when the latter is turned round, rectilinear motion is given to the frame. The barrel to the right is large and excavated, so as to admit the ratchet-wheel, which latter is driven by a catch and spring planted in the edge of the cavity in the former. The end of the barrel to the left is embraced by a ring, which is capable of being turned round or set fast at pleasure. A stopping-piece is fastened to the frame by a fingerscrew, and by means of a slit, through which the screw passes from the ring of the barrel, varied through a considerable extent. The elevated part of the stopping-piece resembles an anvil, and the hither side of the ring of the barrel, a hammer: the contact of these determines the point from which divisions begin: cach division is terminated by similar means: an anvil is found in the elevated part of the frame Fig. 1106. the anvil sooner, the tread would be shortened; and if shifted the contrary way it would be lengthened. Thus, by changing the position of the anvil, the number of complete revolutions can be varied; and as parts of a revolution are obtained by shifting the hammer, the angular value of a tread may be varied from 6 revolutions of the screw down to a single tooth of the ratchet-wheel. The most useful number for the teeth in this wheel is 120, for it answers to the division of the vernier that gives 5" of the usual degree, or 10" in instruments of reflexion, as well as to many others. For other purposes ratchet-wheels, of 80, 100, &c. teeth, may be substituted. On the end of the screw-arbor to the left, Fig. 1106, is attached a milled head and divided micrometer; the latter, like the ratchet-wheel, changeable PART OF ENGINE PLATE, WITH THE MILLED HEAD AND behind, and a hammer in a screw-head projecting at pleasure, and carrying the same number of divisions that the wheel does teeth; the micrometer turns round with the screw, and a cock fixed to the frame, bearing a fiducial line, serves as an index for counting the divisions. By the help of this the stopping apparatus can be set to any part of the revolution of a screw without the trouble of a second trial; and by it, in case of a false tread, or other accident, the parts can be again adjusted. The frame and apparatus for cutting the divisions, and their connexion with the engine, have now to be described. Upon the two remote branches of the tripod, and beyond the border of the wheel, are erected 2 pillars, the upper parts of which are formed into screws. Four screw-nuts work, two and two, upon the screw part of these pillars, and, embracing the ends of a strong brass bar, K K, which they support, allow the height to be adjusted so as to suit the thickness of the work to be divided. To the near branch of the tripod a cross-piece, L, Fig. 1103, nearly the length of the screw-arbor and parallel to it, is firmly fastened. This carries upon its extremities 2 pillars similar to, but smaller than the others. Upon the strong bar, K K, at equal distances from the middle, are roller-bars fixed by finger-screws. They extend from the strong bar to the pillars in front, to which they are secured by double-nuts like the former. These 2 bars, м M, Fig. 1102, are bound together by a cross-brace at the remote end, and by another a little way beyond the centre. In no other part can crossing-pieces be allowed; for as they form the support for the apparatus that cuts the divisions, uninterrupted motion along the whole line of the radius is required. The cutting apparatus consists of 3 principal pieces, a, e, o, Fig. 1102. The first is a bridge which crosses the space between the bars, M, M, and to which it is attached at the ends by sliding sockets: these run along the bars, and can be clamped thereto at any part so as to suit the length of the radius of the instrument which is to be graduated. Two steel screws, with conical points, are tapped through the perpendicular ends of the bridges above the sockets, and by working in holes of the second piece, form an axis or joint round which the latter has a free and steady motion. The third piece, the form of which, as well as of the second, is seen in the plan, has also steel screws with conical points tapped through its ends, and these, like the others, act in the middle piece, forming another horizontal axis parallel to the former, and in every respect like it. In Fig. 1102, the parts are extended, for the purpose of being better shown, into a position in which they cannot work. The best effect is produced when the middle piece is vertical, and the third horizontal. Sufficient freedom of action is found in this contrivance of Hindley's to produce a rectilinear motion of the pointril of at least one-third of an inch, a quantity fully sufficient for the required purposes. The part of the third piece next the centre, is that in which the pointril is placed. It is so contrived that its length below the piece may be varied at pleasure; that it may be turned round upon a horizontal axis so as to make any angle with the plane to be divided upon, and that its action may be viewed by a properly-attached magnifying-glass. In Fig. 