Fig. 1815Fig. 1815.
Fig. 1815.
Fig. 1816Fig. 1816.
Fig. 1816.
Fig. 1815may be taken to represent a machine in which the pipe is held and the die revolved, andFig. 1816one in which the pipe is revolved and the dies are held in a head, which allows them to move laterally to suit the pipe that may not run true, while it prevents them from revolving.
In the former figure the bolt or pipe is shown to be out of line with the die driving spindle, and the result will be that the thread will not be parallel with the axis of the pipe. Whereas inFig. 1816the thread will be true with the axis of the work, because the latter revolves, and as the die is permitted more lateral motion it can move to accommodate itself to the eccentric motion of the work, if the latter should not run true.
If the end of a piece of pipe is not cut off square or at a right angle to the pipe axis, and the die has liberty to move, it will thread or take hold of one part, the longest one, of the pipe circumference first, and the die will cant over out of square withthe pipe axis, and the thread cut will not be in line with the pipe axis.
The two important points in operating threading machines is to keep the dies sharp and to well lubricate them with oil. When dies are run at a maximum speed and continuously at work they should be sharpened once or, if the duty is heavy, twice a day, a very little grinding sufficing.
In nut tapping the oil lubrication is of the utmost importance, and is more difficult because the cuttings are apt to clog the tap flutes and prevent the oil from flowing into the cutting teeth.
When the tap stands vertical and the nuts are put on at the upper end (the point of the tap being uppermost), the cuttings are apt to pass upwards and prevent perfect lubrication by the descending oil. When the taps stand horizontally, gravity does not assist the oil to pass into the nut, and it falls rapidly from the tap, hence it is preferable that the tap should stand vertical with its point downwards, and running in oil and water.
In machines which cut the bolt threads with a solid die, it is obvious that after the thread is cut upon the bolt to the required distance, the direction of rotation of the bolt or die, as the case may be, requires to be reversed in order to remove the bolt from the die, and during this reversal of rotation the thread upon the bolt is apt to rub against and impair the cutting edges of the chasers or die teeth.
To obviate this difficulty in power machines the dies are sometimes caused to open when the bolt is threaded to the required distance, which enables the instant removal of the finished work, and this saves time as well as preserving the cutting edges of the die or chaser teeth.
In machines in which the bolt rotates, the machine must be stopped to take out each finished bolt and insert the blank one, which is unnecessary when the bolt is stationary, because so soon as the bolt is threaded to the required distance the dies may open automatically, the carriage holding the bolt at once withdrawn and a new one inserted.
When the dies open automatically the further advantage is secured that the bolts will all be threaded to an equal distance or length without care on the part of the operator.
Fig. 1817Fig. 1817.
Fig. 1817.
A hand machine for threading bolts from1⁄4inch to3⁄4inch in diameter is shown inFig. 1817. It consists of a head carrying a live spindle revolved by hand, by the lever shown at the right-hand end of the machine, being secured to the live spindle by a set-screw, so that the handle may be used at a greater or less leverage to suit the size of the thread to be cut; on the front end of this spindle are the dies, consisting of four chasers held in a collet that is readily removable from the spindle, being held by a spring bolt which, when pressed downwards, frees the collet from the spindle.
The work is held in a pair of vice jaws operated by the hand wheel shown, and this vice is moved endwise in its slideways on the bed by means of the vertical lever shown. The bolt being stationary, the small diameter of the die enables it to thread bent or crooked pieces, such as staples, &c.
For bolts of larger diameter requiring more force than can be exerted by a hand lever, a geared hand bolt cutter is employed.
Fig. 1818Fig. 1818.
Fig. 1818.
InFig. 1818is represented a hand bolt cutter. In this cutter the bolt is rotated, being held in a suitable chuck. The revolving spindle is hollow in order to receive rods of any length, and is operated by bevel-wheels as shown, so as to increase the driving power of the spindle by decreasing its speed of rotation. To provide for a greater speed of rotation than that due to the diameters of the bevel-pinion and wheel, the lever is made to slide through the pinion, effecting the same object and convenience as described for the machine shown inFig. 1817.
The threading dies are held in collets carried by a head or cylinder mounted horizontally on a carriage capable of being moved along the bed by means of a rack and pinion, the latter being operated by a handle passing through the side of the bed as shown. The cylinder also carries a collet adapted for recessed plates so as to receive square or hexagon nuts of different sizes for tapping purposes, the taps being held in the rotating chuck. The collets are capable of ready and separate extraction, and by removing the collet that is opposite to the one that is at work, the end of a bolt may pass if necessary entirely through the head or cylinder threading the work to any required length or distance.
