Chapter X: Introduction (3)

This Invention is under the protection of a Patent. It is applied to the spindles of my spinning machinery called Eagles, from their analogy to the machines named _Throstles_. It is in my opinion an excellent machine; as it secures a mathematical equality of twist to _any_ number of spindles from permitting the use of geering to turn them, which could not have been done without some means of stopping a single spindle. This mechanism (see Plate 19 fig. 1 and 2) consists of a toothed pinion _A_ soldered to the box _B C_, (partly cut down in the figure to shew its contents) and with it running loose on the lower part of the spindle _E D_. In this box are placed two weights _M N_, like that _M_ fig. 2, which both together, fill the box loosely, and, rising above it, are pinned at _O P_ through the spindle. They are moreover kept from quitting the latter by the ring shewn in section at _q q_, which holds them _loosely_, yet prevents their flying away or hurting any one. When now the spindle _E D_, turns swiftly, the centrifugal force of the two weights _M N_, projects them from the centre as far as possible; and they lay hold, by friction, of the cylindrical surface of the box _B C_, and thus _keep_ the revolutions of the spindle to the same number of turns per minute, as the pinion _A_ receives from the driving wheel. But when the spindle is stopped and held by the fly as usual, then the centrifugal force ceases to act, and the box _B C_ does _not_ wear out much, by its further revolutions. And when as before, the spindle is again let loose, _that_ friction which takes place on the bottom of the box sets the spindle running again, when the centrifugal force comes to its aid, so as to unite again the box and the spindle, thus renewing that valuable property of all spinning machinery, the mathematical correctness of its movements.

OF
A MACHINE
_For forging Screws, Beads, &c._

The effect which this Machine is intended to produce, is analogous to several culinary or officinal processes that might be named. It is called _rolling_: but not in the same sense in which that word is used in manufactories, where _rollers_ form or modify the body acted on. Here this body itself _rolls_ between two surfaces moving different ways and receives from them the desired impressions, and this idea I have extended to _screws_; proposing to _finish_ them on some metals and in some dimensions; and to _rough them out_ in others. The Machine is represented in figs. 6 and 7 of Plate 19, where fig. 7 shews the _faces_ of the arcs _A B_ of fig. 6. By the form and connection of the arms _A C_ and _B D_, these arcs move opposite ways: and since they are grooved obliquely as shewn in fig. 7, if a prepared cylinder of soft metal _a_, be put between them, and the handle _C_ be sharply pressed into the position _A E_, the cylinder _a_ will be made to _roll_, and the grooves of fig. 7 be impressed on it so as to meet and form the screw in question. The only conditions are, that the arc _B A_ be at least equal in length to the circumference of the screw, when finished; and that the grooves (fig. 7) be rightly sloped, and have the _form_ intended to be given to the threads of that screw. It will occur of course, that the opening between the arcs at the point where the blank cylinder is introduced, must be larger than the distance between the arcs by the whole depth of the threads to be impressed: which therefore will begin to be formed at two opposite points the moment the screw _a_ begins to roll. This however, might and would be otherwise, if it were thought best to form the arcs _A B_ spirally; and let the deepening process be gradual: in which latter case another consideration would occur, namely; that the grooves themselves (see fig. 7) must diverge a little instead of being parallel, so as to permit the screw to lengthen as the pressure should displace a part of the metal. In all cases the upper surface of the grooves should be _milled_ so as to lay hold of the soft metal, and insure the rolling motion: and should this material be hot-iron, the stroke should be taken in an instant, and the machine be kept cool by every proper method, in the intervals of working.

I need not add that this rolling process would be still easier performed, if the impressions to be made were circular and _not_ oblique: such as beads, balls, &c. but these considerations I leave to my readers.

OF
A DIFFERENTIAL STEEL-YARD,
_To weigh vast Weights with short Levers_.

Plate 19, figs. 8 and 9, offers two representations of this Machine--one intended to shew its manner of acting, and the other _one_ of its practical forms. By means of the first, (fig. 8) we may compare it with the common steel-yard; and even shew the latter as a part of the former. If a weight, or load to be weighed _M_, were suspended to the arm _A B_, and the counter-weight _W_, placed at the point _C_, of the arm _A C_, we should have a common steel-yard whose power would be as 5 to 1: for the arm _A B_ is just 1/5 of the arm _A C_, and this is the principle on which steel-yards are commonly made. But instead of this, my steel-yard _G E B D C H_ fig. 8, is now infinitely powerful: so much so indeed, as to be infinitely useless. If millions of pounds were now to be suspended at _P_, they would not raise the weight _W_ one tittle, for they hang _entirely_ on the point of suspension _A_. But although the Machine is _now_ useless, it can be altered in a moment and made both useful and commodious; only I thought its principle would be the better understood from being thus shewn _in excess_. To make it a useful and powerful Instrument, I only move the hanging bar _D G_, to _a b_; and the bar _E B_ to _c d_, the lever _b d_ being similar to that _E G_. In this state of things, the whole load _P_ is found at the point _o_ of the lever _B H_, (for the lever-arms _c o_ and _d e_, and those _e b_, and _a o_ are equal) and the power of this steel-yard is as the line _A C_ to the line _A o_; that is as 20 to 1, instead of being as 5 to 1 which it before was. But this is not _yet_ a powerful Machine; being chiefly intended to shew the principle on which it acts--and to prove that however small the distance _A o_, that distance, dividing the arm _A C_, gives the real power of the steel-yard. And supposing now the arm _A C_ to be four feet in length, and the distance _a D_, _B c_, and _A o_, to be 1/10 of an inch, then the power of the weight _w_ to raise (or weigh) the load _P_ is as 48 inches to 1/10 of an inch, or as 480 to 1: so that if the weight _w_ were 10lbs. this steel-yard would weigh 4800lbs. or upwards of two tons; and it is easy to see that this power can be almost indefinitely extended.

