Some knowledge of the nature of this geering may be gathered from its very appearance: see fig. 5 Plate 14. To represent these teeth properly, no light must appear between them. The tops of the teeth offer a continued circular line, similar to what it would be if there were no teeth at all: and the latter are distinguished only by a different shading of their front and lateral surfaces. The reason (as has been already observed) is, that they are necessarily so placed, as that the last end of any tooth shall not quit the plane of the centres, until the first end of the succeeding tooth arrives at it; which principle precludes the possibility of any space remaining between the teeth, that an eye directed parallelly to the axes could penetrate. Such a space indeed would introduce a portion of the properties of the old geering, which it is the object of this System to avoid. As this wheel then appears in fig. 5, so it acts: that is equally and perpetually.

It were well also to observe the appearance of these wheels on their edges; or in the planes which, as wheels they occupy. The 4th. figure of this Plate is outlined with some care, in order to shew the varying, and seemingly anomalous form which the teeth assume as they approach the boundaries of the figure. Although cut as obliquely to the axis there, as any where else, the receding cylindrical surface, thus seen, appears to take this obliquity away; and the very outward teeth seem nearly parallel to the axis of the wheel. But this is only appearance: and we give here one example of it, that we may not be obliged to lose much time hereafter, in drawing correctly, wheels on this principle—a process indeed which in many cases, would be found very difficult, if not impossible.

We have already adverted to the oblique tendencies of these wheels, when used with a single inclination of the teeth; from which, among other things, it follows that, in the act of urging the shafts endwise, they tend also to bend these shafts: for which reason the shafts require to be stronger than those of common wheels—that is, when the effort bears any proportion to their stiffness—a circumstance which, in light rapid movements, is of small moment. And in heavier works, when it is desirable to get rid of these tendencies altogether, we have peremptory means of avoiding the very appearance of this evil.

Suppose then (fig. 2 and 3, plate 14) a b to be a straight rack on this principle; driven by the wheel or pinion c. The motion, backward, of the pinion, tends, clearly, to urge the pinion endwise towards d, and the rack sideways towards a b. But either of these motions is prevented by fixing to the pinion, or the rack, a cheek e f, to support them against this lateral pressure. But then, exclaims a doubting friend, you introduce friction: and it is true: there is now a real rubbing of the ends of the teeth against this cheek; but the pressure there being only one quarter of what it would be on the front of straight teeth, we avoid (on a rough estimate) three quarters of the friction; while preserving all the constancy and smoothness of motion which the system gives; and which after all, is the most important part of the business.

This idea then applies among other things to the racks of slide-lathes; giving a regular motion to the rest and cutting tool, thereby adding to the perfection of the turning process: and many other cases might be adduced.

But instead of using a rack and pinion, as thus described, two wheels, of any desired proportions might have been thus treated, and the result would have been the same. They would have worked with perfect smoothness, under about one quarter of the friction attendant upon common wheels in similar circumstances. There are cases therefore, in which it would be expedient thus to employ the System. I cannot but observe likewise, that this method of using cheeks to prevent any side motion in spur wheels, might also be applied to bevel-wheels, to prevent the angular tendency which the obliquity of their teeth gives them: and that I prefer such a method of obviating this evil (where it is one) to any attempt at using teeth in the V form, on bevel wheels. Still however, as before observed, this counteraction of the oblique tendencies is not always necessary. It may be dispensed with in all light and rapid movements; especially in the use of perpendicular shafts; and where the driven wheels are small and distributed round a central wheel in positions nearly opposite each other: of all which cases we shall see examples in the spinning machinery to be described hereafter.

OF
THE CUTTING ENGINE,
To form Spur-wheels, on my late Patent principle.

The figures of this Engine (see Plates 15 and 16,) are drawn to a scale, from the Machine itself, now before me. The scale of the objects on Plate 15, is one inch and three quarters to the foot; and that of the objects on Plate 16, one inch and one third. These were convenient proportions for introducing this object into the present work; but the size itself of the Machine is arbitrary. I did not make it according to my ideas of the best dimensions: but bought it as a common cutting Engine, and gave it those other properties that my System required.

