Let a b c d, Fig. 169, be the form of the required groove. Mark a series of centers so that circles struck from them will just overlap one another, and at the same time nearly reach the edge of the groove. Then turn out all the circular sinks, indicated by shaded lines, to the required depth.
Center the plate by the point o from which the arc a b is struck; now bring the cutter to such a position that its outer cutting edge coincides with the arc a b, and bring it against the plate; set the face-plate in motion, not, however, by using the treadle, but by the hand at its circumference, and traverse the arc from b to a; then withdraw the cutter. By this means the projecting angles, left white in the figure, will be removed, and a clean edge will be left to the groove.
As an operation of this description will not present any difficulty, further explanation appears unnecessary; for the information above given will enable any watchmaker to make curved grooves of the kind indicated.
If it is required to smooth the surface of the groove, replace the cutter by a pegwood stick that can be rotated with friction, and the end of which just fits into the groove, charging it with pumice or other stone and oil. One hand moves the face-plate backwards and forwards, while the other rotates the stick.
365. To Cut the Cylinder Escape-Wheel Cock Passage. As a rule the cock is cemented, inverted, to a wax chuck, and the passage cut or enlarged on the lathe. It is more expeditious to use a plate provided with a clamping bridge, as shown at Fig. 170. The face-plate should be made to oscillate backwards and forwards by hand, and not rotated by the wheel.
366. To Make a Straight Groove. First method. The tool devised by M. Chopard, director of the school of horology at Besançon, and shown in Fig. 171, is used for this purpose. As will be seen, it consists of a small lathe which is adapted to the slide-rest as follows:
Two pins, a a′, are planted in the top of the tool-holder, the cutter together with the plate by which it is clamped having been first removed. Holes drilled in the frame f f fit accurately onto these pins, while a screw, h, passing through an intermediate hole, affords a means of firmly fixing the apparatus to the tool-holder M.
This tool should satisfy the following conditions: The arbor C should fit into a recess that receives a cutter, but without coming into contact with it; this arbor should be parallel to the bed of the lathe; and, lastly, the axis of C should be on a line with the lathe center.
367. Having set this little appliance in position, trace on the watch-plate two lines indicating the directions of the sides of the groove as well as lines fixing its length. Now place the plate in the dogs, setting the point of the pump-center anywhere on the line drawn along the middle of the groove. Turn the plate so that this line is horizontal, and fix it in any way that is convenient.
The arbor C carries a revolving cutter k, which can be changed as desired, and is held in position by the clamping screw d. Assume that the diameter of this cutter corresponds exactly with that of the required groove; advance it towards the plate, turning the wheel rapidly, the cord being round the ferrule b; a circular sink will thus be formed in the plate of the same diameter as k.
When this has been cut to a sufficient depth, the tool is moved parallel to the face-plate, and the cutter k, continuing its movement of rotation, will now cut, not with its extremity i, but with its sides. It will thus form a straight groove of any desired length.
368. The cutter is a three-sided prism, or it may have four sides with four cutting edges on the sides, and only one cutting edge at the extremity i. If it is preferred to retain only the two acting edges that start from either end of the cutting edge i, they may be made more acute, and the other pair reduced by means of a file.
369. Second method. This is simpler than the one just considered. At the end of a rod G, Fig. 172, which takes the place of the cutter in the slide-rest, a plate p is fixed. A line is drawn across the face of this plate in such a position that, when G is clamped in the tool-holder, this line is horizontal, and in the plane that contains the axis of the pump-center.
Let it be required to cut a straight groove in the piece of brass l. Wax it to the plate p so that the axis of the required groove is over the line traced on the plate. Now fix G in the tool-holder and replace the pump-center by a rod D, the extremity of which is formed into a cutter of a diameter equal to the width of the required groove; the rod D should be fixed in the hollow arbor by a screw. It is then only necessary to set the cutter in motion, forcing the piece l against the revolving cutter, until the requisite depth is attained. Then, by making the tool-holder travel parallel to the face-plate, the groove will be elongated until of the desired length.