Fig. 9 of this Plate shews a real steel-yard made on this principle; the power of which, under its present length, is as 40 to 1. In this Machine all the centres are fixed: and the load is suspended on knife-edges, the distances of which from each other and from the common centres are invariable--as they _must_ be in all instruments of this nature.

OF
A RETROGRAPH,
_Or a Machine to write backwards, for Engravers_.

This Machine is exhibited in the two figures 10 and 11 of Plate 19. It is composed of a straight ruler _A B_, having an exactly dove-tailed mortice made along it, to receive the rollers, (or slides) by means of which the parallelogram _C D E_ _F_ slides up and down in this mortice. This parallelogram is composed of four rulers _C D_, _D E_, _E F_, and _F C_, connected by cannons or tubes fixed to every-other arm: and on which the contiguous rulers turn very correctly. Through which moreover, in two cases, _F D_ the drawing pencils are introduced, and under which in other two cases, _C_ and _E_, the guide rollers already mentioned are nicely fixed by the screws on which they turn. This is seen by an elevation in fig. 10, where _p_ marks one of these rollers, and _o q_ the end of the ruler supposed fixed to the paper by proper blunt points, &c. At _r_ is seen one of the tubes which form the joints _C_ and _E_: and _r t_, are, one the writing pen, and one the retrographic style or pencil. Fig. 11 is a plan of the whole Machine: where if the hand guiding the pen _D_ goes upward, the tracer _F_ rises too. But if the pen or hand _D_ moves to the right, the tracer moves to the left at the same moment. In a word this is to write backward in the sense of engravers, who thus write that their letters may proceed forward after _one_ impression.

If it were desirable to give the engraver the same facility he has in the use of a pen, the tracer _t_, fig. 10, would be terminated above as a hollow conical cup, into which he would introduce a pointed style held as a pen. In this case the tracer _t_, would be made as short or _low_ as possible, to bring the style so much the nearer to the paper; and thus to prevent all anomalous movements.

OF
AN EYE MACHINE,
_Or Machine for making the Eyes of Hooks and Eyes_.

If it were enquired why this Machine is offered to the public without the Hook Machine; the answer would be, this only is _finished_: and it is wished to present nothing here that admits even a doubt of its utility. The drawings given in Plate 20, figs. 1, 2 and 3, are more intended to be useful in the construction of this Machine than complete in _appearance_: so that nothing has been done by way of shading, but what it was thought would the better distinguish the parts from each other, and facilitate their assemblage in one effective Machine. The Machine consists first of a slide _A B_, (worked by a lever-handle, a crank, or any proper first motion.) It glides between two cheeks _C D_, (see the _end_ view in fig. 1) connected with the several parts about to be mentioned. This slide is marked _A B_ in all the three figures. It carries (by means of the screws _a b_, coming through the slits _c d_, in the main Plate _E F_) a plate _g_, the chief use of which is to support a tumbler _e_, whose use is to throw the eye, when made, from the machinery: which tumbler is kept to its work by the spring _i_, as will be further explained presently. This slide itself has a peculiar form at the end _B_, (fig. 2) which is shewn by dotted lines at _c d_ in fig. 1. It is a slit, with the corners rounded off for the purpose of working the springs _now_ to be described. These springs _m n_, (see fig. 2) are fixed to a _cock_, itself screwed behind the main plate: and they come through the latter to the _left-hand-ends_ of the small curved mortices seen (with the springs) at _m n_ fig. 1. The slide _A B_ then, with its forked end shewn by the dotted lines at _c d_, is destined to take the springs _m n_ and carry them to _r s_, where they are _now_ seen surrounded by the eye _almost_ formed: for in this motion these springs take the wire (shewn by the lines dotted _across_ the Machine and previously _cut_ by the sheers _u_) and meeting with the obstacles _t v_, being the thicker parts of the clams _t v w_, they bend it into the form _r s_--when the screws _a b_ lay hold of the sloping ends of the clams _c t w v d_, and squeeze them together; by which operation the hooks _t v_ finish the _eye_, by rolling its two ends round the springs _m n_ now in the position _r s_. Where note, that the slit _c d_ of the slide _A B_ is so formed as, when it has carried these springs _m n_ to _r s_, to slide forward without doing any thing more to them, while closing the clams. It performs, however, some other less important operations, to which it is now necessary to allude: among other things this slide works the sheers _u_ that cut the wire, and _that_, by means of the doubly wedged hook _x_, which goes back with the plate _G_, doing nothing: but which by the action of its springs fixed at _a_, falls _under_ the sloping end of the sheers _u_; and, when the slide, by the screw _b_, carries it to the right hand, raises the end _x_ of the sheers _u_, and cuts the wire near _v_, to prepare it for the operations already described. The part _y_ in the two figs. 1 and 2, is the other cheek of the sheers fixed by screws to the main plate, and covered by a small plate _z_, in which a _nick_ is cut to form a passage for the wire, and present it to the sheers, that they may cut it to the proper length, after having directed it right across the springs _r s_, then placed by their elasticity at _m n_. It hardly need be added that a _stop_ is placed at _o_, to determine the length of the wire so as to form the eye complete, and not to admit more wire than is sufficient; all which is regulated between the sheers and the _stop_, by proper adjusting screws, which it is very easy to suppose or supply.

