Chapter XVIII: Part VI: Practical Recipes (2)

Place it on the dividing plate (see article =343=) to mark out the three arms, and remove the metal between them, either in the lathe, as explained above, or by drilling a series of holes parallel to the arms and rim. These holes should be so arranged that they can be enlarged with a fine-pointed graver (while the balance rests on a flat wooden block or is cemented to it), and a turn with a sharp edged broach, or the passage of a thin rat-tail file should be sufficient to separate the useless metal. As a rule, the series of holes is drilled with the disc held against a wooden block, but the burrs produced on the under side by the drill prevent it from being maintained flat, unless they are removed after each hole is drilled, and this might occasion a distortion of the disc. It would, perhaps, be better to cement the rough balance to a sheet of zinc; the color of the shavings would suffice to indicate whether the hole was through.

The arms and rim must be made smooth and even with nicely formed crossing files, the edges of which are smoothed to the most convenient angle, as already indicated.

In filing the crossings the balance should rest against a small block in the vise, and they are rounded while resting in a groove at the edge of a similar block, specially shaped for the purpose. This block is also useful as a support in finishing the angles between crossings and rim.

The under face of the balance is smoothed with oilstone dust; and the arms by drawing the polisher along them while the balance rests on a flat block; it is then cleaned and fitted on a very true arbor, as A, Fig. 233. This should pass through the center hole of the balance without play after a broach has slightly enlarged it, and the balance is clamped by a cap and three screws, _j_. It only remains to set the arbor in the lathe and polish the rim, first turning it to a half oval if desired. In the latter case the rim, after being smoothed, is polished first with coarse rouge on hard pith, and subsequently with fine rouge on softer pith.

=535.= If the arms of a balance are found to be too long, so that they curve, the rim must be lengthened by hammering with the greatest possible care; the inside and outside of it must then be trued on an arbor of the form A.

The boss at the center will be found thicker than is desirable; its height can be reduced with the balance merely adjusted on a smooth taper arbor, but it is necessary to observe that the balance and arbor must not be adjusted to each other by pressing or by rotating the balance with the rim held in the fingers. It must be pushed on or off the arbor by applying pressure at the center of the boss on one side or the other with a piece of hard wood resting firmly against the =T=-rest, while you cause the arbor to rotate.

Instead of the form of arbor shown at A, a screw arbor might be used, with its cone pressing against a cap, but the balance must always be carefully adjusted on the arbor, and this latter must run perfectly true.

=536.= =To Make a Number of Identical Wheels.= If it is desired to make a number of brass wheels of the same size and shape, the workman will find it much to his advantage to employ the punching machine. By adopting the following method he can make his own punches and bed-plates.

With a view to secure same length in the matrices that are used for forming the crossings, without augmenting the difficulty of construction, proceed thus: Each of the pieces V, V, Fig. 248, consists of two parts: 1. The star-piece, _a c b d_, of three, four, five or six arms, according to the number of crossings of the wheel. 2. The collar, V. The star-piece is of the same length as the collar, and is made in the wheel-cutting engine in the same manner as the leaves of a pinion. The punches, of which one is shown at P, are fitted by hand to the recesses of the star-piece, and then cemented in position; the whole is then chucked in the lathe and turned as one piece, so that its diameter is slightly greater than the interior of the collar. Now harden the star-piece, and temper it to a blue color. When cold harden the collar V _v_, and temper it to the same degree, but, while expanded by the heat in tempering, introduce the cold star-piece and drive it home. By proceeding in this manner, no subsequent hand fitting will be required. V _n_ must not be hardened.

Tools for punching the crossings of wheels are sometimes made on this system in which the disc of brass is fixed to a support that can be made to revolve by quarters of a revolution at a time, and a single punch serves to remove the metal by four separate operations. But as a rule it is better to use four punches together.

=537.= =To Repair Wheels.= When the teeth of a wheel are damaged, the only possible remedy is to provide a new one. If, however, a single tooth is broken, the following method can be adopted, on an emergency, for inserting a new one:

=538.= _To insert a new tooth in a wheel._ Cut a small notch in the rim of the wheel, shown at _a_, Fig. 249, which should be dovetailed if possible, and the two sides spread out slightly from the upper towards the under side, as indicated at _c c_. Cut a small piece of well-hammered brass, of the form B, so that the part _d d_ fits exactly into the notch in the rim. Now invert the wheel and grip it near to _a_ in a pair of long-nosed pliers, which must be held in the vise. Moisten the inner faces of the notch with soldering fluid and, placing B in position, put particles of solder round its edge; holding the lamp beneath the nose of the pliers, the solder will presently melt, and a drop of the fluid should be added to facilitate its running into the joint. Cool the wheel and wash thoroughly, first with water and subsequently with alcohol.

It only remains to file both faces smooth and level with the rim of the wheel; then shape the tooth carefully.

By introducing B from the side opposite to that which is visible in the watch, and sloping the faces _d d_, to a less degree than _a_, the inverted wheel will present a recess to receive the solder; so that, on looking at the upper surface, at which the edges fit very closely, the joint will be scarcely visible.