370. The cutter may be of the form shown in Fig. 171, or it may be as shown at b in Fig. 172, since the movement is always in the same direction. The cutting edges are each formed by two small inclined faces, one pair of which is shown at b; they occupy half the diameter of the cutter. At the back of this pair the cutter presents the appearance of the lower half shown in the figure and vice versa.
It will be evident that the two sides of this cutter will act while its motion is continuous in one direction.
Besides the numerous operations that can be performed on the lathe as we have hitherto indicated, it may be employed, if divided on the head stock, for tracing out angles, marking the crossings of a wheel, a balance, etc., and for other purposes, many of which are referred to in the course of this work.
PRODUCTION OF SCREW THREADS.
SCREW PLATES AND TAPS.
371. The lathes employed in the manufacture of screws are of two kinds; those intended for polishing and, where necessary, modifying the form of screw-heads, much used by watch examiners and repairers, and those specially designed for cutting the threads, which are mainly in use in factories.
Before discussing them, however, we will give some account of the screw-plates and taps in ordinary use.
372. Common Hand Screw-plates. The use of these is much facilitated by providing a second plate perforated with holes of such sizes that a spindle which just passes into a hole of any given number will be of the size most convenient for forming a screw in the hole of the same number in the screw-plate. For a long time we have made use of two Latard screw-plates so made that a rod which would enter one hole without play was of the most convenient size for forming a screw in the next smaller hole but one (thus the plate perforated with plain holes can be replaced by a second screw-plate, or by using the successively larger holes on a single plate as gauges).
In order to form a screw that is clean-cut and even, with the least possible straining of the metal, the holes in the screw-plate should have notches cut as shown at F, Fig. 173; they should be carefully hardened and well polished on each side of the notch, and this system is now even applied in the case of the smallest jewel screws.
373. Screw Dies. The ordinary plate, in which notches are not cut at the sides, squeezes up and strains the metal. This effect is less marked when separate dies are used, and disappears entirely if only a small quantity of metal is removed at a time, and the cutting edges of the dies are smooth and in good order. In addition to possessing other advantages, this form of screw-plate enables us to obtain at will screws of the same thread and different diameters or of the same diameter and different threads. The dies must be carefully fitted to the slides that receive them. Dies cannot be employed for cutting very small screws.
374. Fine-threaded Screw-plates. At the present day these can always be obtained at the material stores; but thirty years ago it was not so, and the watchmaker was obliged to make them for himself. The following method was adopted:
Take a screw formed with an ordinary plate, in which the thread is broad as compared with the hollow. If the screw does not satisfy this condition it must be modified thus:
Having ascertained that it runs true, and that it is larger than will be ultimately required, insert it in a chuck in your lathe. The T-rest must carry a smooth horizontal rod of hardened steel.
Rotating the screw, hold a slitting file in the hollow; the file should fit into this hollow accurately, and should be smoothed on its two sides, only cutting with one edge. The bar of hardened steel will determine the depth to which the file is allowed to cut. By this means a screw is obtained that has a thread thick at the bottom. With the graver remove the top of this thread, round off its corners, and harden the screw, filing three facets along its entire length, that make it taper.
The tap, having been thus prepared, is employed for cutting a thread in a piece of steel, not too thick, that has been previously annealed, and in which a hole is drilled of the proper size. The thread of this internal screw will be thin and the hollow proportionately broad.
The plate is now hammered cold with care until the thickness is so far diminished that the thread and hollow are as nearly as possible of equal thickness. Harden it and chamfer the ends of the hole with a conical steel point and oilstone dust. Then clean it and cut a thread on a piece of soft steel which may be formed into a tap.