Fig. 3 is intended chiefly to shew the mechanism by which the eye, when finished, is thrown off the pin round which it is bent by the springs _m n_. It consists of a _tumbler_ _e_, placed in a mortice in the end of the plate _g_, and kept to a given position by the pressure of the spring _i_. When the slide _A B_ is carried forward, toward _E_, to perform the operations already noticed, this tumbler _e_, gives way to the angle _G_ of the _doffing lever_ _m G_, (this lever being shewn also between _c m_ & _d n_ in fig. 1) and rides towards _m_ without producing any effect either on the plate _G_ or the lever _m G_: but when it has once passed the said angle _G_, it cannot go again toward _F_ without depressing smartly the end _G_ of that lever, and thereby raising the end _m_, thus starting the eye from the stud _m_, round which it had been bent by the processes above described.

At the right of fig. 1 near _F_, is an object, the use of which is too evident to need description. It is a double spring for the purpose of keeping the _hooks_ _c t w v d_ pressed against the pins, near _t v_, which determine the position of the said hooks; and the degree of _bend_ first given to the wire by passing the points _t v_.

There are some less important parts and operations left undrawn, in order to prevent confusion in the figures: but they are such as would strike any person having the above under his eye. In a word I have done what I thought best to aid the construction of this Instrument:--which is represented at two thirds of its natural size--but whose dimensions, of course, would vary with that of the objects to be produced by it.

OF
A VENTILATOR,
_Rotatory yet by pressure_.

By this title I wish to distinguish this Ventilator from all such as act by the mere centrifugal force of the air: and to make this distinction the more palpable, I would add that _this_ Machine acts like a pump, that is by means of a space alternately contracted and expanded, into which the air enters, and from which it is expelled _by force_ as water is from a pump. The means are the following: _A B_ (fig. 4 of Plate 20) is a hollow cylinder, of a diameter proportioned to the effect wanted to be produced. _C_ is a cylinder closed at both ends, which fills that just mentioned as far as the length goes, excepting _a play_ of about 1/8 of an inch. This interior cylinder revolves in the former; but _not_ on its own centre. It revolves on an axis _E_ eccentric to itself, but exactly concentric with the outer cylinder _A B_. The centre therefore, of the inner cylinder _C_, describes a circle within the outer one, which is always parallel to its circumference. On the axis _of motion_ of this cylinder _C_, and outside of that _A B_, are fixed two cranks _E F_ fig. 5, which exactly reach from its centre of motion to its centre of figure: so that whatever circle the latter describes _in_ the large cylinder, the former describe the same line _without it_. And hence any slide or valve _D_, driven by these cranks, will always touch, or be equally near, the circumference of that interior cylinder _C_. The valve _D_ then, worked by the bars _G_ from without, forms a constant separation between the right and left hand parts of the _lunular_ space left between the fixed and moveable cylinders; and if the latter turns from _C_ by _B_ to _D_, the right hand space _C B G_ is the _plenum_, and the left hand space _C A D_ is the vacuum of this Instrument; or in other words the air will flow _in_, through the passage _H_, and flow _out_ through the passage _I_: and by a contrary motion of _C_, it would do the contrary--but I prefer the first process because any pressure within the valve _D_ is not liable, then, to press the valve upon the drum _C_, and produce contact and friction; which in the second case it might do. Suffice it to add, that the quantity of air displaced at each revolution of _C_ round its centre of motion, is the difference between the area of the drum _C_ and that of the cylinder _A B_: and that its quantity at each part of the revolution is proportionate to the curvilinear triangle _G B_, multiplied by the length of either cylinder.

In the prospectus, this Machine was said to be good as “a gas meter,” which I still think it is. For such a purpose however, _friction and eccentricity of weight_ should be obviated, by placing the axis _E_, _in a perpendicular position_: when I doubt not it would measure flowing gas better than many of the machines that have been proposed for that purpose.

OF
A COMBINATION OF WHEELS
_To raise Water_.