To insure that the die shall stand axially true with the revolving spindle, bolt holes are drilled in the lower part of the cylinder, and a pin passes through the carriage carrying the head, and projects into these holes, which are so situated that when the pin end projects into a hole and locks the head a collet is in line with the spindle.
The dies consist of four chasers inserted in radial slots in collets held in place and bound together by a flat steel ring, which is let into the face of the collet and the external radial face of the chasers, and secured to the collet by screws. One chaser only is capable of radial motion for adjusting the diameter of thread the die will cut, and this chaser is adjusted and set by a screw in the periphery of the collet.
The other two chasers being held rigidly in a fixed position in the ring act as back rests and cut to the diameter or size to which they are made, or according to the adjustment of the first chaser. The shanks of the collets are secured in the cylindrical head by means of either a bolt and key or by a set-screw.
The chasers are sharpened by grinding the face on an ordinary grindstone or emery wheel.
The chasers are numbered to their places and are so constructed that if a single chaser of a set of three should require renewal, a chaser can be obtained from the manufacturers that will match with the remaining two of the set, the threads on the one falling exactly in line with those on the other two, whereas in other dies the renewal of one chaser involves the renewal of the wholenumber contained in the die. This is accomplished by so threading the dies that the thread starts from the same chaser (as No. 1) in each set.
Fig. 1819Fig. 1819.
Fig. 1819.
InFig. 1819is represented one of these machines, which is intended for threads from3⁄8to 1 inch in diameter. It is arranged to be driven by belt power, being provided with a pulley having three steps; on this pulley spindle is a pinion operating a gear-wheel on the die driving spindle, as shown.
The oil and cuttings fall into a trough provided in the bed of the machine, but the oil drains through a strainer into the cylindrical receiver shown beneath the bed, whence it may be drawn off and used over again.
Fig. 1820Fig. 1820.
Fig. 1820.
InFig. 1820is represented a bolt threading machine which is designed for bolts from3⁄16to 1 inch in diameter.
The bolt to be threaded is gripped in the vicel, operated by hand by the hand wheelm, and is moved by hand up to the headd, by the hand wheelqoperating the pinion in the rack shown at the back of the machine. When the dies or chasers have cut or threaded the bolt to the required distance, the threading dies are opened automatically as follows:—-
Athis a clutch ring for opening and closing the threading chasers, and atnis the lever operating the shoes in the groove of the clutch ring. This lever is upon a shaft running across the machine and having at its end the catch piecep; atzis a catch for holdingpupright against the pressure of a spring that is beneath the bed of the machine, and presses on an arm on the same shaft as the catch piecep. On the back jaw of the vicelis a bracket carrying a rodr, and the bolt or work is threaded until the end of rodrlifts catchz, when the before-mentioned spring pulls levernand clutch ringhforward, opening the dies and therefore stopping the threading operation. The length of thread cut upon the work is obviously determined by adjusting the distance rodrprojects throughv. The handlewis upon the same shaft as catch piecepand clutch levern, and therefore affords means of opening the dies by hand.
The operation of the machine obviously consists of gripping the work in vicel, moving it up to the headdby the hand wheelq, setting the rodrto open the dies when the bolt is threaded to the required length, and moving the vice back to receive a subsequent piece of work.
The construction of the headdand clutch and ringhis shown inFigs. 1821and1822.
Fig. 1821Fig. 1821.
Fig. 1821.
Fig. 1822Fig. 1822.
Fig. 1822.
The bodyfis bolted by the flangeito a face plate in the live spindle or shaft of the machine, and through slots in this body pass the holders or casesccontaining the chasers or dies. Uponfis the piecedprovided with a slot to receive the die cases and a tongue to move them. This slot and tongue, which are shown ate′, are at an angle to the axis off; hence ifdbe moved endways uponfthe cases and dies are operated radially in or through the bodyf. To operatedlaterally or endwise uponfthe clutch ringhand the togglesgare provided, the latter being pivoted in the bodyf, andhbeing operated endwise uponfby the lever shown atnin the general view,Fig. 1820. The amount to which the dies will be closed is adjustable by means of the adjusting screwse, which are secured in their adjusted position by the set-screwsr,Fig. 1821; it being obvious that whenhmeets the shouldersofgand depresses that end of the toggle, headdis moved to the right and the dies are closed when the end ofgmeetse, and ceases to close whenghas seated itself infand can no longer movee. The backward motion of the clutch ringh, and therefore the amount to which the dies are opened, is regulated by the screwband stopainFig. 1822, it being obvious that whenbmeetsathe motion ofhanddto the left uponfceases and the dies are fully opened. The amount of their opening is therefore adjustable by means of screwb.jis simply a cap to hold the dies and cases in their places.