If the operation has been properly conducted, this tap will satisfy the prescribed conditions, and, when hardened, it is to be employed to cut a thread in a second steel plate, which will be employed as a screw-plate; for that first formed must, in consequence of the hammering to which it was subjected, present irregularities in the hole, and can only be used to cut one or two taps cautiously. It is useless for making screws or tapping brass. (See also 378.)
375. To Clear a Stopped Hole in a Screw-Plate. Drill a hole through the center of the piece of metal that fills up the hole, taking care to maintain it central, and to employ a drill that is sufficiently small to avoid all risk of contact with the screw threads. Pass a broach through this hole and, after tightening it with a few gentle blows with the hammer, turn it in such a direction that it tends to unscrew the broken screw, which will in nearly every case, be removed without difficulty by this means.
TAPS.
376. Screw-cutting comprises two distinct operations—the formation of a spiral thread on the circumference of a cylindrical spindle, and of a spiral groove within a cylindrical hole to receive this thread.
Taps are made either by means of a screw-plate or in the lathe; we shall presently refer to this second method. Every watchmaker may be supposed to have received, early in his career, instruction as to the cutting of a tap with a screw-plate. Great caution is necessary in the hardening, for if the tap is not true or the metal burnt it will cut badly and be apt to break. Taps are cleaned after hardening with a piece of wood in the lathe or between two hard pieces of pith covered with oilstone dust, and either three or four cutting facets may be made. It is important to avoid the production of a burr in making these facets; a good plan is to make them while the metal is still soft, and to pass the tap through the plate subsequently, as a sharp cutting edge is thereby produced. The facets should be carefully smoothed, and the use of coarse rouge is an advantage.
A tap with three facets gives the cleanest cut and leaves the most space to receive the metal that is removed, but with four facets the roundness of the hole is more certain to be maintained.
We have seen taps formed as represented at M, Fig. 174, so that the object in which a thread is being cut is loose at the part o, when the direction of movement of the tap is reversed. They are also at times made semi-cylindrical, as at G, and work well in the lathe for tapping brass, but we have not tried this form with steel.
377. To Cut a Tap when of Considerable Length. The following precautions must be observed in order to ensure that a long screw shall be both round and true.
The steel must be of very goad quality, and loose dies should be used in preference to a screw-plate. It is a good practice to employ two pairs of dies (or even more); one to rough out the screw, leaving the thread somewhat larger than it will finally be, and the other to finish after having trued it, and even sometimes lightly turned the surface in places. Very little metal must be removed at a time, the dies should have sharp cutting edges, and a rather large number of threads.
A screw can be made in the ordinary manner in a screw-plate rather larger than is required, then reduced to the requisite diameter, and finished with a plate in which the holes are of the form shown at F, Fig. 173, or in a screw-cutting lathe; in either case, however, care must be taken to avoid straining the metal in its passage through the first plate, on account of the tendency which it then possesses to become distorted in the hardening.
If a micrometer screw is required, that is, a screw of absolutely uniform pitch, it is necessary to apply to makers of astronomical and other similar instruments of precision.
378. To Cut a Screw of any Desired Pitch and Diameter. Let it be required to cut a thread on the stem B, Fig. 175, of any pre-determined pitch that already exists in a screw-plate. Turn down the portion d to such a diameter that a screw can be cut on it in this hole, and fit two runners to the lathe of the form shown at G and H. The end of H is drilled and tapped so that d turns freely in it, and a hole is drilled in G to receive the stem B freely, but without sensible play, and a fine notch is cut at a.
It will be obvious that if now the ferrule r is caused to rotate, while a fine saw or file is inserted in the notch a, a screw will be formed on B of the same pitch as that on d, although there may at the same time be a very considerable difference in their diameters. This method may be adopted in place of that explained in article 374 for obtaining a fine-threaded screw.
