Chapter IX: Introduction (2)

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:

No. 1, a wheel _equal to the plate rim_ _c d_;
2 do. do. to 1/2 do.
3 do. do. to 1/3 do.
4 do. do. to 1/4 do.

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.

Both proportions being effected, the first plate is 5896 parts.
And the second 491.33 do.

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_.

The pinion wire of clock and watch makers is well known. I am not wholly acquainted with the manner in which it is drawn: but I have made my pinion wire, of brass, in lengths of about a foot, by the Machine described below.

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._

The present description of this Machine, will consist, chiefly, of a translation from my own specification, given at Paris with the application for a _Brevet_, or Patent, obtained in the year 1795, and which is thus introduced.

“It is a well-known fact, that the longer any Boat or Vessel is, in proportion to its width, the less power it requires to convey a given load, from one place to another. But these lengths cannot be extreme, without introducing a degree of _weakness_, that would offer great danger in the use of such vessels. If then a Boat of a given volume, be divided into several long and narrow ones, the head of each adapted with a certain exactness to the stern of its forerunner, they will (with the trifling difference arising from the asperities of their surfaces) _all_ move through the water with the same ease as any single one; and carry, unitedly, the same weight as did the large Boat before it was divided. This idea constitutes the principle of my Serpentine Vessel.”

“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.”

“The fourth figure in this Plate 18, presents a general view of the vessel, comprising five articulations, (or Boats) besides the head and stern--which latter would fit each other without any intermediate parts, and form a Boat alone. Nor do these five parts by any means limit the useful number: but the Plate would not have contained more, unless on a scale too small to be distinctly understood.”

“Returning now to fig. 1, we observe the ropes _A D F H_ and _B C E G_, which are supposed fixed to the stern Boat, and carried to the capstans represented in the _Head_. These ropes consolidate the whole fabric, and act, occasionally, as a kind of _muscle_, to govern the larger evolutions. These ropes pass in the brackets placed near the joints _A B_ and _C D_, &c. being _under_ the gang ways, of which a portion appears at _S_ fig. 3, hung upon hinges, that they may be turned up when the Boat is used in narrow water.”

To the above specification were added the following remarks, which still apply to this kind of vessel, navigating on canals and inland rivers: “this vessel admits of the use of every kind of _mover_; such as men, horses, wind, or the steam engine; the latter of which I propose to apply to it in a manner equally simple and effectual; especially so as _not_ to injure the banks of any canal, &c. by acting against and disturbing the water.”

I need not repeat that this Invention dates as high as 1795: as the _Brevet_ was issued in that year. It may be added that four _parts_ of such a Boat were executed about the same time; namely, the head, the stern, and two intermediate _pieces_: making together a length of 100 feet; and these, loaded to a certain depth with stones, were drawn _up_ the river Seine by a single horse _on a trot_--which would likewise have taken place had the Boat been ten times as long; since, as before mentioned, _the resistance of this kind of vessel bears no given proportion to the Load it carries_.

OF
A MACHINE
_For destroying, or lessening Friction_.

I think it may be assumed that _friction_ is fully expressed by the word _rubbing_: and that where rubbing cannot be found, friction does not exist; especially that _kind_ of friction which opposes the motion of machinery--in which respect, the subject is chiefly thought interesting to mechanicians. It would be abandoning my intended plan in this work, to treat largely of friction, or any other accident in practical mechanics; but having already declared myself “no believer in several sorts of friction,” I am in a measure bound to introduce my description of the two following articles, by a short reference to the general subject. I offer then the following remarks, more as hints for the consideration of learned experimenters, than as conclusions sufficiently proved to become rules in practice. What I cannot help urging strongly is, that _rolling_ is not _rubbing_. If it were, I would ask in what direction it takes place? Is it in that of the plane rolled over? or in that of the radii of the rolling body? If in the former, it would indeed _glide_ over that plane, and occasion or suffer _real_ friction; but this, I think, is not pretended. If this motion is in the latter direction, (that of the radii of the rolling body) it is indefinitely _short_, compared with the progressive motion of the rolling body, so that the _power_ of the latter, to overcome any resistance in that direction, is _infinite_. Whenever therefore, in experiments of this kind, a finite resistance is perceived, it must, I should think, be ascribed to other causes, and not to _friction_. In my wheels for example, (see a former article) where there is a real and deep _penetration_ of the surfaces, I have proved that the friction between the teeth is _less_ than the distance between two of the last particles of matter: and surely, when penetratration is purposely made as small as possible (by the use of _smooth_ rollers) the friction thence arising must be still more imperceptible. But I hear it answered, that _this_ friction is both known and measured! and certain celebrated experiments are adduced to prove it. But what I most wonder at is, that a person so truly learned as the author of those experiments, should have adopted so remarkable a misnomer; in which to all appearance, indentation has usurped the name of friction. Nor let this surprise, surprise any body: nor especially, offend this learned author himself; for I am persuaded that the sole act of placing these wooden rollers, on these surfaces of wood, must indent them both sufficiently to account for all the facts observed; and still more so when loaded with weights of 100, 500, or 1000lbs. No friction, therefore, is requisite in accounting for the resistance of these rollers to horizontal motion. Nay, I submit, whether a resistance, arising from indentation alone, would not prove to be “directly as the pressures and inversely as the diameters of the rollers?” To me the subject presents itself under three aspects: either the whole indentation takes place on the rollers, when they are very soft and the _rulers_ very hard; or the latter, when _they_ are very soft and the rollers very hard: or, which is most likely, this indentation takes place on both bodies at once; so as to produce a _surface of contact_, intermediate between the _straight surface_ of the _rulers_, and the _cylindrical_ surface of the rollers. But in either case, the _place_ of resistance to horizontal motion, must be _out of the line of direction_ of the roller’s centre of gravity: and thus would the roller present more or less resistance, independently of every thing that can be called friction: and which degree of resistance will continue to exist as long as the place of contact is made to change on the rulers--for thus to change this place of contact is to renew this indentation; which process will elicit a resistance equal to what would be observed were the roller (without indentation) forced _up_ a plane, inclined to the horizon in the same angle as a line, drawn from the centre of the roller to the extreme edge of the _surface of contact_, makes with the perpendicular.