Fig. 1823Fig. 1823.
Fig. 1823.
In the end view,Fig. 1823,e,eare the adjustment screws for the amount of die closure, andb,bthose for the amount they will open to,trepresenting the screws for the capj, which is removed for the insertion and extraction of the dies and die cases.
Fig. 1824Fig. 1824.
Fig. 1824.
The construction of the diespand casescis shown inFig. 1824. Two screws atnsecure the dies in their cases and a screwmadjusts them endways so as to set them forward when recutting them. By inserting the dies in cases they may be made of simple pieces of rectangular steel, saving cost in their renewal when worn too short.
Fig. 1825Fig. 1825.
Fig. 1825.
Fig. 1825shows the machine arranged with back gear for bolts from 2 to 21⁄2inches in diameter, the essential principles of construction being the same as inFig. 1820.
Fig. 1826Fig. 1826.
Fig. 1826.
Fig. 1827Fig. 1827.
Fig. 1827.
InFig. 1826is represented a single and inFig. 1827a double “rapid” machine, constructed for sizes up to5⁄8inch in diameter, the double machine having a pump to supply oil to the dies. This pump is operated by an eccentric upon the end of the shaft of the cone pulley.
Fig. 1827aFig. 1827a.
Fig. 1827a.
The construction of the head of this machine is shown inFig. 1827a.zis the live or driving spindle, upon which is fast the heada. Inaare pivoted atmthe leverslwhich carry the diesd, which are secured in place in the levers by the set-screwsband adjusted to cut to the required diameter by the screwse. The leverslare closed upon the clutchcby means of the springsrands, each of these springs acting upon two diametrically opposite levers, hence the action of the springs is to open the diesd. The clutchchas a cone attand slides endways upon the live spindlez. The clutch lever and shoes are upon a shaftrunning across the machine and actuated by a rod corresponding to the rodrinFig. 1820. When the clutch and leverslare in the position shown in the figures the dies are closed for threading the bolt, and when this threading has proceeded to the required distance along the work, clutchcis moved by the aforesaid rod and lever in the direction of arroww, and the springsr,sclose the endspof leverldown upon the bodyxof the clutch opening the dies and causing the threading to cease.
Fig. 1828Fig. 1828.
Fig. 1828.
Fig. 1828represents a “double” rapid machine for threading work up to four inches in diameter, and therefore having back gear so as to provide sufficient power. The gauge rod from the carriage here disengages a bell crank from the end of the long lever shown, and thus prevents the spring to operate the cross shaft and open the dies.
Fig. 1829Fig. 1829.
Fig. 1829.
InFig. 1829is represented a bolt threading machine or bolt cutter, which consists of a head carrying a live spindle upon which is a head carrying four bits or chasers that may be set to cut the work to the required diameter, and opened out after the work is threaded to the required length and the bolt withdrawn without losing the time that occurs when the dies require to run backward to release the work, and also preventing the abrasion and wear that occurs to the cutting edges of the die bits or chasers when revolved backward upon the work. This head is operated by the upright lever shown in the figure, this lever being connected to the clutch shown upon the live spindle. The details of construction of the clutch and of the head are shown inFigs. 1830,1831,1832, and1833. The work to be threaded is gripped between jaws operated by the large hand wheel shown, while the vice moves the work up to or away from the head by means of the small hand wheel which operates pinions geared with racks on each side of the bed of the machine as clearly shown in the figure.
Fig. 1830Fig. 1830.
Fig. 1830.
Fig. 1831Fig. 1831.
Fig. 1831.