379. Left-handed Screw Taps. The manner in which these are made in the screw-cutting lathe will be subsequently explained; in its absence the watchmaker may adopt one of the following methods:
First method. If, when an internal screw has been cut with a right-handed tap, B, Fig. 176, it be required to tap a second hole in the reverse direction, the following plan may be resorted to:
File the original tap B on two opposite sides, so as to give it the flattened shape shown at A in the same figure. Insert the end into the hole to be tapped and turn the tap to the left with the application of considerable pressure, so as to force the tap to bite. When the tap has been passed in and withdrawn there will be found to be a left-handed thread cut in the hole. For, if the tap is turned towards the right, the thread f passes into the groove already formed by the thread a; but, if turned towards the left, f will originate a groove into which b will pass, traveling in an inverse direction to that previously given to it.
The finer the thread of the screw, the better is the chance of success, and with a wide thread it is often necessary to recommence two or three times. If a plate or pair of dies be cut in this manner and hardened, they will serve to cut an even left-handed tap.
Second method. Attach a comb to one or two sides of a cylinder, as indicated at F, Fig. 177. This can be used to cut a thread in the piece of metal S, that is either right or left-handed according to the direction of rotation of F, sufficient pressure being at the same time applied to force it into the plate. The pitch of the thread will depend on the amount of pressure applied. This plan is only a modification of the one described above, and, as in that case, success can only be guaranteed when a means is adopted for securing a definite relative amount of motion in F around its axis and S vertically.
Third method. A tap of unhardened steel is filed into a triangular form, C, Fig. 178, and twisted so as to bring the angles b, f, towards a, d, etc.; we thus obtain a tap which will serve, throughout a certain portion of its length, to cut a left-handed thread, but the part that is not so adapted, at the extremities, will require to be removed before hardening.
380. To Make a Left-handed Tap by Means of a Right-handed Tap. A portion of the right-handed tap is filed off on three faces to the section shown at b, Fig. 179, and firmly set in the die d so as to be held in the frame for screw-cutting dies. A second die, f made of brass and having a semi-cylindrical recess opposite b is fitted to the frame. The diameter of this semi-cylinder should be the same as that of the rod on which a left-handed thread is to be cut. Now grip this rod as shown at a by means of the screw g, so that it is held between the die f and the block b, and rotate the frame or the rod a towards the left; a spiral groove will thus be cut by the thread on b. It is sometimes an advantage to cut this thread lengthwise in the manner indicated at b′.
This method enables us to cut a given thread on a rod of any given diameter. From an examination of Figs. 179 and 180, it will be seen that a simple comb of the form of C or D, carefully made by hand and fixed in the place of b, can be employed to cut a right or left-handed thread on any given rod; it is advisable, however, that the teeth of the comb be inclined to the axis of the screw, like the thread of an ordinary tap, as otherwise the operation becomes more difficult and success less certain.
The method may be simplified by taking a brass plate, D, Fig. 181, of sufficient thickness, and firmly setting in it the right-handed tap, v, having only filed away two opposite faces before hardening. The rod to be tapped is then introduced with considerable pressure into the hole j, and, if rotated towards the left, it will receive a left-handed thread of the same pitch. The notch shown at b′, Fig. 179, will facilitate the operation, as a cutting action will take the place of compression.
381. M. Gontard has suggested a modification of this arrangement, which consists in forming the die f, Fig. 179, so that the original right-handed tap can be embedded in a hole previously tapped in it and filed away on the side towards b so as to expose a cutting edge; and he points out that, by suitably inclining the frame with reference to the axis of the rod to be tapped, the appliance can be used to cut a double or even a triple-threaded screw, right or left-handed. He further draws attention to the fact that in a screw formed in this manner the sides of the thread are smooth and polished, a condition which cannot be secured when either a plate or dies are used.
382. To Increase the Diameter of a Tap. It sometimes happens that a screw will not penetrate to a sufficient depth, or fits too tightly into its hole, owing to the tap employed being of a less diameter, either in consequence of the hardening, polishing or wear, or through having been formed in a different screw-plate. In such a case the following expedient may be resorted to:
Make a fresh tap in soft steel and file away two opposite sides so as to give it the section shown at A or B, Fig. 182: after measuring the diameter at several points in its length, hammer gently on the flattened sides. With a little care and by using a micrometer at intervals for testing the alteration in diameter, it will be found that the required increase can be obtained without much difficulty. The tap is then hardened and polished, etc.; indeed, it is best to make a fresh tap.
