clamp or dog at the opposite end, which works by a joint W, firmly fixed into the carriage CCCC. Y is a bridge, likewise screwed into the carriage, through which the screw X passes, and presses with its lower end against the upper side of the clamp V; under which clamp the other end of the file ZZ is placed, and held firmly in its situation while it is cutting by the pressure of the said clamp V. 7777 is a bed of lead, which is let into a cavity formed in the body of the carriage, something broader and longer than the largest size files; the upper face of this bed of lead is formed variously, so as to fit the different kinds of files which may be required. At the figures 2 2 are two catches, which take into the teeth of the ratch-wheel Q, to prevent a recoil of its motion; 3 3 is a bridge to support one end, 4, of the axis of the ratch-wheel Q; 5 a stud to support the other end of the axis of that wheel.

When the file or files are laid in their place, the machine must be regulated to cut them of the due degree of fineness, by means of the regulating screw L; which, by screwing farther through the arm M, will make the files finer, and, vice versa, by unscrewing it a little, will make them coarser; for the arm G will, by that means, have liberty to rise the higher, which will occasion the arm P, with the claws, to move further along the periphery of the ratch-wheel, and consequently communicate a more extensive motion to the carriage C C C C, and make the files coarser.

When the machine is thus adjusted, a blind man may cut a file with more exactness than can be done in the usual method by the keenest sight; for by striking with a hammer on the head of the cutter or chisel HH, all the movements are set at work; and by repeating the stroke with the hammer, the files on one side will at length. be cut; then they must be turned, and the operation repeated for cutting on the other side. It is needless to enlarge much on the utility or extent of this machine; for, on an examination, it will appear to persons of but indifferent mechanical skill, that it may be made to work by water as well as by hand, to cut coarse or fine, large or small, files, or any number at a time; but it may be more particularly useful for cutting very fine small files for watchmakers; as they may be executed by this machine with the greatest equality and nicety imaginable. As to the materials and dimensions of the several parts of this machine, they are left to the judgment and skill of the artist who may have occasion to make one; only observing, that the whole should be capable of bearing a good deal of violence.

RAMSDEN'S DIVIDING MACHINE.

THIS valuable instrument is the invention of Mr. Jesse Ramsden, to whom the Commissioners of Longitude gave the sum of 6157., upon his entering into an engagement to instruct a certain number of persons, not exceeding ten, in

the method of making and using this machine, in the space of two years, say, from the 28th October, 1775, to 28th October, 1777; also binding himself to divide all sectants and octants by the same engine, at the rate of three shillings for each octant, and six shillings for each brass sectant, with Nonius's divisions to half minutes, for as long time as the Commissioners should think proper to let the engine remain in his possession. Of this sum 300l. were given to Mr. Ramsden, as a reward for the usefulness of his invention; and 3157. for his giving up the property of it to the Commissioners.

The following is the description of the engine given by Mr. Ramsden, upon oath:

This engine consists of a large wheel of bell-metal, supported on a mahogany stand, having three legs, which are strongly connected together by braces, so as to make it perfectly steady. On each leg of the stand is placed a conical friction-pulley, whereon the dividing wheel rests; to prevent the wheel from sliding off the friction-pullies, the bell-metal centre under it turns in a socket on the top of the stand.

The circumference of the wheel is ratched or cut (by a method which will be described hereafter) into 2160 teeth, in which an endless screw acts. Six revolutions of the screw will move the wheel a space equal to one degree.

Now a circle of brass being fixed on the screw-arbor, having its circumference divided into sixty parts, each division will, consequently, answer to a motion of the wheel of ten seconds, six of them will be equal to a minute, &c.

Several different arbors of tempered steel are truly ground into the socket in the centre of the wheel. The upper parts of the arbors, that stand upon the plane, are turned of various sizes, to suit the centres of different pieces of work to be divided.

When any instrument is to be divided, the centre of it is very exactly fitted on one of these arbors; and the instrument is fixed down to the plane of the dividing wheel, by means of screws, which fit into holes made in the radii of the wheel for that purpose.