=539.= _To true a wheel._ When the teeth are found to be in good condition, but the wheel does not run true, or one or more of its arms are strained, the fault can be corrected, in a case of absolute necessity, as follows:

Remove the pinion from its wheel. Enlarge the central hole in the lathe and rivet or solder in it a brass ring that is slightly thicker than the wheel, and perforated with a smaller hole than that required for the riveting. Now center the wheel from its circumference; increase the central hole with the slide-rest cutter, and turn down the two faces of the ring level with the wheel. Rivet the pinion in its place, after testing the truth of its riveting neck, when the wheel should be found to turn both true and flat.

If the wheel under repair is likely to be subjected to much force, at least two small notches should be left in the enlarged hole in the wheel to receive corresponding projections in the brass ring.

=540.= If the _crossings of a wheel are broken_ and the wheel cannot be replaced, it must be chucked in the lathe and the arms turned out with a graver, the inner edge of the rim being at the same time turned circular, and a step turned on this edge where the metal is to be left of half its original thickness.

Take another wheel of the same size and thickness, or a plain disc, and turn it of the same diameter as the outer ridge of the step; reduce its thickness at the edge by one-half and a disc will thus be obtained with a ridge round the edge corresponding exactly with that of the wheel, and the one will fit in the other. They are, of course, soldered in this position, care being taken to prevent the solder from reaching the teeth, and the old wheel will thus be provided with a new interior.

If the disc is made to fit closely on the upper side, a wedge-shaped ring being left to receive the solder in the manner explained in article =537=, the joint will be scarcely perceptible on the exposed face, even with a glass.

In repairing delicate wheels in any way it is a good precaution to cement the rim to the edge of a hole in a brass plate, so that only the arms or other part to be operated upon is exposed.

=541.= =To Make a Stem-Wind Wheel.= We will suppose that the old wheel is available as a pattern; if it is not, the several dimensions must be ascertained by calculation in accordance with the laws of depths.

Prepare a thick plate, and drill a central hole, fitting a steel pin into it as shown at _o d_, Fig. 250. The diameter of _d_ must be exactly the same as that of the pump-center in the universal head. Fit the wheel-blank R to the pin _o_ without play, and cement it to the plate. Remove the pump-center and insert _d_ in its place, clamping the plate P firmly against the face-plate by the dogs. By using well-sharpened gravers or cutters, the wheel may be rapidly shaped.

The pin might be forced in from the under side to the level of that face of the plate; and if it were perforated as shown by the dotted lines, it might be centered by means of the pump. Or the plate P might be made circular and centered from its circumference.

=542.= To cut the teeth on the circumference the wheel need only be fixed on the chuck of the wheel-cutting engine as usual by means of the steel cone. The crown teeth are cut while the wheel is firmly cemented to a pin-chuck like that used in turning it.

Other keyless wheels can be made on the same principle, and such modifications as may be necessary experience will suggest. Sufficient information in regard to wheel-cutting has already been given in =397= and following articles.

PINIONS.

=543.= =To Make a Pinion.= At the present day pinions of all sizes can be obtained of the material dealers, so that it is very seldom that a watchmaker is obliged to make one for himself.

In an emergency, however, he can adopt the following method for making one out of the ordinary drawn steel; but it should be added that, in all probability, some practice will be needed before success is arrived at. Cut a length of steel wire of suitable diameter about two-thirds as long as the files that are to be used for shaping the teeth. Turn it down to form the axis, leaving a block near each end equal in length to the required pinion, as if three pinions were to be made on the same staff. Then cut and round leaves on all, keeping the file always in contact with a leaf of each pinion. By proceeding thus the sides and roundings of the leaves will be maintained parallel to the axis, and there will be no risk of the pinion being barrel-shaped, as is nearly always the case when a short pinion is held in the fingers or rested on a block in the vise.

Proceed in the same manner in smoothing and polishing, using pieces of some close-grained wood, such as walnut.

It is much easier to make the pinion of the required form by means of a revolving cutter in the lathe, if the workman is not provided with a special tool for the purpose: the arrangement of the lathe is described in article =402=.

In some factories the leaves are cut in two operations: a cutter with plain fine saw teeth divides the circumference into the requisite number of equal parts, the leaves being subsequently made of the correct shape by a special cutter, the method of making which has already been very fully explained in articles =417-435=.

=544.= =To Determine the Size of a Pinion.= The following table is usually employed for this purpose. See also =562= and the following articles.

To give the approximate diameter of a pinion, the pinion caliper should include:

For 16 leaves, 6 full teeth; that is to say, measuring the distance
between the two external faces;
” 15 ” rather less than 6 teeth, or 5 teeth, and just beyond
the point of the sixth;
” 14 ” 6 teeth, measuring at the points.
” 12 ” 5 teeth, measuring at the points (or rather 4½ teeth);
for a clock-wheel, 5 full teeth;
” 10 ” 4 full teeth;
for a clock-wheel, 4 _squared_ teeth;
For 9 leaves rather less than 4 full teeth, or 3 full teeth to the
point of the fourth;
” 8 ” 4 teeth, measured at the points, minus a quarter of a
space;
” 7 ” rather less than 3 full teeth;
for a clock-wheel, 3 full teeth, plus a quarter of
a space;
” 6 ” 3 teeth, measured at the points, or rather more;
for a clock-wheel, 3 full teeth.

