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, 671, 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, inade 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 A 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 révolutions 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 a, it, by a small chamfer, presses down the piece x of the angular lever; this brings the other end, n, of the same lever forwards, and stops the endless-screw by the steel pin, μ, striking upon the top of it: the foot of the lever is raised again by a small spring pressing on the brace v

Y

D, two clamps, 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 finger. screws e, which 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 finger

nuts N.

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

As there is frequent occasion to cut divisions on inclined planes, for that purpose the piece, y, 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 8.

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

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.

be

K is a small triangular oar 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 fixed by tightening the screws c, 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 cul, were proportioned to each other to produce that effect, by giving the wheel L198 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.