The visitor to an engineer’s workshop cannot fail to be struck with the operation of the powerful _Lathes_ and _Planing Machines_, by which long thick flakes or shavings of iron are removed from pieces of metal with the same apparent ease as if the machine were paring cheese. The figure on the opposite page represents one of the larger forms of the planing machine, as constructed by Sir J. Whitworth. The piece of work to be planed is firmly bolted down to the table, A, which moves upon the Ꮩ-shaped surfaces, running its whole length, and accurately fitting into corresponding grooves in a massive cast iron bed. The bevel wheel, of which a portion is seen at B, is keyed on a screw, which extends longitudinally from end to end of the bed. This screw works in nuts forming part of the table, and as it turns in sockets at the ends of the bed, it does not itself move forward, but imparts a progressive movement to the table, and therefore to the piece of metal to be planed. As this table must move backwards and forwards, there must be some contrivance for reversing the direction of the screw’s rotation, and this is accomplished in a beautifully simple manner by an arrangement which a little consideration will enable any one to understand. It will be observed that there are three drum-pulleys at C. Let the reader confine, for the present, his attention to the nearest one, and picture to himself that the shaft to which it is attached is placed in the same horizontal plane as the axis of the screw and at right angles to it, passing in front of bevel wheel B. A small bevel wheel turning with this shaft, and engaging the teeth of the wheel B, may, it is plain, communicate motion to the screw. Now let the reader consider what will be the effect on the _direction_ of the rotation of B of applying the bevelled pinion to the nearer or to the farther part of its circumference, supposing the direction of the rotation of this pinion to be always the same. He will perceive that the direction in one case will be the reverse of that in the other. The shaft to which the nearest pulley is attached carries a pinion engaging the wheel at its farther edge, and therefore the rotation of this pulley in the same direction as the hands of a watch causes the wheel B to rotate so that its upper part moves towards the spectator. The farthest pulley, _a_, turns with a hollow shaft, through which the shaft of the nearest pulley simply passes, without any connection between them, and this hollow shaft carries a pinion, which engages the teeth of B at the nearer edge, and, in consequence, the rotation of the farther pulley, _a_, in the direction of the hands of a watch, would cause the upper part of B to be moving from the spectator. The middle pulley, _b_, runs loosely on the shaft, and the driving-strap passes through the guide, _c_, and it is only necessary to move this, so as to shift the strap from one drum to