It is important to notice that these measures can only be regarded as a first approximation, and it is only by actual trial in a depth-tool that we can be certain that a pinion is correctly sized. By taking the measures in a micrometer, or other accurately divided gauge provided with a vernier, the work of selecting will be much abridged; but how long will it be before the generality of watchmakers will make use of these convenient appliances? The well-known wheel and pinion sector, although convenient, is not equal to them in point of accuracy, and is affected by an error in measuring a chord, not a true diameter of the wheel or pinion.

=545.= =To Increase or Decrease a Pinion.= The pitch circle of a pinion may be increased by reducing the thickness of the leaves in such a manner that their flat faces are continued further on to the rounding; conversely, a pinion may be decreased by carrying this rounding farther down towards the base of the leaf.

=546.= =To Decrease a Pinion Without Removing the Wheel.= Some watchmakers recommend that the wheel be removed from the pinion, and, after the necessary reduction has been effected and the leaves re-polished, again riveted on the pinion-neck. Very few workmen, however, can do this well, so that after the operation the wheel is seldom found to run true. If a new pinion cannot be procured, the old one must be reduced.

When a pinion that is too large is replaced by one that is smaller, it is necessary to take care that the hole in the wheel is well centered and not too large; in either of these cases it must be enlarged and bushed after being centered by the circumference.

=547.= =To Polish Pinion Leaves Mechanically.= It was formerly the custom to polish the leaves of a pinion, holding it on a block or between two fingers and traversing a strip of metal with oilstone dust backwards and forwards in each space for the smoothing, and a similar strip of walnut wood (with rouge) for polishing.

This method has long been abandoned in factories, where all pinions are polished in a machine.

We will proceed to explain a simple arrangement for polishing pinions in the ordinary lathe, but it is advisable first to describe one form of tool that is actually in use on the large scale for this purpose. The two only differ in their dimensions.

=548.= _Pinion-polishing Machine._ A frame B B, Fig. 251, supports at its upper end an =H=-shaped piece, of the same form as the cutter-holder in an ordinary wheel-cutting engine; but the arbor, instead of carrying a cutter, is provided with a wooden drum R. On the base of the frame is a plate P, which can be fixed by the screw E, and carries a second plate _p_ to serve as a bed for the slide, which supports the pinion to be polished freely between two brackets _a_, _a_. The plate _p_ can be set a little oblique and clamped by the screw _v_.

The machine acts as follows: Present a corner of a pinion-leaf to the circumference of R (which is caused to revolve by a cord passing round the pulley _n n_), the axis of the pinion being not quite at right angles with that of the drum, in order that the groove formed in the soft wood may resemble the thread of a screw, and so cause the pinion to revolve. When the groove is of sufficient depth, apply rouge if operating on a small pinion, and emery for a large one: after a few turns of R, the slide carrying the pinion being at the same time moved backwards and forwards, the pinion will be found to be polished. A better surface can be obtained by using flour emery.

The steel wheels of keyless work can be polished in the same manner.

=549.= The spindle of the screw E passes through a rectangular slot in B in order that the slide and its support can be moved parallel to the axis of R.

The grain of the wood must be at right angles to the axis of rotation of the drum, and a wood that is non-fibrous is preferable. It must evidently not be too hard, and, if too soft, the thread formed on its circumference will get rough, and often will suddenly change position. When the entire surface has been worn it must be re-turned smooth and cylindrical. The larger a roller is, the quicker it will polish and the less it will wear. Moreover, it will render a proportionately less amount of motion of the slide necessary. The root of the walnut tree is especially sought after, but, when this cannot be obtained, other woods can be used.

In factories where clock pinions are made, thin discs are employed in place of the drums. They are at least a decimetre (4 inches) in diameter, and very narrow at the edge, and can be re-turned with a graver when worn without being removed from the tool, if a =T=-rest be fixed in some convenient position.

The screw _d_ is for limiting the descent of the drum, but some workmen prefer to dispense with it, and, instead, hold the frame C C in the hand, pressing it gently against the pinion. They urge that the wood is never of the same degree of hardness round its circumference, and therefore must of necessity wear irregularly; by holding C C in the hand the pressure on the pinion can be more evenly adjusted, as it is possible to feel at once whether the drum is polishing or scratching.

The inclination of the slide to a plane at right angles to the axis of R is measured by the pitch of the screw formed on the drum. But in practice no special precautions are taken, and it is only necessary to incline the slide slightly to the right or left, until the pinion is found to revolve freely.

