piece D, fig. 318, was screwed on as before directed, which after this ought not to be removed.

From a very exact centre a circle was described on the ring C, figs. 316, 317, and 318, about four-tenths of an inch within where the bottom of the teeth would come. This circle was divided with the greatest exactness I was capable of, first into five parts, and each of these into three. These parts were then bisected four times, (that is to say,) supposing the whole circumference of the wheel to contain 2160 teeth, this being divided into five parts, each would contain 432 teeth; which being divided into three parts, each of them would contain 144; and this space bisected four times would give 72, 36, 18, and 9; therefore each of the last divisions would contain nine teeth. But, as I was apprehensive some error might arise from quinquesection and trisection, in order to examine the accuracy of the divisions, I described another circle on the ring C, (fig. 322,) one-tenth of an inch within the former, and divided it by continual bisections, as 2160, 1080, 540, 270, 135, 674, and 334; and as the fixed wire (to be described presently) crossed both the circles, I could examine their agreement at every 135 revolutions; (after ratching, could examine it at every 334;) but not finding any sensible difference between the two sets of divisions, I, for ratching, made choice of the former; and, as the coincidence of the fixed wire with an intersection could be more exactly determined than with a dot or division, I therefore made use of intersections in both circles before described. The arms of the frame L, fig. 322, were connected by a thin piece of brass of three-fourths of an inch broad, having a hole in the middle of four-tenths of an inch in diameter; across this hole a silver wire was fixed exactly in a line to the centre of the wheel; the coincidence of this wire with the intersections was examined by a lens seven-tenths of an inch focus, fixed in a tube which was attached to one of the arms L. Now a handle or winch being fixed on the end of the screw, the division marked 10, on the circle K, was set to its index, and, by means of a clamp and adjusting-screw for that purpose, the intersection marked 1 on the circle C was set exactly to coincide with the fixed wire; the screw was then carefully pressed against the circumference of the wheel, by turning the finger-screw S, then, removing the clamp, I turned the screw by its handle nine revolutions, till the intersection marked 240 came nearly to the wire; then, unturning the fingerscrew S, I released the screw from the wheel, and turned the wheel back till the intersection marked 2 exactly coincided with the wire; and, by means of the clamp before-mentioned, the division 10 on the circle being set to its index, the screw was pressed against the edge of the wheel by the finger-screw S; the clamp wire removed, and the screw turned nine revolutions till the intersection marked 1 nearly coincided with the fixed wire; the screw was released from the wheel by unturning the finger-screw S as before; the wheel was turned back till the intersection 3 coincided with the fixed wire; the division 10 on the circle being set to its index, the screw was pressed against the wheel as before, and the screw was turned nine revolutions, till the intersection 2 nearly coincided with the fixed wire, and the screw was released; and I proceeded in this manner till the teeth were marked round the whole circumference of the wheel. This was repeated three times round, to make the impression of the screw deeper. I then ratched the wheel round continually in the same direction without ever disengaging the screw; and, in ratching the wheel about 300 times round, the teeth were finished.

The intersections are marked for the sake of illustration, though properly invisible, they lying under the brass plate.

It is evident if the circumference of the wheel were even one tooth or ten minutes greater than the screw would require, this error would in the first instance be reduced to

part of a revolution, or two seconds and a half; and these errors or inequalities of the teeth be equally distributed round the wheel at the distance of nine teeth from each other. Now, as the screw in ratching had continually hold of several teeth at the same time, and these constantly changing, the above-mentioned inequalities soon corrected themselves, and the teeth were reduced to a perfect equality. The piece of brass which carries the wire was now taken away, and the cutting-screw was also removed, and a plain one (hereafter described) put in its place; on one end of the screw is a small brass circle, having its edge divided into sixty equal parts, and numbered at every sixth division, as before mentioned.

On the other end of the screw is a ratchet-wheel c, having sixty teeth, covered by the hollowed circle d, fig. 320, which carries two clicks that catch upon the opposite sides of the ratchet when the screw is to be moved forwards. The cylinder S turns on a strong steel arbor F, which passes through and is firmly screwed to the piece Y; this piece, for greater firmness, is attached to the screw-frame G, fig. 319, by the braces v; a spiral groove or thread is cut on the outside of the cylinder S, which serves both for holding the string, and also giving motion to the lever J on its centre, by means of a steel tooth n, that works between the threads of the spiral. To the lever is attached a strong steel pin m, on which a brass socket, r, turns; this socket passes through a slit in the piece p, and may be tightened in any part of the slit by the finger-nut f; this piece serves to regulate the number of revolutions of the screw for each tread of the treadle R.

T, fig. 316, is a brass box containing a spiral spring; a strong gut is fastened and turned three or four times round the circumference of this box; the gut then passes several times round the cylinder S, and from thence down to the treadle R, fig. 316. Now, when the treadle is pressed down, the string pulls the cylinder, S round its axis, and the clicks catching hold of the teeth on the ratchet carry the screw round with it, till, by the tooth n working in the spiral groove, the lever J, fig. 319, is brought near the wheel a, and the cylinder stopped by the screw-head, a, striking on the top of the ever J; at the same time the spring is wound up by the other end of the girt passing round the box T, fig. 316. Now, when the foot is taken off the treadle, the spring, unbending itself, pulls back the cylinder, the clicks leaving the ratchet and screw at rest till the piece t strikes on the end of the piece p, fig. 316; the number of revolutions of the screw at each tread is limited by the number of revolutions the cylinder is allowed to turn back before the stop strikes on the piece p.