The first remarkable deviation from the usual form is in the shaft or axis of the dividing plate. See fig. 1 and 2 of the Plates 15 and 16. The dividing plate a b, is concentric with, and fixed to an axis A B made as perfectly cylindrical as possible, so as both to slide and turn in the bars C D, and E F composing the frame. These bars are bushed, to fit the axis A B, either with a contracting ring of brass, as usual in some mathematical instruments; or with type metal, cast around the axis into rough holes in those bars:—which metal, closing upon the axis makes a good centre; and will last a long time. My Engine is made in this manner; and has been renewed in this part only twice in several years. This frame C D E F of the Engine, is strongly connected with the feet G G H H, by means of the nuts E F in the plan: and by these feet it is fixed to its bench or table, as will be seen in Plate 16.

Figure 2 of the present Plate, represents the plan of the Machine, but turned upside down; so that the feet G H screwed under the lower plate E F, are wholly visible. In this figure, also, is shewn at c d, the edges (without the bottom) of the horizontal slide which carries the stand for the cutter frame represented in fig. 4. This stand is indicated by the dotted lines of this figure 2, as situated under the arm D of the bar C D; but it is better shewn in fig. 5, where e f marks the slide in which the cutter frame (fig. 4) moves up and down, by means of the screw and handle e f. In general I avoid dwelling much on these smaller parts, because they exist, probably in a more perfect state, in most other machines. In this fig. 5, g h shews the screw that moves this stand nearer to, or further from the axis A B of the Engine, according to the diameter of the wheels: which is also a common process in Machines of this kind, on which therefore much need not be said. But a somewhat greater importance attaches to the cutter frame represented in the 4th. figure: which is a kind of small lathe whose spindle n o, carries the cutter n, outside the frame, for the purpose of changing the former without displacing the latter. The cutter (of any proper section) is placed in or near that line which is a continuation of the centre of the fixing screw o p. It is in that line for wheels whose teeth can be finished with once cutting: but near it for those whose teeth must be cut at twice. In this same figure, i k represent the ends of the standards that form the vertical slide e f of fig. 5; and the separate figure p q, shews the back of the cutter frame l m, the flat part of which, p, presses correctly on these uprights i k, and thus fixes this instrument at any desired height, and to any given angle with the perpendicular: the use of which arrangement we shall soon have occasion to exemplify.

Turning now to fig. 3 of this Plate, we there see the main shaft A B, broken off at B: and the letters a b again shew the dividing plate of figs. 1 and 2: under this Plate is seen an alidade or moveable index, shewn by section only at c, and in elevation at d e; where it clips the plate as far as n and carries a boss between n and e, on which the dividing index e f, turns; and to which it is strongly fixed by a nut o, when the proper number to be cut is determined. Moreover, this boss forms, itself, the nut of a thumb-screw s, which, carrying a circular plate at its lower end, clothed with leather or any soft substance, connects strongly, without injuring the plate, the moveable index with any point of it, as determined by the dividing index e f. This brings us into the midst of things, as it respects the use of this Engine; for the former index c d, is furnished with a small roller, p, the motion of which all the foregoing objects must obey, when they have been fastened together by the thumb-screw s. We turn then to the figures 1 and 2 of Plate 16, in order to shew those parts in action: after remarking only that the form p q r of this fig. 3, is that of the moveable index shewn before at c d; requiring only, to become complete, that the part q should be sufficiently lengthened to make the arc r q a complete semi-circle—for purposes that will shortly be explained.

In the two figures of Plate 16, the Machine is shewn as placed on its bench or table, accompanied by the parts which give it a distinctive character, and in fact embody the System. In addition to the parts already described, we first remark the circular rim c d, fixed to the ends of the bar E F; and made perfectly concentric with the main shaft A B, and the dividing plate a b. This rim is shewn in section only, at v fig. 2. Its section resembles an L, and thus forms a basis for certain plates that will soon appear; and receives the screws by which these plates are fastened to it. This being sufficiently clear, we now proceed to describe the table and the connection of its mechanism with the foregoing.