The drum may be from two to three inches in diameter, and, in order to ensure the same degree of hardness throughout the entire circumference, it is a good plan to make the drum of a series of wedges cut so that the grain in all radiates from the center. Beautiful polished surfaces are obtained in this manner.

=550.= _To polish a pinion in the ordinary lathe._ Various methods may be adopted, but the following is one of the commonest:

Support the pinion between the two centers _b_, _d_, of the pinion-carrier shown in Fig. 252, the form of which will be evident without explanation. Rest this carrier by the portion M against the =T=-rest, pressing it against the drum at the same time with one finger. Rotating the drum first by hand, make the pinion cut a groove varying the inclination until it is found to be correct, and, when sufficiently deep, charge with polishing material, and rotate it with wheel, at the same time moving the pinion-carrier backwards and forwards endwise. A little experience will give the requisite skill.

If the pinion is not held at a sufficient inclination it will scrape and will not revolve. If too much inclined, only the roundings of the leaves will be polished, the sides being left untouched. A well-formed groove will last for a long time.

=551.= =To Tighten a Cannon Pinion.= If it is simply slack it will be sufficient to increase the diameter of the set-hands arbor as described in article =336=. But if the cannon pinion is in the habit of working off this arbor when setting the hands, the arbor can be tapered a little downwards; or proceed as follows:

Drill a hole in the square that receives the minute hand in the position shown at _a_, Fig. 253, and also indicated by dotted lines at _c s_; now turn a groove round the arbor, also shown by dotted lines, at the point _n_, to correspond with the hole _a_. Insert a pin in this hole, filing it off smooth with the surface at the side at which it enters, and nearly level at the other side, to be hammered over just sufficiently to prevent the pin from working its way out. The cannon pinion will now be found to turn with the requisite degree of friction, and without any tendency to work up. It will last all the longer if both the pin and the groove in which it works are polished.

SET-HANDS SQUARE.

=552.= =To Make a Set-Hands Nut.= This is a small square nut pinned to the pivot of a solid cannon pinion that projects beyond the top-plate in some watches after passing through a hollow center pinion. This construction has been latterly discontinued, but it may be well to explain the mode in which such a nut can be renewed when necessary.

Take a rod of soft steel of a diameter half as large again as that of the square to be made. Drill a hole along its axis rather less in diameter than the set-hands arbor and cut off the ends a little longer than the square is required to be. Put this nut on an arbor and turn it flat on each end (although still a little long) and truly cylindrical. Having inserted a loose fitting coned brass wire of oval section into the nut, hold it on its side on an anvil. With a sharp blow of the hammer cause the cylinder to assume an oval form, so that the round hole is as seen at A, Fig. 254, this being the section of the end of the set-hands arbor itself. If the work has been carefully performed up to this point, the steel nut should now pass a short distance on to the arbor on applying a moderate pressure, and it will suffice to slightly alter the form of this latter in order to ensure a perfect fit. As there should be no shake, it is advisable that this adjustment be made after the nut is hardened.

File the two faces _d_ and _f_ parallel to each other and to the axis of the oval, reducing the total thickness very nearly to the amount ultimately required, then holding the nut in the pincers by these two faces firmly, but without scratching them (or it may be held by a rod fitted to the oval hole), form the square, removing all the metal that is beyond the two vertical lines in the figure. Then set it on an oval arbor and turn the corners down to the exact diameter required; pass the graver over the two ends so as to adjust the length. It will then be easy to finish off the square and round the lower end, holding the nut on a steel rod in a pin-vise. Drill the hole for a pin after marking its two ends on the nut as explained in article =518=, then, holding the nut so that it rests on its lower face, form a recess with a chamfering tool held in its axis; the form of this can be modified if required with the rounded end of a rod and oilstone dust.

Harden the square and temper it to a blue color; then smooth its faces and ends, and fit the square to the set-hands arbor. The hole for the pin must now be made through this arbor, taking care not to allow the square to rise out of its place during the operation. It only remains to polish the recess formed in the nut with a rod rounded at one end and rotated with a ferrule, and finish off the corners with a burnisher and rouge; the lower end is finished in the same manner as the head of a screw.

=553.= We have here considered the case of a new arbor, but, if fitting a nut to one that is already drilled, proceed as follows: Make the nut rather longer than necessary and drill a hole higher than the point at which measurement shows it ought to be; then remove metal from the lower face until the two holes coincide. The work is simplified if the nut be made of the correct height at once and, instead of drilling a hole, a slit be formed as in the head of a screw, the bottom of which must correspond with the lower edge of the hole in the arbor.

=554.= =To fit the Set-hands Arbor to the Center or cannon pinion.= We have pointed out in article =364=, the objections to hammering the set-hands arbor so as to secure sufficient friction to make it hold in either of the pinions through which it passes in the ordinary form of watch. Tracing a spiral line on its surface is not much better, as the metal thus caused to project soon wears off. A better method is explained in article =337=, but, when only a slight increase of diameter is needed, the following will suffice:

Roll the arbor on a hard flat wood surface with a file of medium cut, applying considerable pressure so that the arbor is forced against the file. If the pressure is sufficient and maintained long enough, a dead rough surface will be formed on it which will increase its diameter so that it will retain a small quantity of oil. It is well to roughen the surface rather more than necessary, subsequently passing a burnisher lightly over it until the arbor fits the pinion with sufficient friction.