This _mode_ of raising water in its simplicity, is I think called the Persian wheel. The buckets hang upon centres, dip in the _under_ water, fill themselves there, and by meeting an obstacle above which turns the buckets aside, they empty themselves into the upper _back_, from which the water is conveyed to the general reservoir prepared for it. This present Machine is such an extension of the above principle as to make it applicable to considerable degrees of elevation, and to many situations where a single wheel would be of no service. Having observed that in every _train of wheels_, the circumferences of any two wheels, have motions _towards_ each other, as well as _from_ each other; I perceived that, in a vertical train, this circumstance might be laid hold of to compose a machine for raising water. Be therefore, (Plate 21, fig. 1) _A B C D_ four of a set of wheels thus intended: on the left of the lowest wheel the buckets move _upward_, as indicated by the arrow; while those at _B_ move downward, coming thus to meet the former. The buckets _A_ are full, and those _B_ are empty; and as the latter, by the motions of the _equal_ toothed wheels on which they are hung will infallibly meet the former, and even plunge into them at _I K_ and _L_, it is only to put a _clack_ of leather or a valve, in the bottom of _all_ the buckets, and we have a machine that will raise water to the top-most wheel, be it ever so high, and there the water will be poured out into the vessel _M_, as in the common Persian wheel above alluded to. On this principle the first change of buckets will take place at _I_; where the lower bucket belonging to the wheel _B G_ will take the water from the upper bucket of the wheel _A H_; when the bucket _I_ will go down, nearly empty, by _H_ and fill itself again in the under water; But the bucket of the wheel _B G_ having now _got_ the water, will rise by _G_ to _K_, where another bucket belonging to the wheel _C F_ will come empty, and plunging itself into _that_, take its water and go upward by way of _C_ to _L_, where a similar change will take place and the water from _L_ will rise by _E_ to _M_, into which vessel it will be poured by the _canting_ of the bucket as seen in the figure. Thus it appears that any number of toothed wheels geering together, surrounded with buckets _valved_ at bottom, and receiving power from any one of their number, will raise simply and effectually a quantity of water _not small_ in proportion to the power employed, and by means that promise great durability to the Machine.

OF
AN ECCENTRIC BAR PRESS,
_For clearing wetted goods of Water_.

This press (see Plate 21, fig. 2) is indefinitely powerful. It was invented for the use of my late beloved brother, then contractor with government for cleansing the sea bedding. It is composed of a centre piece _A_, strongly fixed to a post in the ground, the bars _A B_ _A C_ being suspended above it, so as to remain horizontally moveable, while describing 1/4 of a revolution round the general centre _A_. The blankets (or other goods) are put into the space _s_, (on a net nailed _under_ the bars) while in the position _A B_; and the whole is then thrown with force towards _B C_; the length _A C_ being so calculated as to cease pressing at the desired moment: for such is the _power_ of this Machine, even without this projectile force, that were the stress not moderated, nothing could remain whole under its operation. It is clear however, that, when this operation _begins_ at _s_, the relative motion of the jaws _s_ and _B_ is assignable, and even visible, as shewn by the dotted circles; but as the whole approaches toward _B C_ that relative motion becomes insensible, the circles parallel, and consequently the power infinite: which is all I shall say on the theory of this Machine.

OF
A COLOUR MILL,
_For Calico Printers_.

This Machine is delineated in fig. 3 of Plate 21. It has several properties which I think important in the process of grinding colours, either in a wet state or a dry. It consists of a frame _A B_, which has a hollow centre, through which the axis of the bevel wheel _C D_ is brought in such manner as to geer with the bevel pinion _P_, in whatever position the frame _A B_ may be placed. The axis of the pinion _P_ carries a vessel _of which_ _E F G_ _is a section_, and in which rolls a well turned and heavy ball _H_, _upon_ the colour to be ground: which it crushes in the line of direction of its centre, and to a greater or lesser _width_ according to the diameter of the ball, as compared with the section of the groove _E G_, in which it rolls. Now as the motion of the vessel _E G F_, is oblique to the perpendicular, the contact between it and the ball does _not_ take place in any great circle of the latter: but is constantly varying by a twist in its motion dependent upon the angle of the vessel’s inclination to the horizon. From hence arises the _impossibility_ of any colour remaining on the ball unground: and in order likewise, that none may remain uncrushed in any part of the vessel _E F G_, the frame _A B_ gives it constantly new positions, _one_ of which is represented by the dotted lines _I K_: where it is seen that the ball bears on a different line of the vessel’s bottom than it did before. This also adds still greater change of action to the ball itself, and occasions (taking both these properties together) an unbounded variety of effect, which necessarily brings every particle of colour under the ball by the mere continuance of motion: and thus grinds it all without any care on the part of the attendants. It may be added, that this vibrating motion of the frame _A B_, is easily made to result from an eccentric stud and proper connecting rods behind the frame; all which is too easy to require further description.

OF
A DYNAMOMETER,
_Or a second Machine to measure power & resistance in motion_.