In Plate 16, K L is the table: to which the Engine is screwed through its feet G H. I, is a square bar of wood, sliding in a mortice through the top of the table; and connected by a joint with the lever M N—itself moving round a pin at O, and carrying a friction roller, P, which pressed by the spiral Q, as turned by the handle R, raises the bar I, and with it the main axis A B of the plate, and of course the wheel to be cut, centered as usual on this axis above B. Finally, p q r, in both figures, is the moveable index first shewn in fig. 3 of Plate 15; prepared to be drawn round by a weight W, hanging to the cord x, passing over the pulley y, and tied to the right end of the arc q r, when this is to move to the left; or to its left end, when the motion is to be toward the right:—these motions depending on the right or left-handed direction of the teeth which it might be wished to cut on the Machine.

Between the two figures 1 and 2 of this Plate, there appears a diagram, the base of which is nothing more than a part of the rim c d supposed straightened, and placed there that its use may be the easier understood. On the rim is seen a right angled triangle e g f, against which the roller p will lean by the action of the weight W on the cord x, and the arc q r of the moving index p q r. So THAT when, by the handle R, the spiral Q depresses the lever M N, by means of its roller P, then the bar I raises the axis A B of the Engine, and the weight W turns it at the same time, as much as the small roller p permits by rolling up the side e f of the plate e g f. And thus may a screw-formed tooth be cut in any wheel centered above B in the usual manner.

Thus then, in describing this Machine, the manner of using it has been also shewn: for the cutter, in this Machine, (to cut spur wheels) is always fixed; and all the motion is composed of the rotatory and longitudinal movements of the principal axis, which carries the wheel along with it. The cutter I say is fixed, at a proper height just above the wheel, and at an angle to the perpendicular, equal to that it is wished the teeth should form at it’s pitch line. This inclination as before observed is 15 degrees; and the tangent of 15° is in round numbers 268, when the radius is 1000. That is, in our present figure, the basis e g of the plate e g f, occupies 268 divisions of a scale, of which the height g f contains 1000. It appears then, that to cut a tooth with 15 degrees inclination, by this Plate, the wheel receiving that tooth, must be just as large as the rim itself; for the surface of the wheel would turn more, with a given elevation, if it were larger than the rim; and would turn less, by the same elevation, if it were smaller. In a word the whole theory of this operation, is now clearly seen. The smaller the wheel to be cut, the longer, horizontally, must be the Plate; or in other words, as the diameter of the wheel is to that of the rim, (c d) so is the length e g of the Plate to the length required. Now this height f g, is always the same; all change therefore, in the plates, takes place on the horizontal length: and this length is most easily found by the foregoing RULE OF THREE. If then, instead of the triangle e f g, I had used the triangle e′ f′ g′ it would have followed at once, that to produce an inclination of 15 degrees, I must have taken a wheel of just half the diameter of the rim; for the plate e′ f′ g′ is just twice as long as that e f g. To prove this, let us suppose the diameter of a wheel wanted, to equal one half that of the rim c d: then the rule will stand thus:

1 is to 2, as 268 is to ...536, the length of the plate according to the theory; which is precisely the length it is drawn to compared with that e f g, namely twice as long. Thus the four triangles, drawn to the right and left in this diagram, represent the plates for the wheels of the following diameters respectively:

A small anomaly, of form, may be mentioned here to prevent mistakes. The shaded triangle e f g in the Plate, looks higher than the rest: but if higher, it is also longer in the same proportion; and the roller p never reaches the bottom: so that the effect of this Plate is the same as though it resembled the others in every respect. In general the effect of the Plates depends on their length compared with their height: and indeed they must be made higher than the thickness of the wheel to be cut, that the latter may disengage itself from the (fixed) cutter both above and below.

It is proper to observe, that for every pair of wheels there must be a pair of plates; one leaning to the right and the other to the left, (see the diagram) but, as before said, the degree of obliquity must be different in each pair, except in the case of equal wheels, when the same plate serves for both; only turning it to the right for one wheel, and to the left for the other. Nor does this offer any difficulty, as the plates are made of common tin plate: which is easily brought to fit the rim, whichever way it is applied. I shall now add another example of the process for finding the length of the plates: and to that end repeat that the plate rim c d, is 22 inches in diameter, or 11 inches radius. Supposing then that we wished to cut a pair of wheels, one of them being 1 inch in diameter and the other 12 inches; both to have teeth inclined 15 degrees to the axes; (as without that they could not work together) to do this we must effect these two proportions:

• (1) ¹⁄₂ inch (radius of small wheel) is to 11 inches, (radius of plate rim) as 268 parts (of which the height of the plate is 1000) to another number, which is the length of the plate sought: measured on a scale of parts of the same magnitude.
• (2) 6 inches, radius of the large wheel; is to 11 inches radius of plate rim; as 268 parts (as before) is to another number, which is the length sought for this second plate.