Fig. 1830is a longitudinal section of the head, andFig. 1831an end view of the same.pare the threading dies or chasers held in slots in the bodyaby the annular ring face platek. The ends of the dies are provided withT-shaped capstfitting into corresponding grooves or slideways in the die ringb, and it is obvious that as the heads of their caps are at an angle therefore sliding the ringbalongaand to the right of the position it occupies in the figure will cause the diespto close concentrically towards the centre or axis of the heada. Atcis a ring capable of sliding uponaand operated by the upright lever shown in the general view inFig. 1829.
Fig. 1832Fig. 1832.
Fig. 1832.
Fig. 1833Fig. 1833.
Fig. 1833.
The connection between the die ringband the clutch ringcis shown inFigs. 1832and1833, the former being also a longitudinal sectional view of the head, but taken in a different plane from that inFig. 1830. The barrel or bodya aof the head is provided with two diametrically opposite curved rocking levers which are pivoted in recesses ina a. The clutch ringcenvelops bodyaand passes between the curved ends of these rocking levers. The upper of the two rocker levers shown in the engraving connects with a levere, which connects to a stud or plungerp, threaded to receive the adjusting screwi, which is threaded into the die ringb. Obviously whencis moved to the right alongait operates the rocking lever and causesbto move to the right and to close the dies upon the work. The amount of die closure, and therefore the diameter to which the dies will thread the work, is adjustable by means of the adjusting screwi, which has a coarse thread inband a finer one inp, hence screwing upidrawsbto the left and farther over the plungerp, thus shortening the distance between the centre of the curved lever and limiting the motion ofbto the right. On the other hand, unscrewingimovesbto the right, and it is obvious that in doing this the captinFig. 1830is forced down by the groove inband the dies are moved endwise towards the axisa a, or in other words, closed.
It will be clear that a greater amount of power will be necessaryto hold the dies to their cut than to release them from it, and on that account the lower curved rocking armdconnects througheto a solid plungerg, the screwhabutting against the end ofgand not threading into it, becausegis only operative in pushingbforward in conjunction withp, whileppullsbbackward, the duty being light. It is obvious, however, that after the adjustment screwiis operated to set the dies to cut to the proper diameter, adjustment screwhmust be operated to bring the ringbfair and true upona aand prevent any lateral strain that might otherwise ensue.
These two adjustments being made the clutch ringcis operated to the left to its full limit of motion to open the dies and to its full limit to the right to close them.
It will be seen, by the lines that are marked to pass through the pivoting pins of the rocking leverd, that the joints marked 2 inFig. 1832are below these lines, and as a result the linkseform in effect a toggle joint locking firmer in proportion as the strain upon them is greater.
Fig. 1834Fig. 1834.
Fig. 1834.
Fig. 1834represents a bolt threading machine having two heads each of which is capable of threading bolts from1⁄2up to 11⁄2inches in diameter.
The levers for operating the clutch rings are here placedhorizontal, so that they may extend to the end of the machine and be convenient to operate, and a pump is employed to supply oil to the dies.
The capacity of a double machine of this kind is about one ton of railroad track bolts per day of 10 hours’ working time.
In American practice it is usual to employ four cutting dies, bits, or chasers, in the heads of bolt threading machines, while in European practice it is common to employ but three. Considering this matter independently of the amount of clearance given to the teeth, we have asfollows:—
Fig. 1835Fig. 1835.
Fig. 1835.
If a die or internal reamer, the cutting points of which were all equidistant from a common centre, were placed over a piece of work, as a bar of iron shown inFig. 1835, and set to take a certain cut, as shown by the circle outside the section, it is evident that if revolved, but left free to move laterally, or “wabble,” the cutter would tend to adjust itself at all times in a manner to equalize the cutting duty—that is, if the die had two opposite cutting edges or points, and the piece operated upon were not of circular form, then, when one cutter reached the part that was not round, it would have either more or less cutting to do than before, and hence, the opposite cutter having the same amount, the tendency would be for the two cutting edges to travel over and equalize the cuts, and hence the pressure. With three cutting points, no two being opposite, the tendency would all the while be to equalize the cuts taken by all three; with four, spaced equally, the tendency would always be to equalize the cuts of those diametrically opposite; with five, the tendency would be to equalize the duty on each, and so on. Thus it will be noticed that there is a difference between the acting principle of a die having an even or an odd number of cutters, independent of the difference in the actual number of cutting edges, or points, as we are now considering them.
Fig. 1836Fig. 1836.
Fig. 1836.