I cannot possibly enter at length into this subject, as it makes no part of my engagement to the public: but I would observe that _this_ resistance is, _a fortiori_, something besides friction, since _greasing the surfaces_ “did not cause any sensible diminution of it;” whereas it made a difference of _one half!_ in some others of the experiments alluded to.[4] Were I asked the reason, I should answer, because friction had little or nothing to do with it; and I would say further, that greasing or oiling these surfaces would most likely _increase_, instead of diminishing, their resistance to horizontal motion: namely by _softening them_, and making them more susceptible of change of figure: which opinion gathers strength from _another_ fact adduced, viz: that “rollers of elm produced a friction (or resistance) of about 2/5 _greater_ than those of lignum vitæ:” but why? because elm is relatively _soft_ and lignum vitæ hard--the only cause that appears sufficient to account for the facts observed.

[4] See Dr. Gregory’s Introduction to his Mechanics. Vol. II.

I must now leave these remarks to persons having more means and leisure than myself, to pursue the subject; wishing only, that _useful truth_ may result from them: and that this unbelief of mine “in several special kinds of friction,” may at least be found to have _some_ reasonable ground to rest upon.

But I may be opposed in some of my statements by the fact, that friction rollers, with centres, have been used with little advantage; and _often_ laid aside. This I acknowledge; and go a step further. Friction is by no means of so much consequence as it was once thought to be: and is _not_ the source of the greatest defalcations that occur in the use of power. Yet, to get rid of it, in some cases, would be of considerable importance; and the subject deserves at least the attention of every intelligent mechanician.

Those who have used friction rollers, know that it is a thing of great difficulty, to place their axes exactly parallel to _that_ which they are intended to support: and even, if rightly placed at first, that a small degree of abrasion, greater on one pivot than another, will soon destroy that parallelism; and thus introduce a _growing_ friction, capable, at length, of rendering the whole completely useless: for although the original friction is _lessened_ by being transferred to a slower-moving axis, yet the latter still resists in some degree, say 1/4 of the whole; (its pivots being 1/4 of its whole diameter) so that the cohesion, or something else, between the main shaft and the friction roller, (thus resisted) must be sufficient to _drag round_ the latter, against about 1/4 of the original friction; which in a word it cannot do without some _relative_ motion between those surfaces, the friction roller lagging behind the main shaft, until its own friction is overcome by _another_. And thus it is, that a friction roller of this kind, does not make so many revolutions on its pivots, as its diameter compared with that of the main shaft, would imply; for example, if the shaft were 4 inches in diameter and the friction roller 8 inches, the latter would _not_ complete one revolution against _two_ of the former. There would thus remain a difference spent in _real_ friction, in addition to that on the axis of the friction roller. Besides this, we have the want of parallelism above mentioned; which occasions a rubbing, in the direction of the shafts, small indeed in quantity, but for that reason very _powerful_ in bringing on a change of form, and thereby hastening the common destruction. Both these accidents, therefore, make friction rollers, in general, an unsatisfactory and perishable expedient: and it is to make them _less so_, if not entirely to cure these evils, that the two following articles are designed.