As to the making of a set-hands arbor, it will present no difficulty to a watchmaker of even average skill in turning and filing.

PIVOTS.

=555.= =The Play Of Pivots.= It may be accepted as an approximate rule that the play of escapement pivots in their holes should be as follows:

In the cylinder escapement, about one-sixth the diameter of pivot.

In the duplex escapement, about one-tenth the diameter of pivot.

In the lever escapement, about one-eighth the diameter of pivot.

A large hole causes the pitching of the depths to vary with position, and a deficient play renders the escapement more sensitive to thickening of the oil.

The depth of a pivot-hole or the length of its cylindrical acting surface may be taken to vary inversely with its hardness. Thus a ruby hole is made less deep than one of brass.

=556.= =To Replace the Pivot of a Hollow Pinion.= It often happens that the pivot of a hollow center pinion is so deeply cut that it cannot be re-polished, in consequence of the careless manner in which too many examiners finish the center holes (=461=). If the pinion itself is found to be still in good condition, it can be made serviceable as follows:

Cement the pinion, with its wheel attached, firmly to the chuck of a lathe after having removed the two worn pivots, and, when it is accurately centered, increase the hole by means of a drill that is a trifle larger than the original pivots (see article =282=); in the hole thus enlarged and carefully smoothed insert a close fitting steel tube that has been hardened and tempered to a blue color, which must be smoothed and run true. The portion of this tube that projects on either side is then adjusted to the proper length, and it only remains to polish the pivots.

If only one pivot requires renewal, ascertain whether there would be sufficient hold with the hole enlarged through half its length, and proceed as already explained.

We have assumed that the shoulders of the original pivots can be made to serve again, but it often happens that the shoulders do not possess sufficient substance, in consequence of the hollows being cut too deep. In such a case it is hardly necessary to observe that the hole must be drilled larger, so that, after the tube has been adjusted, new shoulders can be turned on it.

=557.= =To Redress a Bent Pivot.= For this purpose some workmen merely use a pair of pliers or tweezers; others place the pivot in a slot of the Jacot tool, and press on it with a burnisher that has little or no cut, at the same time causing the staff to rotate. Either of the two following methods may be adopted:

Drill a number of straight holes in a plate exactly at right angles to its surface. Now introduce the pivot into a hole that it fits with very little play, and redress it by causing the staff to rotate, at the same time holding the plate in the hand. Caution is necessary since there is some risk of bending the pivot too far.

=558.= =Pivoting a Cylinder, etc.= This operation will not present any difficulty if the several heights are properly taken. See also the articles on Beaupuy files (=240=), and on compasses for measuring heights, etc. (=243=).

=559.= =Polishing Pivots in the Lathe.= Pivots are as a rule polished by metal polishers provided with suitable materials, and held in the hand; in Fig. 255, however, is given the design of a machine by which this work can be accomplished when the pivoting is done in the chuck-lathe, the pivot itself being free and unsupported by a runner.

The bed P of the instrument carries a wheel R which engages with a pinion on the axis of the polishing lap _m_. The wheel R is mounted on a clock stud passing through a slot and fixed by a nut, so that the pitching of the two mobiles may be modified; motion is communicated to the lap by simply placing the finger against the teeth of R. The bed can move in a vertical plane, being pivoted on two screws, _v_, _v_, and the block that receives the points of these is riveted to the disc _d d_, which can be made to rotate, with friction, on the second disc _n n_. This latter is riveted to a plate _e_ fixed at the end of a cylindrical rod F.

It will be evident that if the rod F is inserted in the =T=-rest support, the plate P extending towards the back of the lathe, this plate can be raised or lowered, and moved towards the right and left, so that the flat face of the lap can always be brought in contact with the pivot that is to be polished. This latter is caused to rotate by a foot-wheel while one hand holds the raised plate by the button _a_, and a finger of the other hand is applied to the teeth of R, causing the lap to rotate.

The upward motion of P may be limited by the edge of the top _s_ of the button _s k_, which is tapped so as to rotate with stiff friction on the pillar H. The stop _l_ is to prevent the polisher from traveling too far towards the left and thus removing too much from the shoulder that is to be polished. The screw _x_, giving motion to the slide _y_, is for securing parallelism between the pivot and the surface of the lap, according as the former is cylindrical or conical in shape.

For fine pivots it is advisable to introduce an additional wheel and pinion. The finger will then be better able to appreciate the degree of resistance opposed, and, owing to the increased velocity, it will be useless to use oilstone dust, but rouge can be applied directly after the turning. At _e_ is a steady-pin for maintaining the position of the instrument.

BUSHING PIVOT HOLES, ETC.

=560.= Every watchmaker knows how to proceed in adjusting an ordinary perforated bushing or stopping. We would make a few remarks on the subject of bushings generally.