1103, a bar, attached to the same pieces that support the screw-arbor, to which it is parallel, and placed below it, together with a cock behind, bear the axis of a vertical friction-wheel, N. This wheel is placed so as to roll in contact with the under side of the limb of the engine immediately below the dividing-screw. Without this the action of the screw in the teeth of the wheel would occasionally produce a harsh jarring sound, but it is rendered mute by this contrivance. A hardened and tempered steel arbor rises full 2 inches above the surface of the plate in the axis of which it is immovably fixed. In the other engines the axis is hollow, so as to admit arbors of different size to suit the centre holes of the instruments to be graduated; but as Mr. Troughton, in using this engine, divided only his own instruments, he made them, whether large or small, so as to suit his arbor, and thus avoided one source of uncertainty and error. This arbor is the principal connexion between the engine and the work to be graduated, and requires the most exact fitting. Tapped holes, variously arranged through the length of the 12 radii, furnish the means of applying holdfasts to prevent accidental circular derangement. With this engine the operator can cut 24 strokes in a minute of time for hours together. The history of machinery during the last half century elicits the remarkable fact, so illustrative of a very high state of civilization, that most of our machines have had impressed upon them the character of self-acting engines. Nothing shows more strikingly the supremacy of intellect than an arrangement of brute matter capable of performing mental operations with unerring precision. The analytical engine, by Mr. Babbage, and the self-acting spinningmule, belong to this class; to which we may also add Mr. Simms's self-acting circular dividing-engine. at a great sacrifice both of time and of health, the effect of which was to add considerably to the cost of the instrument. Mr. Simms (of the firm of Troughton and Simms) therefore determined so to arrange the engine as to bring it under the yoke of some external moving power, such as a descending weight, a steam-engine, or a boy turning a winch, and having performed its work of dividing an instrument, to throw itself out of gear. The accompanying steel engraving represents an elevation of this engine, showing the apparatus for moving the engine-plate, and for cutting the divisions, together with the manner in which their operations are connected; and the following description will show in what respects it differs from E. Troughton's engine just described in detail.1 The circle or engine-plate is of gun-metal, 46 inches in diameter, and was cast in one entire piece by Messrs. Maudslay and Field. The centre of the plate is also peculiar; it being so arranged that it can be entered by the axis of the instrument to be divided, and the work thus brought down to bear upon the surface of the engine-plate. In former cases it was necessary, either to divide the instrument originally, which on account of the expense was seldom done; or to separate the part intended to receive the divisions from its axis and contiguous parts, in which state alone could it be placed upon the engine. The danger of detaching the instrument from its centre and framing is, that when reframed there is frequently a sensible excentricity; that is, the centre of the divided circle is not in the axis of rotation. This, however, does not lead to error, if two or more opposite readings be used. The great danger is distortion of the circle when the instrument is again put together. When the divided limb is only part of a circle, as in the sextant, any error of excentricity may become sensible, notwithstanding the care of the artist. In the present engine these difficulties are obviated, as already stated, by not dismounting the instrument. Fig. 1107. Fig. 1107 is a section of the engine-plate and centre. In order that it may serve for all cases, the plate a is Although Troughton's engine, just described, was a great improvement on its predecessors, yet it (1) The description of Mr. Simms's Engine is contained in the required the constant attention of a skilful operator, Memoirs of the Royal Astronomical Society, vol. xv. 1846. truly fitted into the recess b, and its upper plane | On the surface, and not far from the edge of the engine-plate, are two sets of divisions to spaces of 5 minutes; one upon a ring of silver, with fine lines for microscopic purposes, and the other upon the gunmetal face, cut strongly, so as to be easily scen without the assistance of a lens. There are also as many teeth upon the edge as there are divisions upon the face of the engine-plate, viz. 4,320; so that one revolution of the endless screw moves the circle through a space of 5 minutes. The circle was divided with extreme care; the first computation of the errors of the original points being merely made use of for the insertion of a second series of points, the errors of which, although exceedingly minute, were measured, computed, and tabulated in like