In Plate 21 fig. 4, there is a representation of this Instrument. It is composed of a frame _A B_, containing a strong shaft _C D_, on which are placed the three following objects. First, a fixed pulley _E_, working by a strap, the Machine whose resistance is to be measured. 2ndly, a loose pulley _F_, receiving the power from the _mover_ whatever it be. And 3rdly, a barrel _G_, which is the acting pulley, when the strap is put on it from _F_ in the common method. But this barrel _G_ acts by means of a barrel-spring within it, which is hooked by one end to the boss of the shaft, and the other to the rim of the barrel, as is usual for barrel-springs in general. Now the power produces the desired motion by coiling this spring to the necessary degree: and to make that degree _visible_, there is fixed to this barrel _G_ a spiral _s_, which as the spring bends, drives _outward_ the stud _t_, and with it the _finger_ _v_, which, pointing to the graduated scale, shews at once the number of pounds with which the spring acts on the shaft _C D_ to turn it. By these means the stress on the straps and on the Machine turned is known; of which also the velocity is easily determined by counting the number of revolutions performed by either of the pulleys _E F G_, which are alike in diameter.

* * * * *

In ending the first part of this work, I gave my readers room to expect _this part_ “within three months,” and am happy now to fulfil that engagement. Although these pages contain fewer errors than the former--an apology is due for those that have crept in: to which I add the promise that every thing shall be done to lessen them further in the future parts, and wholly to correct them before the work closes.

Page 100, line 2, for “:”, read ∷;
„ 126, „ 4, „ “on its surface” read at its pitch line.
„ 126, „ 17, „ “its height _f g_,” read the length required.
„ 129, „ 16, „ “2,” read 4,
„ „ „ 20, „ “imperfect,” read homely.
„ 144, „ 7, take away “_alone_.”
„ „ „ 8, for “usually” read chiefly.
„ 146, „ 23, for “the friction,” read it.
„ 147, „ 1, for “nothing,” read little or nothing.
In fig. 7 of Plate 19, slope the groove of both _faces_ the same way.

* * * * *

A few words seem wanting to complete the description of the Cutting Engine above given. They relate principally to the cutter-frame and cutters. Although, with a view to celerity, I have shewn the cutter _out_ of the frame (fig. 4) yet a common frame, carrying the arbor on points, may be used with propriety; and would often be an eligible substitute for the frame above described. In cutting bevel wheels however, either on this Machine or that to be described, there is a form of the cutter frame which leaves less freedom of choice, as the cutter itself _must_ have a peculiar form and position. To return to the cutter for spur wheels, their form (or section) depends on the degree of _finish_ which the wheels require. For _rough_ work they may be cylindrical on the face, the sides being _under cut_, so as to leave them thickest at the circumference--whence a certain coarseness of cut ensues, but without _any injury_ to the spiral form. But, generally speaking, the cutters are best, when made a little tapering towards the edge, and toothed on both sides as well as on the circumference. The teeth should be tolerably fine, but not very so, unless great _smoothness_ of surface were required: and we have seen above that, in this System, great smoothness is very seldom necessary, _provided the obliquities be correct_. I may add, that those cutters used on common engines, whose great rapidity compensates for the small number of their teeth, would not answer here, on account of the twisting motion in the wheel. But nothing prevents using cutters, so formed on the sides, as to round off the teeth in the act of cutting--only the cutter must be so thin as that its thickness, added to the aforesaid twist, may not make the _spaces_ too wide. A little observation will render these things familiar to an attentive observer: nor shall this work conclude before all that I have gathered from long observation on this subject, be fully known to my readers.

J. W.

_5, Bedford-street, Chorlton Row,_

_20th. November, 1822._

PART THIRD.
A NEW CENTURY OF
Inventions.

It has been observed and regretted by a well-known writer, that “a periodical work resembles a public carriage--which _must_ depart at the usual hour, whether full or empty;”--and having undertaken to deliver _this_ work at stated periods, I have found myself in a situation not unsimilar: the consequence of which has been a too cursory view of some of the subjects. I feel however, that _this_ is not a sufficient apology for any essential defect: nor would it be more so to say that, although verging to old age, I am still a young author. Yet I may claim the privilege of supplying, in the latter parts of the work, what is most deficient in the former; and thus of proving that I do not intentionally neglect any thing that might make it practically useful.

With these views I commence this third _part_: intending first to continue the description of the Cutting Engine given at page 121, _and here applied to Bevil Wheels_; and then to re-consider, shortly, one or two other objects, that were too rapidly passed over in their proper places.

Plate 22, repeats at fig. 1, the first figure of Plate 15; by way of shewing the additions required to extend this method of cutting teeth, to Bevil Wheels. These additions are _first_, a disk _n n_, concentrically fixed to the main axis _A B_ of the engine. And, _second_, an inclined plane _o_, of _variable_ obliquity, connected by a joint with the _forked_ sliding bar _p q_, by which the plane _o_ is put in contact with the disk, at whatever distance the cutter-stand _e f_ may be from the common centre, _which distance_ depends, of course, on the diameter of the wheel to be cut; and to secure which is the office of the fixing screw _r_, in the figure.