The instrument being thus fitted on the plane of the wheel, the frame which carries the dividing point is connected at one end by finger-screws, with the frame which carries the endless-screw; while the other end embraces that part of the steel arbor which stands above the instrument to be divided, by an angular notch in a piece of hardened steel; by this means both ends of the frame are kept perfectly steady and free from any shake,

The frame carrying the dividing-point or tracer, is made to slide on the frame which carries the endless-screw to any distance from the centre of the wheel, as the radius of the instrument to be divided may require, and may be there fastened by tightening two clumps; and the dividing-point or tracer, being connected with the clumps by the doublejointed frame, admits a free and easy motion towards or from the centre for cutting the divisions, without any lateral shake.

From what has been said, it appears that an instrument thus fitted on the dividing-wheel, may be moved to any angle by the screw and divided circle on its arbor; and that this angle may be marked on the limb of the instrument with the greatest exactness by the dividing-point or tracer, which can only move in a direct line tending to the centre, and is altogether freed from those inconveniences that attend cutting by means of a straight edge. This method of drawing lines will also prevent any error that might arise from an expansion or contraction of the metal during the time of dividing. The screw-frame is fixed on the top of a conical pillar, which turns freely round its axis, and also moves freely towards or from the centre of the wheel, so that the screwframe may be entirely guided by the frame which connects it with the centre: by this means any eccentricity of the wheel and the arbor would not produce any error in the dividing; and by a particular contrivance, (which will be described hereafter,) the screw when pressed against the teeth of the wheel always moves parallel to itself; so that a line joining the centre of the arbor and the tracer continued will always make equal angles with the screw.

Fig. 316 represents a perspective view of the engine.

Fig. 217 is a plan of which fig. 318 represents a section on the line IIA. The large wheel A is 45 inches in diameter, and has 10 radii, each being supported by edge-bars, as represented in fig. 318. These bars and radii are connected by a circular ring B, 24 inches in diameter and 3 inches deep; and, for greater strength, the whole is cast in one piece in bell-metal.

As the whole weight of the wheel A rests on its ring B, the edge-bars are deepest where they join it; and from thence their depth diminishes, both towards the centre and circumference, as represented in fig. 318

The surface of the wheel A was worked very even and flat, and its circumference turned true. The ring C, of fine brass, was fitted very exactly on the circumference of the wheel; and was fastened thereon with screws, which, after being screwed as tight as possible, were well rivetted. The face of a large chuck being turned very true and flat in the lathe, the flattened surface A, fig. 318, of the wheel, was fastened against it with holdfasts; and the two surfaces and circumference of the ring C, a hole through the centre and the plane part round b, and the lower edge of the ring B, were turned at the same time.

D is a piece of hard bell-metal, having a hole, which receives the steel

arbor d, made very straight and true. This bell-metal was turned very true on an arbor; and the face, which rests on a wheel at b, was turned very flat, so that the steel arbor d might stand perpendicular to the plane of the wheel; this bell-metal was fastened to the wheel by six steel screws.

A brass socket Z is fastened on the centre of the mahogany stand, and receives the lower part of the bell-metal piece D, being made to touch the bell-metal in a narrow part near the mouth, to prevent any obliquity of the wheel from bending the arbor; good fitting is by no means necessary here; since any shake in this socket will produce no bad effect, as will appear hereafter when we describe the cutting-frame.

The wheel was then put on its stand, the lower edge of the ring B, figs. 316, 317, and 318, resting on the circumference of three conical friction pulleys W, to facilitate its motion round its centre. The axis of one of these pulleys is in a line joining the centre of the wheel and the middle of the endless-screw, and the other two placed so as to be at equal distances from each other.

Fig. 316 is a block of wood strongly fastened to one of the legs of the stand; the piece g is screwed to the upper side of the block, and has halfholes, in which the transverse axis h, fig. 319, turns; the half-holes are kept together by the screws i.

The lower extremity of the conical pillar P, figs. 316 and 319, terminates in a cylindrical steel pin k, fig. 319, which passes through and turns in the transverse axis h, and is confined by a check and screw.