The tapped bushing is very firm, but, in order that it may be well centered, it is essential that its thread fits exactly the tube of the tool (=322=), and that the pointed rod is exactly central. A turned bushing, especially when a broach can be passed into it after it is in position, is more easily made central (see article =342=).

When bushing holes that are rather large with solid bushings, after the hole has been marked with the pointer it must be drilled with a small drill, a larger one being subsequently passed through, so as to increase it. Otherwise there is great danger of the hole turning to one side.

If a hole, such as that of the center wheel, is bushed with a perforated bushing, it will often be found to incline towards the barrel or fusee, so that the hole is displaced. Such an inconvenience may be avoided by using a bushing with a hole smaller than is ultimately required, afterwards enlarging it with the plate centered in the lathe.

=561.= =Riveting of Bushings.= Some watchmakers have found considerable advantage in replacing the sudden and irregular impacts of a hammer by gradual pressure, without shock, obtained by a small press worked by hand on the principle of a punching machine. With a well made bushing, the flat end of which is slightly rounded, and the inside of the hole in the plate finished with a rat-tail rather than with a cross file, it is found that the riveting is always perfect. Others employ an ordinary pair of sliding tongs, the noses of which are drilled to receive two punches, one flat and the other rounded, as in the mainspring punch. Three pairs of punches suffice for all sizes of bushings, and the same tool can be used for closing up screw-holes, etc.

=562.= =Movable Bushings.= These are for use in regulator clocks and others of large dimensions, and a few words must suffice for their description. They are the invention of M. Alleaume, and will be understood from Fig. 256. It is always desirable, with a view to prevent wear, that when metal pivot-holes are used, the pivot should bear on a length equal to about three times its diameter; but for such a condition to be satisfied, it is essential that the axes of both holes and pivots be absolutely parallel. The figures will at once show in what manner such parallelism is secured. C C is the plate, in section, in which a hole is made of the form indicated by the lines that bound the cross-hatchings. The movable bushing A is held against a shoulder, and prevented from rotating by a screw, the point of which enters a small hole in the bushing. The pivot of B passes into A, and this latter is capable of such slight motion as will insure contact between the surfaces throughout their length.

DEPTHS.

=563.= =To Secure a Good Depth.= The least skillful of watchmakers can, without much difficulty, place a wheel in the depthing tool in conjunction with a pinion, and change this latter until the two are found to run easily together. But there are comparatively few that are sufficiently acquainted with the subject of depths to be able to select a pinion whose proportions are such as to satisfy the greatest number of the conditions to be fulfilled by a good depth.

This unsatisfactory state of things is due in great measure to the employment, without any correction, of tables of the sizes of pinions (=544=), according to which these sizes are determined by a measurement on the teeth of the wheel, taken with a pinion caliper. This method, although sufficient for ascertaining the size approximately, and even for securing a depth that runs more or less easily, cannot be accepted as an unvarying rule.

Far from resting on any mathematical law, as ignorant men urge in their attempt to instruct others, it is only true for a particular number and form of tooth in regard to the wheel, and a definite thickness of leaf and shape of the rounding in regard to the pinion. It ceases to be true if applied to other numbers of teeth, or to pinions that have their leaves thicker or thinner, or the roundings different from those of the pinion first determined upon.

=564.= _Theoretical and practical depths._ The fundamental principle of every depth is as follows: To determine what curvature should be given to the teeth of the wheel which drives, in order that the tooth that follows (whether its side be straight or formed according to a pre-determined curve) shall be driven in such a manner as to secure the best transmission of force, a transmission which is in part influenced by the uses to be made of the machine.

=565.= Teeth formed like the involute of a circle have very marked advantages, but they cannot be adopted in practice, especially in the case of the leaves of pinions. The epicycloid can be realized very approximately in the teeth of wheels in horology, and such teeth can be used in conjunction with pinion leaves having straight faces, the construction of which does not present any difficulty. This explains why the epicycloidal form has been adopted by watchmakers; but, although it is more easily drawn than the majority of other curves, there are still some obstacles in the way of its general application, mainly dependent on industrial requirements. The difficulty is usually got over by forming the tooth according to a circular arc, nearly identical with the epicycloidal curve, see articles (=440-42=).

=566.= When two mobiles are of the _same diameter_, the theoretical depth will be characterized by having teeth and spaces of equal width; but, since in practice the friction with such an arrangement would be excessive, owing to its taking place on both sides of the tooth, the teeth of the wheel that are driven are so far reduced in thickness as to secure the necessary freedom.

=567.= When the two mobiles are very highly numbered, the lead is short, so that the tooth of the wheel may be a trifle broader or narrower than the space without inconvenience.

But when using pinions of low number (from 6 to 10 leaves), this is not the case. In proportion as the width of the wheel tooth is reduced, its ogive becomes shorter, and the most advantageous portion of the lead (that beyond the line of centers) becomes less. And, besides this, account must be taken of the slipping towards the end of the lead, and the reduction in the difference between the geometrical and the total diameters of the wheel.