It is now evident that for the disk _n n_, and the shaft _A B_ to rise, the slide _p q_ and the cutter-stand _e f_ must recede: and _this_ more or less according to the degree of obliquity of the inclined plane _o_, that is according to the slope of the _bottom_ of the teeth in the wheel _w_: see the dotted line _w p_.

A circumstance presents itself, that should be here explained: when the bevil of the wheel _w_, or the cone of which the wheel is a part, is very obtuse, the cutter-stand _e f_, can not be driven back by the action of the disk _n n_ on the plane _o_, without too great a stress being applied from below, to the axis _A B_. (See the apparatus _I M O N_, Plate 16, fig. 2.) In this case therefore, the handle _R_ is not used: but a weight is suspended to the end _N_ of the lever _M N_, sufficient to give the whole System _A B_, a tendency _to rise_; and the operator now acts on the screw _g_, so as to draw back the plane _o_; by which motion the disk _m n_ with it’s axis _A B_ is _suffered_ to move upward, and the wheel is cut, as desired. But on the other hand when the wheels are portions of _acute_ cones, they are cut by means of the aforesaid handle; by which the plane _o_ and the cutter-stand are _forced_ backward as before intimated.

We proceed now to describe the perpendicular part of the cutter stand _e f_; which is made double, as shewn at _i k_ in fig. 4 of Plate 15; and is also perforated at various heights to receive the bolt which forms the centre of motion of the arm _m u_, the latter having a cylindrical boss _u_, fitted into the _fork_ of the stand _e f_, and so graduated as to determine the angle of it’s obliquity to the horizon, or it’s parallelism to the dotted line _w p_, which indicates the slope of the bottom of the teeth on the wheel. Finally, the cutter-frame _x_ is fastened to this arm at right angles to it, and thus forms a right angle (or nearly so) with the surface of the wheel: and is, moreover, directed to the centre, produced, of the shaft _A B_. This latter fact is strictly true, only when the teeth required are of so common a kind as _not_ to require greater exactness: for in theory the sides of the cutter (supposed cylindrical) must alternately direct to that centre--namely, _that_ side which is actually cutting: so that a provision must be made to shift the cutter spindle sideways, a distance equal to it’s diameter; this being no more than what is necessary in every system of wheel cutting.

We may also consider here, the form of the cutter itself, _v_, fig. 1. It is slightly conical, (more or less so according to it’s use) and of no greater diameter than the smallest width of the _spaces_ between the teeth of the wheel. A common disk-like cutter would not produce perfect, nor even tolerable teeth on a bevil wheel. The reason of this will appear by considering that a spiral line, either on a cone or it’s base, _turns_ more the further it is from the centre, and less the nearer it comes to it. So that a _flat_ cutter placed at _any_ angle, is parallel to the curve at _one_ place only; whence the propriety of using a cutter of the kind represented in this figure. It is however true, that the first opening of the spaces may be made with a common cutter; but it should be very thin comparatively with the spaces required: and it’s cut would serve only as a _sketch_ of such space, serving principally to permit the metal to escape while finishing the teeth with the cutter just described.

I proceed now to the examination of _the plates_, and the manner of adapting their length to the process of cutting _spiral teeth on bevil wheels_. But before entering on this subject, I would explain a kind of inadvertency into which I fell at the close of my former description of this Engine (see page 129). In my zeal to be candid in stating the properties of my Machines, I have suffered it to _appear_ that I thought this an “imperfect” one:--an expression which, although modified among the errata, may still cause it to be looked upon as radically defective; than which nothing could be further from the idea I wished to convey. I intended merely to express the want of _absolute_ connection between the two movements of the shaft--the rotatory and longitudinal motions. I meant that the process by this Machine was not theoretically _certain_, because dependent on the action of a weight (Plate 16, fig. 1 and 2) and an _unforced obedience_ to the direction of the plates. But this small remove from rigourous principle is in my opinion _much_ overballanced by the facility of cutting _good wheels of all diameters_, by the sole change of a morsel of tin, which leaves untouched every other part of the Engine.

Entering then on this branch of the subject, I first observe that if we chuse for the teeth an inclination of 15 degrees (in imitation of the cylindrical wheels) it can only be for one point of such wheels--as observed above. This point therefore I have placed at _r_ in the middle of the face. And supposing now that at this point the wheel _O_ were 4 inches in diameter and the wheel _S_ two inches, these plates would be found as before by these analogies:

(1) _wr_, or 2 inches : 11 inches (rad. of plate rim) ∷ 26.8 : 294.8/2 = 147.4 plate required.

(2) _vr_, or 1 inch : 11 inches (rad. of plate rim) ∷ 26.8 : 294.8/1 = 294.8 2d. plate required.

But it is plain that the conical face, _b C_, (common to both wheels) is _broader_ than the supposed cylindrical ones _b e_ and _b d_: and therefore that the above plates must be made longer (to furnish the said obliquity) in the following proportions, namely: for the wheel _O_ in the ratio of _b e_ to _b C_; and for the wheel _s_ in that of _b d_ to _b C_: that is, these plates should be lengthened as the tabular cosines of the angles _B A C_ and _D A C_ to radius (for _b e_ : _b C_ ∷ _A B_ : _A C_; and _b d_ : _b C_ ∷ _A D_ : _A C_.) Thus then,

(1) Cos. 63°27′ : radius ∷ 147.4 (present plate) : required plate _x_, = 147.4 r/Cos. 63°27′; and

(2) Cos. 26°33′ : radius ∷ 294.8 (present plate) : required plate _y_, = 294.8 r/Cos. 26°33′.