METHODS OF TAPPING HOLES.
383. It is needless to refer to the method of tapping by hand, as it is well known to all practical men.
384. Tapping in the Lathe. The plate of a watch is gripped in the dogs of a face-plate, the hole to be tapped being centered by means of the pump-center, which is then withdrawn, and a tap held to the hole; the face-plate is then caused to rotate either by the hand resting on its circumference, a slight backward motion being given after each advance, or the motion may be continuous and be given by the wheel. In the latter case, however, the tap must have a good cutting edge and only be held in the hand with the degree of force required to make it cut, so that it may rotate without breaking in case the resistance opposed becomes too great. The tap may be steadied on the T-rest.
385. To Tap with a Mainspring Winder. The ordinary mainspring winder will, if the click work is removed, be found very convenient for tapping holes, and indeed, for forming the external thread on screws. Having removed the winding arbor, replace it by a tap carefully centered; then introduce its coned end into the hole in the plate, which must be pressed forward while the handle is turned, a short backward motion being given to it at frequent intervals. When the tap is engaged sufficiently in the hole it is merely necessary to maintain the plate at right angles without applying pressure.
386. To Tap with a Bow. Instead of the mainspring winder, one of the small drill-stocks to be driven by a bow, consisting of an arbor, with a coned hole at one end and ferrule at the other, supported in a frame that is clamped in the vise, may be used. They are to be obtained at any tool-shop.
The bow being on the ferrule and the tap properly centered in the arbor, the hole is held against the coned end and the bow worked with an alternate forward and backward movement; but if the tap has a good cutting edge and the bow is strong (of steel or cane), a hole may be tapped with a single stroke of the bow. After a few trials the method will be found very easy and certain.
A regular and rather slow motion should be given to the bow, which should be long and strong. It is well to ascertain the number of revolutions of the ferrule that correspond to a stroke of the bow, so as to ensure that the tap is not introduced to a greater depth than is required. If it is desired that the screw work easily in the hole, the tap should be moved several times backwards and forwards.
387. The little turns here referred to, some of which are perforated throughout their entire length and others only at one end, are very cheap and will often be found useful; they can be adapted to receive drills, broaches, taps, etc.
388. To Tap in an Ordinary Lathe. In factories it is a common practice to tap the holes in plates, etc., and even to cut the threads of screws in a lathe specially arranged for the purpose. The tools adapted for such work are of two kinds: in some the tap enters to the required depth, when it is immediately arrested, disconnected, and then rotated in an opposite direction; in others, the tap advances to a definite point, and is immediately withdrawn. As a rule, however, the tap remains stationary and the object is caused to rotate.
389. Beillard Lathe for Tapping Screws. The axis F M, Fig. 183, is perforated throughout its length. At F, the screw-plate G is dovetailed into it. The inner end of the hole in this plate is slightly coned to facilitate the insertion of the brass wire D, and it must be exactly in the axis of F M. A guide B sliding on two rods c, c, is traversed by the rod D which can be clamped in it by the screw a.
By pushing D against the screw-plate at the same time that the handle N is rotated, a thread will be traced on it and it will emerge at k. When B has advanced to the point m, the screw a is released, B is drawn back, and a again clamped.
When a long screw, such as X x has to be tapped, the screw-plate is fixed at m, and the guide B is fastened on to the portion X. Of course the hole in the screw-plate must always be abundantly provided with oil.
If the screw-plate F is replaced by a plate perforated with a round or square hole, a drill, broach or tap may be substituted for k, being clamped by the screw h, and the tool is at once available for drilling, broaching or tapping any given hole.