=568.= To secure a good depth with low numbered pinions, the leaves should not be more than half the thickness of the space. If they are thicker than this, it may be found necessary to reduce the width of the wheel teeth, when the pitching is insufficient; but the most serious objection lies in the fact that the pitch circle of the pinion will be diminished in diameter. Let there be two pinions with circular roundings and of the same total diameter, but having leaves of different thicknesses—that with the leaves thick will be found to be too small, etc.

=569.= =To Calculate the Vibrations of a Pendulum or Balance.= Multiply together the numbers of teeth of the wheels, starting with the one that carries the minute hand (which therefore makes one revolution in an hour), but exclude the escape-wheel.

Multiply together the numbers of leaves of the pinions, commencing with the one that engages with the center-wheel.

If the first product be divided by the second, the number obtained gives the _number of revolutions_ of the escape-wheel in an hour.

Multiply this figure by _twice the number_ of teeth of the escape-wheel, and the product is the _number of single vibrations performed by the balance or pendulum in one hour_.

ON THE APPLICATION OF THE GEOMETRICAL LAWS OF DEPTHS TO PRACTICE.

=570.= It has been urged that when the geometrical forms of the leaves and teeth, as given in scientific treatise, are accurately carried out in practice, the depths are found to be unsatisfactory and liable to cause occasional stoppage; and these facts are brought forward as evidence that theory and practice are at variance.

On the contrary, theory and practice are in perfect accord: the apparent disagreement arises from an error in the application of the geometrical laws.

In copying the theoretical forms of the teeth of wheels and leaves of pinions, it would be necessary to ascertain that they were mathematically exact, and this is impracticable. Two conditions must be borne in mind:

1. Theory shows that the mobile which drives should be made a trifle larger than the geometrical size, so as to counteract imperfections in the workmanship.

2. A pinion is _never_ made of the exact mathematical proportions, in consequence of the processes that have to be adopted for cutting, polishing, centering, etc. If a number of pinions be taken, and if the several dimensions of each be determined by means of a micrometer measuring to hundredths of a millimeter (or from two to three-thousandths of an inch), differences that are, comparatively speaking, large will be found in the diameters, measuring between corresponding leaves; in the thickness of leaves; in the diameters of the circles at which the roundings join the straight faces, and the general truth of the pinion will nearly always leave something to be desired. It should be added that these faults will be more marked according as the leaves have been more quickly made.

The teeth of wheels will be found to be characterized by similar faults, although they are less marked.

=571.= It follows from these facts that, in watches and timepieces, the _pinion is always a little smaller_ than theory would require; thus the epicycloid should be struck with a somewhat smaller generating circle, and the ogive of the tooth will be proportionately reduced.

The _practical conclusion_ at which we arrive, then, is as follows: As it is impossible to secure absolute perfection in the teeth of small horological mechanisms, their ogives must be slightly more rounded at the points than the designs given in scientific treatises indicate, since these latter are drawn exactly in accordance with the geometrical laws.

These remarks are of the greatest possible importance to the manufacturers of both watches and timepieces; they point to the fact that not only the ogives of all wheel teeth should be lower than theory indicates, but also that, in commoner work, they must be still lower, according as the pinions are of more inferior quality.

=572.= =To Alter a Stem Winding Pinion Depth.= The depth of the Stem Winding Wheel and Pinion often occasions considerable inconvenience, and its adjustment requires to be accurately made: when the depth is too deep, its alteration is easy, as the roundings of the pinion leaves can be reduced, or the stud or other piece that carries the winding wheel can have its base a little reduced on one side, so as to set the wheel a trifle out of upright (but so slightly as not to be perceptible to the eye, and taking care that the teeth remain on a level with those of the barrel-arbor wheel). A shallow depth is somewhat more difficult to correct. If a sufficient change cannot be made by altering the support of the winding wheel, one of the following methods must be resorted to:

1. Reset the pendant of the case.

2. Make a new winding pinion of greater diameter, increasing the number of its leaves by one, to correspond to this change.

3. Alter the position of the movement in the case.

The two first methods are more especially applicable to new work, while the third is more convenient for repairers, although of course it can only be resorted to with advantage when the pinion has a bearing in the pendant. The requisite change in the position of the movement can be produced by raising the rim of the case that supports the plate, or by soldering two thin strips of metal on this rim, producing a similar effect; one on either side of the pendant will suffice, except when a considerable change is necessary, in which case they should be set at intervals around the rim to avoid an obvious inclination of the dial. Or four holes can be drilled at equal distances apart around the edge of the plate and in its plane, so that their edges overlap the position occupied by the rim of the case; pins are then set in these holes and filed away until they produce the requisite amount of elevation. Or, again, flat-headed screws may be fitted around the edge with their axes at right angles to the plane of the plate and their heads on the dial side.[7] The depth will then be adjusted by screwing these screws more or less into the plate.

It is advisable to ascertain that the dial is not forced too near the glass, as such is occasionally found to be the case, necessitating the bevelling of the edge of the former.