To the upper end of the conical pillar is fastened the frame G, fig. 319, in which the endless-screw turns; the pivots of the screw are formed in the manner of two frustrums of cones joined by a cylinder, as represented at X, fig. 320. These pivots are confined between half-holes, which press only on the conical parts, and do not touch the cylindric parts; the half-holes are kept together by screws a, which may be tightened at any time, to prevent the screw from shaking in the frame.

On the screw-arbor is a small wheel of brass K, figs. 316, 317, 319, and 320, having its outside edge divided into 60 parts, and numbered at every sixth division with 1, 2, &c. to 10. The motion of this wheel is shown by the index y, figs. 319 and 320, on the screw-frame G.

H, fig. 316, represents a part of the stand, having a parallel slit in the direction towards the centre of the wheel, large enough to receive the upper part of the conical brass pillar P, which carries the screw and its frame; and as the resistance, when the wheel is moved by the endless-screw, is against the side of the slit H which is towards the left hand, that side of the slit is faced with brass, and the pillar is pressed against it by a steel spring on the opposite side; by this means the pillar is strongly supported laterally, and yet the screws may be easily pressed from or against the circumference of the wheel, and the pillar will turn freely on its axis to take any direction given it by the frame L.

At each corner of the piece I, fig. 319, are screws, of tempered steel, having polished conical points; two of them turn in conical holes in the screw-frame near o, and the points of the other two screws turn in the holes in the piece Q; the screws p are of steel, which being tightened, prevent the conical pointed screws from unturning when the frame is moved.

L, figs. 316, 317, and 321, is a brass frame, which serves to connect the endless-screw, its frame, &c. with the centre of the wheel; each arm of this frame is terminated by a steel screw, that may be passed through any of the holes g, in the piece Q, fig. 319, as the thickness of the work to be divided on the wheel may require, and are fastened by the finger-nuts, figs. 316 and 317.

At the end of this frame is a flat piece of tempered steel b, fig. 321, wherein is an angular notch; when the endless-screw is pressed against the teeth of the circumference of the wheel, which may be done by turning the finger-screw S, figs. 316 and 317, to press against the spring t, this notch embraces and presses against the steel arbor d. This end of the frame may be raised or depressed by moving the prismatic slide a, fig. 317, which may be fixed at any height by the four steel screws v, figs. 316, 317, and 321.

The bottom of this slide has a notch K, figs. 316 and 321, whose plane is parallel to the endless-screw, and by the point of the arbor d, fig. 318, resting in this notch, this end of the frame is prevented from tilting. The screw S, figs. 316 and 317, is prevented from unturning, by tightening the finger-nut w.

The teeth on the circumference of the wheel were cut by the following method:

Having considered what number of teeth on the circumference would be most convenient, which in this engine is 2160, or 360 multiplied by 6, I made two screws of the same dimension of tempered steel, in the manner hereafter described, the interval between the threads being such as I knew by calculation would come within the limits of what might be turned of the circumference of the wheel: one of these screws, which was intended for ratching or cutting the teeth, was notched across the threads, so that the screw, when pressed against the edge of the wheel and turned round, cut in the manner of a saw. Then having a segment of a circle a little greater than 60 degrees, of about the same radius with the wheel, and the circumference made true, from a very fine centre, I described an arch near the edge, and set off the chord of 60 degrees on this arch. This segment was put in the place of the wheel, the edge of it was ratched, and the number of revolutions and parts of the screw contained between the interval of the 60 degrees were counted. The radius was corrected in the proportion of 360 revolutions, which ought to have been in 60 degrees, to the number actually found; and the radius, so corrected, was taken in a pair of beam-compasses; while the wheel was on the lathe, one foot of the compasses was put in the centre, and with the other a circle was described on the ring; then half the depth of the threads of the screw being taken in dividers, was set from this circle outwards, and another circle was described cutting this point; a hollow was then turned on the edge of the wheel, of the same curvature as that of the screw at the bottom of the threads, the bottom of this hollow was turned to the same radius or distance from the centre of the wheel, as the outward of the two circles before-mentioned.

The wheel was now taken off the lathe, and the bell-metal