Description of Polishing Machine. Power is applied through belting to the speed cone A. By means of a bevel pinion rotation is communicated to the wheel D, which is of solid metal and carries a T-slot, C. A pedestal forming a crank-pin can be clamped so as to have any desired radius of motion by the screw E. A train of wheels E F G H K (ordinary cast lathe change wheels) communicate any desired ratio of motion to the tool-holder, which simply consists of two pins projecting vertically downwards from the spokes of wheel K. These pins form a fork, and each prong engages in a corresponding hole in the back of the slate-grinding tool (not shown in figure). The connection with the tool is purposely loose. The wheel E, of course, cannot rotate about the crank-pin D. Provision for changing the ratio of tool rotation is achieved by mounting the wheels composing the train on pins capable of sliding along a long slot in the bar supporting them. The farther end of this bar is caused to oscillate to and fro very slowly by means of an additional crank-pin S and crank-shaft, the projecting face of the bed-plate W being placed so as to allow V to slide about easily and smoothly. Motion is communicated to this part of the system by means of gears at 0 and P, and a belt working from P to Q. Thus the vertical shaft R is set in motion and communicates by gears with S. A pulley placed on the axle of the wheel carrying the crank-pin S gives a slow rotation to the work which is mounted on the table M. A small but important feature is the tray L below the gear K. This prevents dirt falling from the teeth of the wheel on to the work. The motion of S is of course very much less than of B--say 100 times less. The work can be conveniently adjusted as to height by means of the screw N. The machine must be on a steady foundation, and in a place as free from dust as possible. Though it looks complicated it is quite straight-forward to build and to operate.