Fig. 3. is designed to spew in perspective the apparatus for carrying the wheel forwards by the screw, the manner how the latter is connected with the foot, and how it is stopped at every division. The chief parts of which this apparatus consists, are more or less seen in all the Figs.; but the manner of its being supported upon the platform of the stand by the intervening block I, is seen only in Fig. 2. The principal piece is a cock J, the horizontal part of which has two branches, (one shewn in the Figure,) be tween which the strings pass. The vertical part supports a cylinder of steel, which, when the screw is in action, forms a right line with its arbor ; but there is left between their ends a space of about half an inch : this affords easy means of changing the ratchet-wheels, which are placed upon the screw-arbor, and move round or stop with it. A. barrel about 2 inches long, and 14 diameter, is fitted upon the cylinder, but so as to admit of its being turned round and moved upon it with perfect freedom from end to end. The middle part of the barrel is formed into a spiral worm or screw, the groove of which receives a cord or catgut 1 of one-tenth of an inch in diameter. There is a slight frame dove-tailed upon the horizontal branches of the cock, as shewn in front of Fig. 3. which has steady and free motion in the direction of the cylinder ; to each side of this frame is attached a pallet, one of which enters in front, and the ether behind, into the spiral worm of the bar rel, by which means, when the latter is turned round, rec tilinear 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, plant ed in the edge 01 the cavity of 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 finger-screw, and ny means of a slit, tluough 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 con tact of these determines the point from which divisions begin : each division is terminated by similar means ; an anvil is found in the elevated part of the frame behind, and a hammer in a screw-head, projecting from the enlarged end of the barrel : a string occupying four or five turns of the groove of the barrel, at one end is attached to a treadle near the floor, and at the other, after passing over two pul lies, to a weight behind. When the treadle is pressed down with the foot, the hammer in front leaves its anvil ; and as the barrel is carried round, the frame is moved for wards by the pallets, so that in the second turn they pass clear of each other, and the motion is continued until the anvil behind is struck by the other hammer: during this time the catch, by the pressure of its spring, has hold of the perpendicular side of a tooth of the ratchet-wheel, car ries the screw round along with it, and moves also the en gine plate through the proper angle. On the pressure of the foot being gradually withdrawn from the treadle, so as to let the weight prevail, the barrel will he brought round in a contrary direction ; the hammer and anvil on the far ther side leave and pass each other, and then those on this side pass and meet as at first, ready for a second tread. During the time that the barrel runs backwards, the screw And engine-plate stand still ; for the sloping sides of the ratchet-wheel allow the catch to escape freely over them. As things stand in Fig. 3. a tread gives only two revolu tions of the screw, but the number may be varied at plea sure as far as six ; for let the anvil in front be placed by its finger-screw so much to the right as will allow the hammer to escape it, the weight will then draw the barrel back through another revolution, and the parts will meet again. Parts of a revolution are obtained with equal ease. It was said before, that the ring of the barrel, to which is attached the hammer in front, might be turned round and fixed at pleasure; now it is evident, that if the hammer were brought down so as to meet 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, we can vary the number of complete revolu tions ; and as parts of -a revolution are obtained by shifting the hammer, we have the power of varying the angular value of a tread from six 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 de gree, or 10" in instruments of reflexion, as well as to many others. To divide the vernier of a reflecting one that spews 15", requires a ratchet-wheel of 80 teeth ; and this number, were it of any use, which it is not, would give the usual subdivision of the 96° arc. To divide the centesimal degree of the French, and its first decimal sub division, requires a wheel of 100 teeth. To the division of odd and prime umnbers, a near approximation may be made by an al tilice contrived by myself, and I believe un known to any except those who have been my assistants: an example will be the best vviv of teaching it to those to whom it may be useful. Let the number to be divided be 331, and let the ratchet-wheel with 80 teeth be chosen; if we divide 2160, the whole number of turns the screw makes in one revolution of the plate, by 331, we shall have a quotient of 6, with a remainder of 174, which latter be ing multiplied by rciltice revolu•hms of the screw into teeth of the gives 13920, .,red this also being divided by 331, quotes 42 with a remainder of 18: that is, a division will be equal to 6 revolutions of the screw, and 42 teeth of the ratchet-wheel nearly. But as we cannot at one tread excein 6 revolutions, we must be content with half of it — 3.21, and tread twice for one di vision ; but as in our arithmetical operation we had a re mainder of 18 teeth, in order to make ends meet, these must, as we proceed, be disposed of in their proper places; now as 18 is the 20th part. of 360, if at every 20° of the
circle we set the screw one tooth foi ward by hand, the thing will be accomplished, and no greater error than tooth — 7".5 will enter the work ; a precision fully suffi cient for any purpose that such numbers can require, and in my opinion greater than can be come at by any other means.
