band-wheel turns. By a moderate exertion, equivalent to walking up a slight incline at a slow rate, a power more than sufficient to polish a 15-1/2 inch mirror is obtained. This machine, in which very little force is lost in overcoming friction, is frequently employed for dairy use, and is moved commonly in the State of New York by a sheep. I have generally myself walked in the one used by me, and have travelled some days, during five hours, more than ten miles. In order to give an idea of the method of using a grinding and polishing machine, the following extract from the workshop note-book is introduced:--