RAPID MODE OF MAKING A SCREW.
390. The methods ordinarily adopted by watchmakers are too well known to need description; we will therefore at once proceed to give a special plan recommended by M. Vissiere.
An eccentric poppet-head with boring-plate, Fig. 185, is fitted to the bed of the lathe, the eccentricity being such that the axis of the centers is at the point a on the circumference of the circle a y. The conical hole, having a center at a, is cut away towards the rim of the plate to the degree indicated in the figure, and its center is so placed that the vertical line f and the radius d are inclined at 120°. The position of the T-rest is shown at s, and by bringing it into actual contact with the disc the steadiness of both is increased.
The fixed headstock of the lathe is provided with a runner of the form B, Fig. 184, terminating in a point m at one end and a hollow cone or funnel n at the other end.
Having filed the ends of a rod T, of any required diameter, square and fitted a ferrule, support it between the two cones, a of the boring-plate and n of the runner. Near the end a cut a hollow r sufficiently small to allow the stem to pass through the notch in the hole a, Fig. 185. After passing it through, the rod will be supported as shown at H, Fig. 184, so that the rim e i rests against the cone.
Further explanation is hardly necessary; after removing the portion c g with a graver, turn down to a point p. When making a screw, turn out a second hollow o o′; it then only remains to turn off the disc at the extremity, and the screw will be roughed out of the form c p g v.
If it is preferred to work with a point at the left-hand end of B, remove the rod after the point v has been turned, replace m B n by a common runner, reverse B, and recommence the operation.
It would be difficult to devise a method for roughing out a screw and making a point that would be more expeditious than the one here described.
SCREW-HEAD TOOLS.
391. These are of various kinds: some work by hand and others by a bow. The jaws are brought together sometimes by a sliding ring, and at others by a milled head placed between them and rigidly attached to a pin tapped with right and left-handed threads that engage in the jaws. But neither of these plans is good; the screws are not held firmly and they are rarely well centered; owing to the slight displacements of the jaws.
A better plan is to arrange, either in the lathe or in the jaws of the screw-head tool (when driven by a bow), a series of chucks of the form shown at T, Fig. 186. They are easily made and tapped, the hole i serving to remove the metal from the inner end of the hole that has to be tapped; such chucks occupy very little space, and, if numbered to correspond with the size of screw, any chuck required can be found without trouble. If the hole becomes too large owing to frequent use, a larger size of tap can be passed through the hole and its number changed.
392. A set of such chucks is almost indispensable at the present day to the watchmaker who wishes to repair watches well; for he rarely makes his own screws, as they are to be obtained well made and very cheap at the material dealers, whereby a great saving of time is effected. But their heads are seldom of the proper size to fit the original sinks, and by being provided with such a series of chucks the watchmaker can at once overcome this difficulty, as he can turn the heads down with a graver.
393. R, Fig. 187, is an arbor for a screw-head tool that is driven by a bow, and is adapted to receive such chucks, or it can be used in an ordinary lathe, d being supported on a pointed center, and g in a boring-plate, Fig. 188, or in a cone-plate center.
394. In this form of screw-head tool the portion A is sometimes perfectly cylindrical, so that the piece V can slide on to it, being clamped by the screw b.
This tube V is cut away through about half its length with a notch, as indicated in the figure; bent pieces of hardened steel c and n are screwed to either side of the notch. Screws, h and f, provided with lock-nuts, determine the distance between these plates, and when V is in position on A the ends of c, n, will rest on the screw-head, leaving just sufficient space between them for inserting the file that cuts the slit.
Hard steel caps of the form shown at M may also be fitted to A, a notch being cut in them to receive the screw b. These will be found useful as guides for filing or polishing screw-heads, or the ends of arbors flat, reducing the heads of several screws to the same height, etc.