manner; and from this second series the divisions were cut. The edge was ratched with a single circular cutter mounted in the endless screw-frame, and as each division in order was brought to coincide with the wires of a powerful microscope, the cutter was entered, and 3 circulations of the engine-plate completed the work. plate i. Now, supposing a division to have just been cut, and the excentric, by its revolution, to be about to lift the point from the work: this having been done, the end m of the bent lever descends the inclined plane, and the cutting point is thereby allowed to return from n toward o: in due time the motion of the excentric allows the point again to descend upon the work: the lifting of the end m of the lever by the next advancing protuberance, and the consequent pressure of the other extremity against the front of the cutting-frame, causes another division to be cut. The respective lengths of the divisions are obviously regulated by the radii of the several projections on the edge of the plate. This cutting apparatus is connected with the endless screw for working the engine-plate by means which are shown in plan in Fig. c, and in perspective in Fig. A, of the steel engraving. In c, h represents the axis of the excentric; p, a pair of bevelled wheels fitted to a box, which slides along the bar q, in order that the cutting point may be adjusted to the required radius, and for the same purpose the bar r consists of 2 tubes, sliding within each other, and capable of being fixed at any point by means of an external clamp. Another pair of wheels, at s, changes the direction of the motion, which now becomes parallel to the endless or engine-screw, and the shaft to which the last bevelled wheel is attached is turned by the external machinery. Each extremity of the shaft to terminates in a crank : that at the end t is connected by the eye, Fig. D, to the cord coiled round the spiral barrel, and thus communicates its motion to the endless screw; the other merely raises a weight, which, in its ascent, checks the accelerating tendency of during the return of the ratchet-wheel, and in its descent acts as an auxiliary in giving motion to the endless-screw, thereby preserving uniformity throughout the whole rupted. The spiral barrel and ratchet-wheel are similar to those described in Troughton's engine. The wheels at p are drawn in Fig. A, of equal size, in which form they serve for graduation into spaces of 5', which is the most usual upon work where the subdivision is effected by reading micrometers, and also in many cases where verniers are used. For other spaces these wheels must be proportioned, or the same thing may be effected by increasing the length of the crank. The cutting apparatus is shown at B in the steel engraving, partly in section, and separated from its supports and other parts which conceal it in the engine e and ƒ are the two members of the cutting-action, which would otherwise be unequal and interframe (which is similar to Hindley's as described in Troughton's engine), but the tail of f is prolonged in order to carry the counterpoise g, by which the pressure of the point upon the work, and consequently the depth and width of the divisions, are determined, and also that the revolving excentrich may alternately lift the point from the work and allow it to descend upon it to cut the division: i is a plate with an undulating edge, by which the alternations of long and short strokes are regulated. This requires to be changed from time to time according to the nature of the work; the one represented is made use of in division to spaces of 5', where the third and sixth lines have not only to be distinguished from the intermediate arcs, but also from each other, by their length. The motion of the plate i is communicated to the cutting-frame ƒ by means of the bent lever kk, one extremity resting on the edge of the plate, and the other pressing against the front of the cutting-frame, contact being maintained by the spring . A pinion upon the axis of h acts in a wheel upon the axis of i; and these are so proportioned that h makes 6 revolutions to 1 of i, a proportion that answers for 5', 10', 15', or 20', upon the circle under graduation, by varying the In the steel engraving all the essential parts are given, which serve for moving the engine-plate, and for cutting the divisions. A is a branch of a strong well-braced stand of wood, upon which the whole machine is placed. B B, the metallic tripod, in the centre of which the engine-plate turns, and to which all the superior parts of the machine are firmly attached. cc, the endless-screw frame, which turns upon finely polished steel pivots. The screw is kept in contact with the edge of the engine-plate with a proper degree of pressure by a spiral spring acting under the lever w, and can, when necessary, be discharged from action by the screw opposed to it. D D are portions of the engine-plate, and x represents a hoop of mahogany by which it is surrounded, and | Mr. Ross objects to the serrated cylindrical screw on its edge protected from injury. H H arc parallel