To take an example, inFig. 1835is represented a die having four cutting points, placed upon a piece of iron of a round section, with the exception of a flat place, as shown. Now, in this position each one of the cutting pointsa,b,c, andd, is in contact with the true cylindrical part of the work only; hence, if the die were set to take the amount of cut shown, each point would enter the iron an equal distance, and the inner circle through the points would be the smallest diameter of the die. Upon revolving the die in the direction denoted by the arrow, an equal cut would continue to be taken off, and hence the circular form maintained, until cutterdhad reached the edgexof the flat, the opposite oneb, being aty(aatrandcatv), proceeding asdmoved fromxtowardsa, its cutting duty would continually become less and its pressure decrease, but as it is the cutting pressure ofdthat holds the opposite pointbto its cut, as the pressure ind, after reachingx, continually becomes less, the die would gradually travel over so as to carrydtoward the centre and cause it to take more cut, whileb, on the opposite side, would travel out a corresponding distance and take less, thus keeping the duty equalized until the cutterdhad reachedh, the lowest part of the flat, when the die would have moved the greatest distance off the centre, assuming the position shown by dotted lines. Thus the cutting point athhas passed inside the true circle that all the cutters commenced to follow, whilefhas passed outside. Meanwhile, ashandfhave shifted over,eandghave, of course, moved an equal amount and in the same direction, but the diameter ofeandgbeing at right angles to that ofhandf, the distances ofeandgfrom the centre would be changed but an infinitesimal amount; hence, they would virtually continue to follow the true circle, notwithstanding the deviation of the other pair. As the die continues to revolve andhpasses towarda, the lateral motion is reversed, the die tending to resume its original central position, which it does upon the completion of another quarter of a revolution, when the cutter that started atdhas passed tohand finally toa. A cutting has now been removed from the entire circumference of the iron, leaving it of a form shown approximately inFig. 1836, whereaz,by,cv, anddx, are the four true circular portions cut respectively by the pointsa,b,c, andd, before the flat place was reached. After the flat place was reachedxais the depression cut byd,ycthe elevation formed byb, andzbandvdare the arcs, differing almost imperceptibly from the true circular ones cut byaandc.
Fig. 1837Fig. 1837.
Fig. 1837.
Fig. 1838Fig. 1838.
Fig. 1838.
Fig. 1837represents a die having three instead of four cutting points—that is, the pointcofFig. 1835is left out, and the remaining onesa,b, andd, are equally spaced. This, placed upon a similar bar and taking an equal cut, would produce a truly circular form untildhad reachedx—withaandbatzandy—after which the die would move laterally, tending to carrydtoward the centre of the work andaandbaway from it, so as to equalize the cuts on all three. Hence, whendhad reachedhand the three-cutter die attained the position shown by dotted lines inFig. 1837,hwould have made an indentation inside the true circle, whileeandfhave travelled away from it, thus forming protuberances. Fromhtoathe lateral movement is reversed, and finally upon the completion of a third of a revolution, the die is again central and a cut has been carried completely around the bar, leaving it as shown inFig. 1838. Comparing this withFig. 1836, it will be seen that there are three truly cylindrical portions—viz.,az,by, anddxinstead of four inFig. 1836, but each one is longer; that there is a depressed place,xa, of equal length to that inFig. 1836, and two elevations,zbandyd, each of equal length to the one (yc) inFig. 1836.
Fig. 1839Fig. 1840Fig. 1839.Fig. 1840.
Fig. 1839.Fig. 1840.
Fig. 1841Fig. 1842Fig. 1841.Fig. 1842.
Fig. 1841.Fig. 1842.
Fig. 1843Fig. 1844Fig. 1843.Fig. 1844.
Fig. 1843.Fig. 1844.
Now, suppose the bar to have an equal flat place on its opposite side, becoming of a section shown inFig. 1839, upon applying the dies and pursuing a similar course of reasoning, the die with four points would reduce the bar to the size and shape shown inFig. 1840, or a true cylinder, while the triple-pointed cutter would produce the form shown inFig. 1841, which is a sort of hexagon, coinciding with the true circle in six places—a,z,b,y,d, andx—while betweenaandz, and opposite, betweenyandd, there is an elevation; also fromztoband fromdtox. A flattenedportion,ax, with a similar oneby, opposite, completes the profile. Suppose, now, that a bar of the form shown inFig. 1842, having two flat places not opposite, be taken, and the four-cutter and three-cutter dies are applied. The product of the four is shown inFig. 1843, and that produced by the three-cutter die inFig. 1844. The section cut with four coincides with the true circle at four points,a,b,c,d, and differs from it almost imperceptibly atz,y,v, andx. There are two elevations betweenaandband betweenbandc; also two depressions betweencanddand betweendanda. The section from the three-cutter die is the perfect circular form betweenaz,by, anddx, with a projection fromztoband two depressions fromytodand fromxtoa. The four-die, applied to a section having three flats likeFig. 1845, would produceFig. 1846, which does not absolutely coincide with the true circle at any point, although the difference is inconsiderable ata,z,y,c,vandx; three equidistant sectionsaz,yc, andv x, are elevated and the three alternate ones depressed.