When the endless-screw was moved round its axis with a considerable velocity, it would continue that motion a little after the cylinder, figs. 316 and 319, was stopped; to prevent this, the angular lever n was made, that when the lever J comes near to stop the screw r, it, by a small chamfer, presses down the piece of the angular lever; this brings the other end, n, of the same lever forwards, and stops the endless-screw by the steel pin,, striking upon the top of it: the foot of the lever is raised again by a small spring pressing on the brace v

screws e,

D, two clareps, connected by the piece a, slide one on each arm of the frame L, figs. 316, 317, and 321, and may be fixed at pleasure by the four fingerwhich press against the steel springs to avoid spoiling the arms; the piece q is made to turn without shake between two conical pointed screws f, which are prevented from unturning by tightening the fingernuts N.

The piece m, fig. 321, is made to turn on the piece q, by the conical pointed screws, 8, resting in the hollow centres e.

As there is frequent occasion to cut divisions on inclined planes, for that purpose the piece, 7, in which the tracer is fixed, has a conical axis at each end, which turn in half-holes; when the tracer is set to any inclination, it may be fixed there by tightening the steel screws B.

Description of the engine by which the endless-screw of the dividing-engins

was eut.

Fig. 324 represents this engine of its full dimensions, seen from one side. Fig. 323, the upper side of the same, as seen from above.

A, represents a triangular bar of steel, to which the triangular holes in the pieces B and C are accurately fitted, and may be fixed on any part of the bar by the screws D.

E is a piece of steel whereon the screw is intended to be cut; which, after being hardened and tempered, has its pivots turned in the form of two frustrums of cones, as represented in the drawings of the dividing-engine, fig. 320. These pivots were exactly fitted to the half-holes F and T, which were kept together by the screws z.

H represents a screw of untempered steel, having a pivot I, which turns in the hole k; at the other end of the screw is a hollow centre, which receives the hardened conical point of the steel pin m. When this point is sufficiently pressed against the screw, to prevent its shaking, the steel pin may be fixed by tightening the screws Y.

N is a cylindric nut movable on the screw H; which, to prevent any shakes, may be tightened by the screws O. This nut is connected with the saddle-piece P, by means of the intermediate universal joint W, through which the arbor of the screw H passes. A front view of this piece, with a section across the screw-arbor, is represented at X. This joint is connected with the nut by means of two steel slips S, which turn on pins between the cheeks T, on the nut N. The other ends of these slips, S, turn in like manner on pins a; one axis of this joint turns in a hole in the cock b, which is fixed to the saddle-piece; and the other turns in a hole d, made for that purpose in the same piece on which the cock b is fixed. By this means, when the screw is turned round, the saddle-piece will slide uniformly along the triangular bar A.

K is a small triangular par of well-tempered steel, which slides in a groove of the same form on the saddle-piece P. The point of this bar or cutter is formed to the shape of the thread intended to be cut on the endless-screw, When the cutter is set to take proper hold of the intended screw, it may be fixed by tightening the screws e, which press the two pieces of brass upon it. Having measured the circumference of the dividing-wheel, I found it would require a screw about one thread in a hundred coarser than the guidescrew arbor H, and that on the stub E, on which the screw was to be cut, were proportioned to each other to produce that effect, by giving the wheel L 198 teeth, and the wheel Q 200. These wheels communicated with each other by means of the intermediate wheel R, which also served to give the threads on the two screws the same direction.

The saddle-piece P is confined on the bar A by means of the pieces g, and may be made to slide with a proper degree of tightness by the screws n

LATHES AND TURNING APPARATUS.

THE lathe is a very useful engine for turning wood, ivory, metals, and other materials.

The common lathe is composed of two wooden cheeks or sides, parallel to the horizon, having a groove or opening between; perpendicular to these are two other pieces, called puppets, made to slide between the cheeks, and to be fixed down at any point at pleasure. These have two points, between which the piece to be turned is sustained; the piece is turned round backwards and forwards by means of a string put round it and fastened above to the end of a pliable pole, and underneath to a treadle or board moved with the foot. There is also a rest which bears up the tool, and keeps it steady.

We shall now proceed to give Mr. J. Farey's description of the improved lathes manufactured by Mr. Henry Maudslay, of Margaret-street, Cavendish-square.