The one of course, to be directed toward the right hand, and the other toward the left, on the plate rim; where note, that if the height (1000 parts) is found so numerous as to create confusion, let 100 parts be assumed; when the length of the plate will become 26.8 or 26 and ⁸⁄₁₀ instead of 268, and the operation will be so much the more simple.

It should be added that this process admits of being further simplified: since the product of 11 inches, radius of the plate rim, multiplied by 268 (tangent of 15 degrees, or length of the plate for a wheel equal in diameter to the plate rim) since this product, I say, is a constant number, namely: 2948—which, divided by the half diameter of any wheel, gives, at once the length of the plate adapted to that operation, in parts of which the height contains 1000; or supposing the height to be 100 only, this constant number becomes (nearly enough for practice) 295. In a word, on a height of plate of 100 parts, when wishing to cut a wheel of 4 inches in diameter, I merely divide 295 by 2, and get for the length of my plate 147.5 parts of which the aforesaid height is 100.

It may possibly be suggested that this method of using plates to determine the obliquity of the teeth is a homely method, giving some trouble in the execution, and leaving a certain degree of roughness in that execution. The fact is allowed; but this method has the advantage of a very general application, which many a better looking apparatus would not present.

Besides, for most uses, these teeth require chiefly that the obliquity should be correct, and not that the surface should be licked like those of a gewgaw. In fine, the principle of this Machine once known, its best form will occur to the reflecting mechanician according to the quality of the work he has in view: And in fact, in the hands of a well known artist, this form has been already varied so as to produce effects much higher wrought than could be drawn from the Machine above described: which latter however in point of generality, still preserves the advantage.

OF
A DOOR-SPRING,
To keep a Door strongly closed, yet suffer it to be opened easily.

That “necessity is the mother of invention,” is a remark none the less true, for having become a trite proverb; I could mention the time, place, and circumstance which gave birth to this little Invention: but such detail would be superfluous. A certain door was, and is still, most inconvenient, from the stiffness of the spring, and the noise it occasions in a place where silence ought to prevail: which state of things suggested to my mind the Machine represented in fig. 5, of plate 17.

A B C in that Plate, is a horizontal section of the door, door jambs, &c. The door spring now in use, is a barrel-spring, with an arm carrying a small roller which presses in a gutter-formed plate, screwed to the door. My door spring is on a different principle. The roller is fastened in and by a small frame to the door, and the arm is fixed to the axis of the spring, which passes up through the top of the barrel. This spring is much weaker than the former, insomuch as only just to close the door by its elasticity; but when the door is shut, there is a sharp bend in the arm that wedges itself against the roller, and decuples at least the force of the spring, as tending to keep the door closed. When therefore it is desired to open the door, by pressing the door itself, a good push is necessary, but only for an instant: for as soon as the bent part of the arm is forced off the roller, there remains only the small resistance of the spring to be overcome; which latter, when suffered to act in shutting the door, will not shut it with that noise a stronger spring would occasion; and yet, when arrived at its first position, it will keep the door as strongly closed as ever. And should it be wished to avoid the necessity of pushing hard against the door, even at first, there is a sliding button and stem B put through it, which, if pressed from the other side, with the force only of the spring, will raise the latter beyond the roller, and thus open the door with perfect facility: and this same process will take place in pulling the door open by the hook D from the inside: yet still the door when closed will be as firmly so as before; the spring-bar acting in the latter position, as much like an invincible stay as the workman shall have desired—this property depending clearly on the nearness of the bend to a right angle.

This device may appear to some an object too inconsiderable to be justly dignified with the name of an invention. But if I should sometimes fall into such an error as this, I intend to compensate for any thing too trivial by giving in other cases, Inventions of ample size and number. I might even mention the Cutting Engine given in this part, where several Inventions are compressed into one, or rather presented as one, of which several examples will occur.

OF
A DRAW-BENCH,
For making my twisted Pinions.