Now, by the tables, cosine 26°33′ = 894, and cosine 63°27′ (it’s complement) = 447, when radius is 1000: whence dividing the two equations by _r_, and substituting these values of cosines 63°27′ and 26°33′ we shall find the two quantities _x_ and _y_, _equal_. Whence it appears that for every _pair_ of bevil wheels, whose shafts lie at right angles, _the same plate serves for both wheels_: only turning it once to the right, and once to the left hand on the plate rim.

And if now we _measure_ on a scale of _equal_ parts, the line _A r_ and call it 100, we shall find the line _w r_ (near enough for practice) to be 90, and the line _v r_ to be 45, and these numbers respectively, put for rad. for cos. 26°33′, and for cos. 63°27′, will make the first equation _x_ = 147.4 × 100/45 and _y_ = 294.8 × 100/90 or _x_ = 327.55 and _y_ = 327.55, &c. confirming the above deduction that the _same plate_ serves for both wheels; and giving, withal, the length of the plate required.

In performing this operation by actual measurement of the lines, I have had in view to trace a path for those of my readers who may not have the tables, or may be unaccustomed to use them. The process, generally, is to take the diameter of any bevil wheel _O_ fig. 4, in the middle of it’s face; and _supposing_ it a spur wheel, to find it’s plate by the method above given: and then to multiply the length of that plate by the line _A r_ and divide the product by the line _A w_, both measured on the same scale of equal parts.

It may be well to observe, likewise, that the same method of finding the plates, applies to bevil wheels of every description or angle: but that it does not give equal plates for every _pair_, except in the above case of wheels placed at right angles to each other.

I would just remark that by the figure near _B_, is shewn a _section_ of the Machine on which I centre the wheels to be cut on this Engine. It is an inverted cup _s t_, into which the _arbor_ is screwed in a _true_ position; and this cup is fixed on the top of the shaft _A B_, by the _three_ pressure screws near _s t_, which enter a triangular neck made round the shaft, against the _upper_ slope of which, the screws press so as to draw the cup downward in the act of centering it. This I say is my present method; but it is in a measure accidental, the shaft not having been perforated to receive arbors of the usual kind. Mine, however, have their utility in the ease with which they are varied in size, and changed on the Machine: but on their _comparative_ usefulness I give no opinion. The other is the most solid method.

In the description of my differential Steel-yard, (see page 163) I stated that the load _P_ was wholly collected in the point _o_; and that dividing the line _A C_ by the line _A o_, the power of the Machine was known. But I should have shewn that this line (_A o_) is _equal to one half the difference between the arms_ _A D_ _and_ _A E_. To do this, here, (see Plate 23, fig. 4) I take the Machine in the state of infinite power, before mentioned; and observe, that in moving the point of suspension from _o_ towards _A_, I at once _lengthen_ the arm _A E_, and _shorten_ the arm _A D_: by which process, (supposing each arm to have been called _a_) that which I lengthen by any quantity _d_ becomes _a_ + _d_, and that which I shorten by the same quantity becomes _a_ - _d_, and the difference of these quantities, is 2_d_: so that the line _A o_ is in reality one half the difference between the two arms _A D_ and _A E_ as was required to be shewn.

But we may go a step further: The two arms of the equibrachial lever _x y_ may likewise be made _unequal_: and the line _s a_ be subdivided in any ratio: which division will augment still more the power of this Machine. If for example, we hang the load on the point _v_, halfway between _a_ and _s_, that power will be doubled; for the line _c v_ (representing the space moved through by the load in this case) is only one half of _that_ _w s_, or _o q_, and might be still less at pleasure. Thus the whole power of the Machine is _now_ found by dividing the length of the long arm, beyond _D_, by the line _a v_, instead of the former line _A o_, or dividing the _motion_ of it’s extremity upward, by the line _c v_, the motion downward, of the load _P_.