A, fig. 325, is the great wheel, with four grooves on the rim ; it is worked by a crank B, and treadle C, in the common way; the catgut which goes round this wheel passes also round a smaller wheel D, called the mandrel, which has four grooves on its circumference, of different diameters, forgiving it different velocities, corresponding with the four grooves on the great wheel A. In order to make the same band suit, when applied to all the different grooves on the mandrel D, the wheel A can be elevated or depressed by a screw, a, and another at the other end of the axle ; and the connecting rod, C, can be lengthened or shortened by screwing the hooks at each end of it further out of, or into it. The end M, fig. 326, of the spindle of the mandrel D, is pointed, and works in a hole in the end of a screw, put through the standard E, fig. 325; the other end of the bearing F, fig. 326, is conical, and works in a conical socket in the standard F, fig. 325, so that, by tightening up the screw in E, the conical end, F, may at any time be made to fit its socket; the puppet G has a cylindric hole through its top to receive the polished pointed rod d, which is moved by the screw e, and fixed by the screw f; the whole puppet is fixed on the triangular prismatic bar H, by a clamp, fig. 332, the two ends of which, a, b, are put through holes, b, in the bottom of the puppet under the bar, and the whole is fixed by the screw c pressing against it; by this means the puppet can be taken off the bar without first taking off the standard I, as in the common lathes; and the triangular bar is found to be far preferable to the double rectangular one in common use. The restj is a similar contrivance; it is in three pieces; see figs. 327, 328, and 329. Fig. 328 is a piece, the opening, a, b, c, in which, is laid upon the bar H, fig. 325; the four legs, dddd, of fig. 329, are then put up under the bar (into the recesses in fig. 328, which are made to receive them) so that the notches in d d d d may be level with the top of fig. 328; the two beads, e ƒ, in fig. 327, are then slid into the notches in the top of d d d d, fig. 328, to keep the whole together; the groove i is to receive a corresponding piece on ef, fig. 327, to steady it; the whole of fig 327 has a metallic cover, to keep the chips out of the grooves. It is plain that, by tight

ening the screw h, in the bottom of fig. 329, the whole will be fixed and prevented from sliding along the bar H, and fig. 327 from sliding in a direction perpendicular to the bar; the piece 1, fig. 327, on which the tool is laid, can be raised or lowered at pleasure, and fixed by a screw, m. On the end, n, of the spindle P, figs. 325 and 326, is screwed occasionally an universal chuck for holding any kind of work which is to be turned. (See fig. 330.) A is the female screw to receive the screw n, fig. 325; near the bottom of the screw A is another screw, B B, which is prevented from moving endways by a collar in the middle of it fixed to the screw A; one end of the screw B B is cut right-handed, and the other left-handed; so that by turning the screw one way, the two nuts, E F, will recede from each other, or by turning it the contrary way, they will advance towards each other; the two nuts, E F, pass through an opening in the plate C, and project beyond the same, carrying jaws, like those of a vice, by which the subject to be turned is to be held.

For turning faces of wheels, hollow work, &c. where great accuracy is wanted, Mr. Maudslay has contrived a curious apparatus, which he calls a slide-tool, represented by fig. 331, where E E E is the opening to receive the bar H, fig. 325, and it is fixed by the clamp, fig. 332, as before described; the tool for cutting, &c. is fixed into the two holders bb, by their screws; these holders are fastened to a sliding plate a, which can be moved backwards and forwards by the screw c, causing the tool to advance or recede; fig. 333 represents the under side (turning upwards) of the part A A, in which the screw c is seen fixed at each end, and the nut d, which is attached to the underside of the plate a, working upon it. When it is necessary, as in the turning of the inside of cones, &c. that the tool should not be parallel to the spindle P, the screw e, and another similar one behind, must be loosened, the tool set at the proper angle, and then be screwed tight again. In order to make the piece A A move truly when it is turned round, there is a hole f, fig. 333, to receive a knob g, fig. 338, upon the plate B, which acts as a centre, and keeps it in its place; there are three holes on each side in the plate B, fig. 336, to put the screw e in at different times, thus giving to the tool a greater range than the circular openings S S will admit.

The part E E E E, represented separately, and inverted, in fig. 334, is of cast-iron, and has a screw, h, working in it, similar to fig. 333; the nut of this screw is attached to the bottom of the slide H, fig. 335, at t, which slides in the groove i, figs. 331 and 334; at one end of it is a box containing a screw m, to be hereafter described, and at the other is a frame of brass K K. Near the same end of the slide is a pin L, projecting above the plate, which is put through an opening, j, in fig. 336, to steady it, while the other end C, of fig. 336, is put through an opening M, in the box D, fig. 335. In the part C is an oblique slit, to receive a stub which projects from the bottom of the nut n, worked by the screw m, fig. 335; by this arrangement it is obvious that if the screw m is worked, the stub of the nut n, acting against the slide of the slit 7 1, as an inclined plane, will move it either backwards or forwards through the opening M; a metal cover r, fig. 338, is occasionally put over the opening for the nut n, and screw m, to prevent the chips from falling in.

Near the four corners of the frame, fig. 336, are four small projections, o ooo, with inclined sides, which fit into the four openings p p p p, of figs. 337 and 331; these openings are cut out in two brass plates, which are screwed on at right angles to the plate B B, figs. 331 and 337; the ends, qq qg, of these plates slide between the edges of the frame K K and the box D, so as to prevent any other motion than a vertical one. When this slide tool is used, the puppet G is to be removed or pushed back further from F, and the tool