A common Draw-bench (not here represented) is worked in the usual manner: but the instrument which forms the pinion (see Plate 17, fig. 1) is of a peculiar construction. It consists of a plate A B, containing—1st. a guide tube a, (fig. 2) to centre and conduct the blank wire;—2d. a ring b c, with nine grooves cut on one of its surfaces, directed to the centre, and in which are well fitted the cutters 1 2 3 4 5 6 7 8 9; and 3d. a ring d e, formed into nine spirals exactly like each other, answering to the cutters, and destined to urge them equally toward the common centre whenever this circle d e, is turned by the endless screw C D, in the direction of the arrow. In fig. 2, f g is merely a top piece to cover at the same time the cutters and the ring d e; which latter is thus duly centered. The points of the cutters 1, 2, 3, &c. are formed like the spaces of pinion teeth; and in the other direction, are sloped 15 degrees to the common axis, as taken at their pitch line.

The third figure represents the drawing clams, or pinchers, with a piece of blank wire d in them, tapered off to give easy entrance to the cutters. These clams have a cylindrical part of about a foot long, in which is cut a winding groove a b, whose use is to turn the wire in the act of drawing; for which purpose also the swivel e f is provided. The method I employ to trace this groove to the obliquity required, is to measure the circumference of the cylinder, and call that 268; and then, to make its length, in the cylindrical part, equal to 1000 of the same divisions. But this is right, only when the pinion to be drawn is of equal diameter with the clam-cylinder a b: so that if it is wished to draw pinions of a smaller diameter, I further say: diameter of clam-cylinder is to diameter of pinion, at the pitch line; As 1000 (present length of clam-cylinder) is to required length of ditto. Thus, for example, if the diameter of the pinion were only ¹⁄₄ that of the clam-cylinder, the length of the latter would be only 250 of the 1000 divisions, before found: and so in proportion for smaller diameters.

The figure shews this groove receiving a guide screw or stud a, which, placed in the fixed headstock a c, turns the clams d, with the wire, just enough to give the teeth an inclination of 15 degrees, thus adapting them to the wheels of which the proportions have been already given; where note, that the real dimensions of this pinion Machine are twice as large as those of the figures 1 and 2: but the size of every thing is of course variable, according to the pinions required to be produced.

OF
A GEERING CHAIN,
Formed to work in the Patent Wheels.

This Chain is shewn in fig. 4 of Plate 17. The links are formed to an angle, in the middle, similar to that of the wheels at their pitch line; of which the obliquity, for the V wheels, is greater than 15 degrees; since the thickness of the wheel, is necessarily divided between the right and left handed slope. Be this slope what it may, the chain and wheels must of course be alike, measured at the pitch line of the wheels; and then, as the chain geers with a straight line of pinions, they work together without sensible friction on the teeth, and with nearly the same steadiness of motions as wheels would work together. Moreover, if the drum be of a pretty large diameter, its action will likewise be nearly equable. The degree of precision depends, however, on the fineness of the pitch, and the largeness of diameter in the drum; since every chain bending round a cylinder must form a polygon of a greater or less number of sides, dependent on these circumstances. I repeat then, that while the chain works on the pinions in a tangent to them all, there is no necessary friction between them; nor yet on the pins of the chain, but only at the drums which actuate and return the latter:—I shall dismiss the subject, by observing, that I have used the term drum, because of the similarity of this chain-motion to that produced by bands, where drums are generally the movers. But here, this supposed drum is a wheel of proper diameter, cut into teeth similar to those of the pinions; and placed at the same height on its spindle. I have reason to think that this chain, carefully made, would be an useful addition to the bobbin and fly frame, applied both to the bobbins and spindles, instead of the bands now in use; which, though a convenient resource, give a result equally uncertain and imperfect.

OF
A SERPENTINE BOAT OR VESSEL,
To lessen the Expence of Traction, &c.

“This Invention is not to be considered as an imitation of the well-known manœuvre of towing one vessel in the wake of another: for the resistance of the vessels thus towed, remains nearly, though not quite the same as if drawn along separately. But here, by the adaptation of the prow of one Boat to the poop of another, the first alone suffers resistance from the water—which, although it enters between the joints, strikes only the first—and from this it follows, that the resistance of these vessels, in passing from one place to another, bears no necessary proportion to the weight they carry.”