PALLETS.

=573.= =To Advance a (visible) Jewel in a Pallet.= Workmen that have had much experience of escapement making do this without any difficulty by holding the pallet arm in a pair of tweezers that have been slightly warmed, but ordinary repairers will not succeed with such a method: they can however, effect the required change as follows.

Make a small brass plate, E, fig. 257, with a piece _c_ projecting upwards, which the screw _v_ traverses with stiff friction. A saddle _b_ is fitted to the edge of the plate by screws. A glance at the figure will suffice to show the mode of using it; the pallet arm whose jewel is to be adjusted is clamped under _b_ with the jewel just opposite the screw _v_. Now turn this screw until it stands at the distance from the impulse face of _a_ through which the jewel is to be advanced; taking the plate in a pair of long-nosed pliers, hold them over a small lamp flame, and press with a small screwdriver lightly against the point _a_ so as to advance the stone by the requisite amount as soon as the shellac is sufficiently soft. A particle of shellac is placed at _a_, if any cavity forms during the process, and the plate is laid on some cool body, avoiding contact with the pallet-staff.

If the stone projects below the lower surface of the pallets, a small washer must be placed underneath before clamping the screws of _b_, of such a thickness that the stone is just on the level with the surface E.

=574.= =To Alter the Form of a Pallet Face.= Workmen that possess the requisite skill and steadiness of hand can alter the form of a pallet jewel, when it is necessary to modify the height or form of the impulse face, by simply using a copper polisher charged with diamond powder. The polishing material employed is always decanted in very pure oil, as otherwise it is apt to scratch instead of polish. The coarser quality is first used when a material change has to be effected, but if only a very slight alteration is necessary, and the adjustment has to be very exact, only the finest quality must be used, as there is a danger of making scratches that would be very difficult to erase. We would also add that this operation requires some skill and patience.

=575.= =To Measure the Lift and all other Angles, etc. of the Lever Escapement.= A very simple instrument for measuring these angles was designed by Curzon, one which any watchmaker can arrange for himself, and is quite sufficient for all practical purposes. This is shown in Fig. 258, and consists of an ordinary depth tool to which a scale is added. A hand adapted to the pallet-staff supported between one pair of runners of the depth tool gives motion to a curved rack (shown by dotted lines), and this causes a pinion carrying a second index to rotate, the radii being so related that the movement of the staff is magnified four times on a scale which can be observed while the glass is at the eye examining the pallets. The index which travels over the shorter scale to the left (divided up to 10° on either side of zero) is connected with the pallet-staff by a fork and a short arm passing through the circular groove; it affords a convenient means of moving the pallets while testing them, and gives a measure, in degrees, of their motion. The graduated arc shown at the top is for measuring the lever and roller.

=576.= =Verge Pallets: to Measure their Opening.= The little instrument shown in Fig. 259 may be used for this purpose; its mode of action will be easily understood from an inspection of the figure.

One of the pallets being held with its flat face against the base of the graduated semicircle by the lever and spring B, so that the axis of the verge is at right angles to the plane of the instrument through the point _n_, an index previously fixed to the other pallet will show by the graduations the number of degrees of opening.

This index, shown at P, Fig. 160, must be very light. It is formed in two parts, the body _c d_, and the small spring _z z_. The pallet when held in the notch _c_, must have its face held flat against _c d_ by the spring _z z_. The face _c d_ of the index must be quite smooth and straight, so as to avoid any error in the reading of the scale.

The pressure-block C, Fig. 259 (shown in plan and elevation at C, Fig. 260), is movable on its center, and this center, which by an engraver’s error is represented on the line _n r_, should be a little to the right of that line.

=577.= =To Open or Close Verge Pallets.= Some workmen cut a notch at the end of a small rod in which the verge is inserted, the two arms of the fork being then drawn together by a screw; then, holding each pallet in a pair of long-nosed pliers, one in each hand, the rod is held in the flame of a lamp and, as soon as the body of the verge becomes blue, it is gently twisted to the right or left according as the pallets require to be opened or closed.

This method is not always convenient, and the following may be recommended:

Support the verge by its shoulders between two cone-plate centers in a pair of finishing turns, as seen in Fig. 261. A carrier _b_ is screwed to the upper pallet, and prevents the verge from rotating; _c_ is a rod through which heat is conducted; _a_, shown both in plan and elevation, is another rod, which is much longer than _c_, and has a notch cut at the end, so that it can be forced on to the lower pallet. The end _d_ is free, and the =T=-rest shown dotted at _s_, must be brought nearly into contact with it, the distance between them corresponding to the angle to which it is required to alter the opening of the pallets. Now hold a lamp under the free end of _c_ and, as soon as the body of the verge changes color, _d_ will descend by its own weight until arrested by _s_, the opening will thus be increased or diminished to the requisite extent.

The operation will be accomplished more quickly by directing the blow-pipe flame against the verge body.

Of course when diminishing the opening, the verge must be held in the reverse direction to that shown in the figure.

CYLINDER.