395. The tool for forming the U-spaces in a cylinder escape-wheel can be easily be converted into a screw-head tool with laps. A glance at Fig. 189 will at once make this evident. A number of chucks are adapted to the arbor A, and in the tube c c either a T-rest or a spindle carrying a lap is fixed.
It will also serve as a tool for drilling; a drill-chuck with drill, f, being adapted to A, and the object to be perforated at b resting against a plate that projects at right angles from a slide d d, which may be advanced by a screw g.
396. The modern watchmaker has so little call to cut screws that it does not pay him to purchase a screw-cutting lathe; for a very small sum he can have screws of any thread or diameter cut by those who make a specialty of such work, always provided that he cannot find what is wanted in the material stores. The same thing also applies to fuzees.
TOOLS FOR CUTTING AND ROUNDING-UP
THE TEETH OF WHEELS.
WHEEL-CUTTING ENGINE.
397. The machine for dividing the circumference of a wheel, termed the wheel-cutting engine, and one form of which is shown in Fig. 190, is well known to nearly all workmen. The wheel is fixed to a chuck at B by wax or screws, or by the pressure of a hollow cone or “sugar loaf” of steel, to the apex of which pressure is applied by the arm D, or in other ways. The wheel may be centered either by a pump-center within the chuck or by an appliance such as is shown in Fig. 191, except that the arm b is curved and its index much longer. This little addition may be fixed to the frame of the engine in any convenient position.
The chuck B that carries the wheel is rigidly connected with a large brass plate A A, on which are concentric circles of divisions, and the whole can be maintained stationary by setting the point of the index C C in any desired hole on the division-plate. The cutter is carried on an arbor (shown separate at L) between horizontal bearings in the frame J, and is caused to revolve by means of the pulley K. The several parts lettered E, F, G, H, are for bringing the cutter against the wheel and modifying the direction in which it moves, so that the machine can cut straight or inclined teeth, bevel or crown wheels, etc. It should be added that the engine here represented is more complex than those ordinarily used for cutting watch wheels, although the principle on which it acts is the same.
The teeth may be cut by circular cutters of the nature of files, by a small straight cutter, similar to those used in a slide-rest projecting from a rotating axis, or by several such cutters mounted on a disc which is caused to rotate. For the sake of distinction it will be well to refer to the first of these as file or mill cutters, while the second and third may be termed respectively single and multiple blade or composite cutters.
Watchmakers rarely possess a sufficiently large assortment of file-cutters for making all the various forms of teeth that are met with in horology; but this deficiency can be supplied by making them for themselves to any required pattern in the manner subsequently described.
398. Observations. The wheel-cutting engine in which the plate is caused to rotate by means of a tangent screw is usually the most accurate. If the pitch of the screw is fine it will give all the subdivisions of a circle that are required for ordinary work, but it is essential that a good form of counter be attached to the screw, and a certain amount of calculation is always needful.
The engine that has a division-plate with conical holes arranged concentrically over its surface is simpler and better adapted for rapid work. The larger this plate, the greater is its chance of being correct and, at the same time, it affords room for a larger number of divisions.
It is preferable that the cutter frame rise and fall in a vertical dovetail, for when the arbor is carried in an H shaped arm pivoted on two screws, the teeth are always slightly dished. The entire apparatus should be somewhat heavily constructed and supported on a solid bed; so as to prevent the vibration of the cutter-arbor from being distributed over the entire machine.
The highest numbers on the plate should be used whenever it is possible, so as to diminish the error due to irregularities in the sub-division. For example, in cutting a wheel of 30 teeth, use the 90 or 120 circles, taking every third or fourth hole.
These remarks will probably be sufficient to enable any watchmaker who possesses a wheel-cutting engine to employ it with success; we will, however, add the description of a few appliances or processes that have a bearing on this question.
399. To Divide a Wheel so that it has one Tooth more or less than any given number on the Division-plate. It is to be observed that neither this nor the following method is mathematically exact, but if it is practiced with care and the division-plate is of sufficient diameter, the error may as a rule be neglected.