The mirror _a_, is carried by an iron chuck or table _b_, covered with a triple fold of blanket, and is prevented from slipping off by four cleets _c c′_. The vertical shaft _d_ passes through a worm-wheel _e_, the endless screw of which _f_, is driven by a band _g_, from the primary shaft _h_. At _i_ is the band-wheel for connection to the foot-power. At one end of the primary shaft is firmly fixed the cogwheel _k_, which drives the crank-shaft _l_. Attached to the horizontal part of _l_, is the crank-pin _m_. The two bolts _n n′_ move in a slot, so that the crank-pin may be set at any distance from 0 to 2 inches, out of line with _l_. Above, the crank-pin carries one end of the bar _o_, the other end passing through an elliptical hole in the oak-block _p_. Down the middle of the bar runs a long slot, through which the screw-pin _q_ passes, and which permits _q_ to be brought over any zone from the centre to the edge of the mirror _a_. It is retained by the bolts _r r′_, which are tapped into _s_. The local polisher is seen at _t_. The curve which the centre of the local polisher describes upon the face of the mirror, varies with the adjustments. Fig. 26 is a reduction from one traced by the machine, the overlapping being seen on the left side. The mirror is not tightly confined by the cleets _c c′_, for that would certainly injure the figure, but performs a slow motion of rotation, so that in no two successive strokes are the same parts of the edge pressed against them. [Illustration: Fig. 26. Hypocycloidal Curve.] The local polishers are made of lead, alloyed with a small proportion of antimony, and are 8, 6, and 4 inches in diameter, respectively. The largest and smallest are most used, the former on account of its size polishing most quickly, but the latter giving the truest surface. The rosin that covers them is just indentable by the thumb nail, and is arranged in a novel manner. The leaden basis, as seen at _t_, Fig. 25, is perforated in many places with holes, which permit evaporation, serve for the introduction of water where needed, and allow the rosin to spread freely. Grooves are made from one aperture to another, and the rosin thus divided into irregular portions. The effects of the production of heat are in this way avoided.