Fig. 1845Fig. 1846Fig. 1845.Fig. 1846.
Fig. 1845.Fig. 1846.
Fig. 1847Fig. 1847.
Fig. 1847.
The three-cutter die would in this case cut the perfectly circular form ofFig. 1847.
Fig. 1848Fig. 1848.
Fig. 1848.
Now, suppose both of the dies to have been made or set to some certain diameter—in fact, presume them to be made by taking a ring of steel having a round hole of the required diameter, say 1 inch, and removing the metal shown by the dotted lines,Fig. 1848, and leaving only the four cutting points in one case (and the three in the other). Then it is evident that our dies are both of the same diameter, and likewise both of the assumed diameter, or 1 inch; then it is fair to presume that the plugs or sections just cut by either one of the dies should enter a round hole of the same diameter as the dies; but it is obvious that only two,Figs. 1840and1847, will do so, all the rest being considerably too large, from their irregularity of form, notwithstanding the fact that the diameter of any of those cut by four cutters is never more than that of the die, while any one of the equal radii, taken at equal distances on any of the forms cut by the three-cutter die, will not exceed the radius of the die. Now, six of the pieces being too large when referred to the standard of a round hole of the size of the die, while two are of the correct size, it is obvious that if the four-die, for example, which cutFig. 1846, were reduced enough to makeFig. 1843just enter the standard, that,Fig. 1840, which is now just correct in size and form, would, when cut, be altogether too small. The same would be the case also with the three-cutter die.
Now let us consider the two productions (Figs. 1840and1847) that answer the requirements, the two different sections (Figs. 1839and1845) from which they were cut, and also the other two pieces (Figs. 1841and1846) that were cut from the same bars at the same time. The general shape ofFig. 1839, is oval or four-sided, and while the four cutters operated upon it to produce perfectly circular work, the three cutters reproduced the general shape started with, only somewhat modified, asFig. 1841plainly shows. Upon the blank,Fig. 1845, the general shape of which is triangular, the very opposite is the case, for the three cutters now produce a perfect circle, while the four modify only the figure that they commenced to operate upon.
Considering that every irregular form may be approximated by a square, an equilateral triangle, or in general by either a parallelogram or a regular polygon, it will be found that from a flat, oval, or square piece of metal the four cutters will produce a true circle; from a triangular piece the three; from a heptagon neither will do so, while from a hexagon both the three and four cutters are calculated to do so. Following in the same manner, and increasing the sides, it will be found that the four cutters will produce a true circle from every parallelogram, whether all the sides are equal or not, while the three cutters will produce a true circle also from every regular polygon the number of sides of which is a multiple of three—that is, four cutters would operate correctly upon a figure having 4, 6, 8, 10, 12, &c., parallel sides, while the three would do so upon a figure having 3, 6, 9, 12, 15, &c., equal sides. Thus, for regular forms varying between these two series neither one would be adapted. Hence, if the general form of the work is represented by the first series, the four cutters are the best; if the general and average form of the material to be operated upon corresponds to the second series, then the three dies are the best adapted, so far as their two principles of action, mentioned at the outset, are concerned; hence, if it is considered that the material or bars of metal to be wrought vary from a circular form indifferently, then there is no choice between an even and an odd number merely on that account.
Placing the same dies that cut these six irregular figures upon their respective productions would not serve to correct their form; as, for instance, if the die that cutFig. 1846were revolved around it—even if set up or reduced in diameter to take a cut—it would remove an equal amount all round and leave the same figure still. Similarly with, say,Fig. 1841, cut by the three; but if the three were run overFig. 1846, cut by the four, it would tend to correct the errors, and likewise if the four were run overFig. 1841, the tendency would be to modify the discrepancies left by the three that cut it.