It has been further suggested, that the description of my excentric Bar Press was not sufficiently explicit. I have therefore added the figure 2 of Plate 22, to assist in elucidating that description. I had, perhaps made an undue use of the principle of virtual velocities by saying, too concisely, (page 174) that “as the whole approaches toward _B C_, the relative motion (of the cheeks _s_ and _B_) becomes insensible, the circles parallel, and consequently, the power infinite.” It is however _vulgarly_ said that _power_ cannot be gained without losing _time_--which implies that if time _is_ lost, power will be gained: and the principle of virtual velocities says the same thing, though in more appropriate terms--that if a small movement be given to a system of bodies actually counterpoising each other, the quantity of motion with which one body ascends, and the other descends perpendicularly, will be equal: so that, as remarked in page 50, by “whatever means a slow motion is obtained, dependent on that of a moving force, the power is great in the same proportion.” Now, in the eccentric Bar Press, (see fig. 2) this is so in an eminent degree: for when the bars are in the position _A B_, the distance of the cheeks is equal to _B s_; and they must move, circularly, as far as _A f_, to bring them closer to each other by the quantity _s a_: dividing therefore, the distance _B g_ by the line _s a_, we find (near enough for practice) the power of the Machine within the limits _A g B_. It is nearly as 10 to 1. In like manner this power at _A e g_, is equal to the arc _e g_ divided by the line _f b_; and at _A l n_ to the arc _l n_ divided by the line _d k_, namely by the difference of the lines _k l_ and _m n_. From the above it appears that the _nearing_ motion of the cheeks of the press, becomes slower and slower as the bars _A_ and _C_ come nearer to the point _C_: insomuch that the difference between the lines _m n_ and _o p_ is nearly imperceptible, and _that_ between the lines _o p_ and _C q_ entirely so. But according to the above process, the distance _p C_ should be divided by this _imperceptible line_, to find the power of the press at the point _C_; which therefore is _immense_. Another proof of this may be drawn from the supposition (see fig. 3) that the small lever _a d_ is turned round the centre _o_ by a bar _o C_ fixed to it, and of equal length with the line _A C_ fig. 2. Fig. 3 shews that the lines or bars _C d_, and _a C_ are moved endwise by the _circular_ action of the points _a_ and _d_; and therefore (by statics) their motion is the same as though caused by the perpendiculars _b o_ and _o c_ let down from the centre _o_, on each of them. Hence the power of this Machine is found by dividing the distance _o C_ by the sum of the lines _b o_ and _o c_; which sum (when these lines _vanish_ by the union of the bars over the centre) becomes infinitely small: the quotient of which division therefore is infinitely great--as was to be shewn.

OF
A PUNCH MACHINE,
_For Engravers to Calico Printers_.

The usual method of making Punches for engraving Copper Cylinders, (otherwise than by the _milling_ system) is to _cut_ the desired pattern on _a die_, and then to transfer that pattern by blows or pressure to the punch, from which it is again transferred to the cylinder. My Machine in this operation, unites motion to the needful pressure; and thus renders the result more easy and complete. This effect I could the better ensure, because the surfaces of _my_ punches are essentially convex, or rather cylindrical; as will appear when my engraving Machine comes to be described. Their convexity however, can be diminished at pleasure--whence this Machine is capable of offering useful assistance to a maker of flat punches.

In Plate 23, _A B_ fig. 1 and 2, is the body of the Machine, with the vibrating bar _C D_ laid upon it; reposing especially on the correct and level parts of the body at _a b_; this bar contains the _die_ _c_, with which it vibrates between the cheeks _B R_, as impelled by the screws _E F_, it’s centre of motion being the pin _P_, duly supported by the strong shoulder _A_. In a line with the bar _C D_, is placed a second _vibrator_ _G_, containing the steel _d_, that is to become a punch, already rounded into the cylindrical shape it must have when finished. This vibrator has it’s centre of motion at _e_ fig. 1, and it need not be added that the curvature of the punch depends on it’s distance _e d_ from that centre: for the centre of the long bar _C D_ is _so_ distant as to have little influence on it’s formation. Further, the cap or bridge _H I_, which furnishes a centre for the smaller vibrator _G_, can be brought forward to any useful position by the nuts _K L_: that cap sliding horizontally between the cheeks _M N_ as directed by the small _arms_ _m n_. This motion, then, taken from the nuts _K L_, serves to impress the _work_ of the die on the steel prepared for the punch; and this being done to a _first_ degree, both the handles _O Q_, are laid hold of: and by turning the screws the same way one of them goes forward and the other recedes, until the punch and die have been in contact over half their surface. At this moment both screws are turned backward, and the motions of the two vibrators reversed: by the repetition of which alternate motions accompanied by the needful pressure, the whole pattern is transferred from the _die_ to the punch--when the latter is taken out of the Machine, and _filed up_ in the usual method.

It should be observed, that the smaller vibrator _G_ can be displaced with ease when the nuts _K L_ are withdrawn: and this should be frequently done to examine the progress of the impression. Nor is there any difficulty in re-entering the figures. In a word, the perfection of this process depends more on _much_ motion than on violent pressure: whence this facility of re-entering is a desirable property. This Machine is usually laid on a bench or tressel, with a long mortice in it, into which the feather _x_ of this Machine enters so as to be firmly fixed.

OF
A DIFFERENTIAL PUNCH MACHINE
_For Engravers_.

I was the rather induced to attend a second time to the differential Steel-yard, because I had it in contemplation to apply that principle to the present purpose; since, to make flat punches, is to some engravers a more desirable thing than to make cylindrical ones. I am not fully persuaded that it is even possible to transfer a large pattern, from a flat die to a flat punch, by _any_ pressure acting simultaneously on the whole surface. In those cases, if there is much _work_, the whole surface _goes_ _down_; and the parts that form the pattern do not _rise_. But, all that can be done in this case, is, I believe, feasible by the Machine now to be described.