bars, to which the cutting apparatus is fastened. (See also Fig. c.) p, q, r, s, and t, exhibit, as before, the parts connecting the motion of the cutting-frame with that of the endless-screw; but in the steel engraving, the crank, and its connexion with the cord wound round the spiral barrel, are more clearly shown than in the figure, where they are represented only in plan. The eye (Fig. D) by which this connexion is made, consists of 2 pieces, one to fit upon the crank, and the other to fasten to the cord: these parts are kept together by spiral springs, which by their elasticity prevent the jerk that would otherwise be given at each revolution of the crank. This part is also clearly shown in the steel engraving. u is the weight connected with the crank ; the opposing weight, or that to which the cord proceeding from the spiral barrel is fastened, is within the framework of the stand: the cord, in its progress towards it, passes over the pulley x, and also over another pulley within the stand. A pair of plates, with serrated edges, is shown at y: these plates serve to establish the connexion between the engine within the apartment and the driving machinery without. One of the plates is fastened to the cylinder z, which passes through the wall of the apartment, and the other can be thrown in or out of action by the handle I; so that the connexion can be made and broken in a moment. The method by which the engine can discharge itself from action, when it has completed its work, remains to be noticed. Against the handle, I, a spring is made to exert a pressure, the tendency of which is to detach the engine from the external machinery: this is opposed by a trigger turning on very delicate centres, and carrying a friction-roller at its other extremity. Upon the engine-plate, a small wellpolished wedge is fastened, which, as it circulates, passes under the friction-roller, which it lifts, and consequently discharges the bolt at the other extremity. This apparatus of course requires careful adjustment before the operation of dividing com mences. In the year 1831 Mr. Andrew Ross received the Gold Isis Medal and fifty guineas from the Society of Arts for his improved method of dividing instruments, and for his circular dividing-engine. We regret that we cannot, within our limits of space and illustration, do more than give a general idea of the principle of this engine. To do full justice to it would require us to copy the numerous illustrative engravings which accompany Mr. Ross's paper in the 48th volume of the Society's Transactions. It will be remembered, that in Ramsden's, and also in Troughton's engine, the circle which carried the instrument to be graduated was moved round by the teeth of an endless screw working in corresponding notches cut in the edge of the circle, and the endless screw was made to turn on its axis by a catgut band passing round a spiral in the same axis, and fastened below to a treadle which was worked by the foot. account of the great pressure required being incon sistent with those delicate operations so necessary to accuracy in such a machine; and he also thinks that variations in density in the steel screw, and porosity and other inequalities in the cast-metal circle, are likely to lead to error. He therefore gets rid of the driving motion of the screw, and obtains a rotary motion by an independent apparatus: he can also stop the circle at its precise angular position by the contact of plane and spherical surfaces of hardened steel. A more steady motion is given to the circle, and it also admits of being so adjusted that the inequalities produced by the wear of the parts may be obviated. The circle c, Fig. 1108, turns on its centre on a vertical axis, the lower extremity of which rests in a cup at one end of a lever, and a counterpoise being hung at the other end, the axis is thus pressed upwards and diminishes the pressure of the circle on the rectangular cast-iron frame which supports it, a portion of which is shown at ▲ B. Around the circle are screwed 48 projections, a a, through which Fig. 1108. MR. A. ROSS'S DIVIDING ENGINE. are passed capstan-headed screws parallel to the plane of and tangent to the circle. The ends of the screws are hardened and ground flat and square to the axis, and the screws themselves may be fixed in any position by means of tightening screws. At one end, A, of the rectangular frame, a sliding apparatus carries a cylinder, D, turning on a horizontal axis: on the surface of this eylinder is a worm, or spiral projection, bb, which enters between the projections a a, and the distance between the two turns of the spiral is rather greater than the breadth of one of the projections, a. A number of steel screws pass through the spiral thread; and the ends of these screws are turned in the form of hemispheres, so that after every movement of the circle c, and of the spiral bb, the engine is held in a state of rest by the abutment of the hemispherical end of one screw against the flat end of the other. On the outer rim of the circle c, below the projections a, is a groove in which an |