“Thus then, I obviate the necessity of having broad vessels to carry the heaviest burdens; for I disseminate the load over an indefinite length: by which method also, my vessel rides in shallower water, and depends less for its passage, on the state of the rivers or the seasons. Besides, they require a much less number of horses, or exertion of power, to transport a given quantity of goods; admitting at the same time, a greater swiftness of motion. And finally, if these vessels travel through different towns on the same voyage, the goods of each town may be lodged in the same part, and merely detached in passing, so as to lose no time in unloading them.”

“Fig. 1 of Plate 18, shews the plan of several forms which I give to the articulations or separate parts of these vessels: so as to connect them strongly, yet leave them, as a whole, in some degree flexible. The form A B, is, for the first boat, a straight line across to form the stern, and for the second an obtuse angle terminated by a semi-sphere or vertical semi-cylinder, which enters a hollow and similar figure in the first Boat—which latter, in this case, forms the Head of the whole Serpentine Vessel.”

“These two parts or joints, of which we have been speaking, are held together by a rope c d e f, which, fastened to the second part at c, passes over two pulleys e d, in the head, to the small capstan f, by which, both parts are bound together as tightly as may be judged proper. If it were thought necessary, the spaces A B might be underlined with a piece of leather or metal, not to prevent the water from entering between the Boats, but to prevent its striking those which follow the others through the water—a precaution less urgent in the other kind of joint we are about to describe.”

“C D, in this same figure, presents another form of the head and stern of two contiguous Boats or parts; (which, to save room, are both supposed to be broken off at some point between their ends:) where as in the former case, the Boats are connected so as to remain horizontally flexible. These forms are semi-cylindrical, the stern concave, and the head convex, to the same radius; and the motion takes place around a bolt and pulley p, reeved with a rope coming from one side of the first Boat near C and led again to a small windlass or capstan placed on the other side near D. E F, is another modification of the same kind of joint: the centre of which is a bolt or stud q, (better seen at q in the 2d. figure) over which a triangular frame falls from the preceding Boat, and thus connects them instantaneously; leaving a certain flexibility in the horizontal direction.”

“Finally, G H shews a simple mean of connecting these Boats, on the supposition that both ends of each are formed alike to an obtuse angle in the middle of their breadth. It is a kind of hook r s, mounted in a frame turning on centres in the preceding Boat, and reaching over into the succeeding one; where it finds a hollow step of metal which receives and fits it, so as to hold these neighbouring Boats with sufficient tightness, but still with a certain degree of flexibility. Many other methods might be suggested, by which to form these joints; and almost any might be made to answer the purpose. I shall therefore leave this branch of the subject, observing only, that the second figure of Plate 18, is an elevation of the same things: which, generally, are marked with the same letters as far as they are visible.”

“The third figure presents the same objects in perspective; to which are now added two masts I K, placed obliquely on that Boat which forms the Head of the whole vessel. This obliquity is useful when the boat is drawn from one side only; but is injurious where the traction takes place indifferently on both sides: so that I should not, now, advise the use of this method—which indeed, I have avoided in fig. 4 of this Plate.”

“In every case, each of the masts carries a pulley near I K, over which passes a rope, the ends of which are fastened to the masts by proper brackets, near the deck: and to the middle of this rope is fastened the track rope L, by which the horses draw the Boat along. By these means the vessel is steered either to or from the land: for if the knot of the track rope is brought near the mast I, the Boat (which as before observed is the head of the whole vessel) veers towards the horses; and the contrary when the knot is drawn towards the mast K: both which effects are rendered the more prompt and decisive, by the use of the lee boards K M, the nature and use of which are already fully known.”

“But there are cases in which, from its great length, this Serpentine Boat would require a particular direction, for some intermediate point between its extremities; as although, in theory, every separate part ought to pass through the same water, yet in canals or rivers much bent, this may not invariably take place; and then a rudder would be useful, even in the middle of the vessel. I have therefore placed a pair at P R, fig. 3. Their motion is a vertical revolution, round a horizontal centre; and as they are formed obliquely to the sides of the Boat, when one of them is plunged into the water, it tends to drive the Boat in a sidewise direction: and if at any time it should be desired to stop the whole vessel, both rudders would be plunged at once into the water, when they would greatly contribute to that effect.”