On the end of the screw arbor to the right, as exhibited in Fig. 5. is attached a milled-head and divided microme ter ; the latter, like the ratchet-wheel, is changeable 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 fidu cial line, serves as an index for counting the divisions. By the help of this we are enabled at once to set the stopping apparatus to any part of a revolution of the screw, without the trouble of a second trial ; and by it, in case of a false tread or other accident, we can adjust the parts again to due position.
The frame and apparatus for cutting the divisions, and their connection with the engine, remain to be described. Upon the two remote branches of the tripod, and beyond the border of the wheel, are erected two 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 bar of brass KK, which they support, enable us to adjust its height, to suit the thickness of the work to be divided.
To the near branch of the tripod, a cross piece Fig.
2, nearly the length of the screw arbor, and parallel to it, is firmly fastened. This carries upon its extremities two pillars similar to, but smaller than, the others. Upon the strong bar KK, at equal distances from the middle, are two other bars fixed by finger screws. They extend from the strong bar to the pillars in front, to which they arc se cured by double nuts like the former. These two bars, marked AI, M in the plan, are bound together by a cross brace at the remote end, and by another a little way beyond the centre. But in no other part can crossing pieces be admitted ; 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 three principal pieces, marked in the plan a, e, o. The first is a bridge, which crosses the space between the bars M, DI, and to which it is attached at either end by sliding sockets. The latter run along the bars, to any part of which the apparatus may be clamped, according to the length of the radius of the instrument to be graduated. Two steel screws having conical points, are tapped through the perpendicular ends of the bridge 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 that of the second, is seen in the plan, has, like the first, 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. I, the parts are extended, for the purpose of being more distinct ly represented, into a position in which they cannot work. The best effect is produced, when the middle piece is ver tical, and the third horizontal. Sufficient freedom of ac tion, however, 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 adequate to the purposes required. 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.
There is one part, which might either have been men tioned sooner, or, as the performance of the engine in point of accuracy is not at all promoted by its introduction, might have been altogether omitted ; but as it bears rather a con spicuous appearance in Fig. 2, it may as well be noticed. 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 very harsh jarring sound, but which is rendered mute by this contrivance.
A hardened and tempered steel arbor rises full two inches above the surface of the plate, in the axis of which it is im moveably fixed. In other engines the axis is hollow, into which may be dropped differently sized arbors, suitable to the centre holes of the instruments to be graduated ; but as I never intended with this engine to divide any other in struments than those of my own construction, and as it was easy to make them, whether great or small, to suit my ar bor, by fixing it, I avoided one source of uncertainty and error. This arbor is the principal connection between the engine and work to be graduated, and requires the most exact fitting ; and tapped holes, arranged variously through the length of the 12 radii, furnish the means of applying holdfasts, to prevent accidental circular derangement.
I will now conclude this long description with observing, that with this engine, and indeed the observation applies equally well to those of Ramsden's construction, the ope rator can cut about twenty-four strokes in a minute of time; for one single minute, indeed, he will be able to make thir ty ; but including short and frequent intervals of rest, the former rate may be kept up for hours together. The vast importance of this expedition, needs no comment with those who know the value of accurately graduated nautical instruments, and the great demand for them. Yours, &C.