In fig. 6 of Plate 17, _A B_ is an axis which it is desirable to divest of its _friction_. To do this, as nearly as may be, I connect with it two rings of hard metal _C D_, formed as truncated cones; and under the shaft, in the same vertical plane, I place two smaller shafts _E F_, carrying on their tops, other two cones, similar to the former. The summits of each pair of cones meet of course in the points _a b_ of the main shaft; and, on the principle of bevel geer, every contiguous part of the touching cones moves with the same velocity: so that there is no sensible _rubbing_ between them--for, 1st. the pivots _c d_, are hard and pointed, and run on the hardest _steps_ that can be obtained; and, 2ndly. the tendency of the cones _u_ toward each other, is repelled without friction by the cylinders _e f_, attached to them, and which _lean_ right and left against each other, turning with the same velocity, without causing any friction, or any _creeping_, between the two pairs of cones _e C_, and _f D_. All the weight therefore, of the shaft _A B_, (which of course is kept in place in the other direction by proper side cheeks, &c.) rests on the points of the vertical shafts _E F_, accompanied by no sensible tendency of these points to quit the places assigned to them.

OF
A SECOND MACHINE,
_To avoid or diminish Friction_.

In Plate 17, figs. 7 and 8, offer a mechanism different from the preceding, though intended to produce a similar effect. Referring to _that_ cause of friction which consists in the want of parallelism between a principal shaft and its friction rollers, I here introduce a form for the latter, which admits of this consideration being in a measure neglected. These friction rollers are only portions of cylinders; and they have _no_ shafts. They turn simply on a sharp edge, placed in a prismatic box _A B_, in a well formed angle of which, they move to and fro, without _rubbing_. When at rest, these axes _D C D_, (fig. 7 and 8) are drawn against the right hand side of the box, by small weights _E_; and the shaft is carried by one or the other of them, according as they are, or are not, within reach of its radius. Thus, in the present position of the shaft, (see fig. 7) the second arc _C_ supports it, the third having fallen behind the first, so as not to be seen: and the first arc _D_ being on the point of taking up the load. In short there are _six_ spaces, either _left_ or _cut_ on the shaft, opposite the three arcs _D C D_. 1st. _one_ space, of 1/3 of the circumference, left concentric with the real centre of the shaft, opposite the first arc _D_, followed by 2/3 of a circumference _cut an eighth of an inch lower_. 2ndly. another third of a circumference opposite the second arc _C_, beginning where the first ends, and followed by 2/3 of a circumference cut an eighth of an inch lower: and 3rdly, another space of 1/3 in circumference, opposite the arc _D_, followed by a similar space of 2/3 cut an eighth of an inch lower. By these means the shaft is never without _a concentric bearing_: and the better to secure this property these arcs _left_, may be each of them _more than one third of a circumference_ in length, so as to avoid the least _drop_ at each change of roller; and even to give the shaft a support from two rollers at once, during a good part of its revolution.

In using this mechanism, the vessel _A B_, would be filled, to a certain level, with oil or water, to prevent any blow from the returning arcs--which latter might be made to fall on a lining of leather, to avoid still further all commotion: and thus, even were these rollers not placed _quite_ parallel to the shaft, this imperfection would be corrected by the frequent _renewal_ of these movements, and the consequent absence of _lateral_ friction between the arcs and the shaft. It may be observed that either of the above methods of destroying friction is not confined to the vertical direction: but may be so used as to receive the pressure caused, in any direction, by the action of a wheel or other agent. And with respect to the best use of each method respectively, I would propose the former for light and swift motions, and the latter for slow-going shafts, heavily laden: it being well understood that the shafts must be kept in their places, in the less essential directions, by proper steps, at the discretion of the person who employs these Machines.

Finally, I consider it as a matter of course, that _all_ the surfaces coming into contact in these operations, should be _as hard and impenetrable as possible_. For if, by neglecting this precaution, any _change of form_ occurred, what is said above could not be practically true: But these properties can be realized, with only those degrees of hardness that are _often_ employed in the mechanical world. Thus _a die_ of hardened steel, bears almost unimpaired, the strokes and pressure it suffers in the coining-press. A chisel, _stands_ thousands of blows and cuts hard metal, without sensibly giving way. The _knife-edges_ which carry a heavy pendulum, suffer it to vibrate many years without wearing out; and the fulcrums of scale-beams, bear enormous weights, for almost an indefinite period, without any injurious effect. I request therefore, that these facts, may be put into the scale, when my foregoing statements are _tried_: whether as applied to these anti-attrition machines, or to my late patent wheel work, _or both combined_: for I foresee the use of these friction rollers, cut into teeth on that principle, to insure the proportionality of their respective motions.

OF
AN EQUILIBRIUM COCK,
_To prevent abrasion and leakage_.

In the common form of this useful instrument, no method seems to have been devised for preventing the _plug_ from being _pressed aside_, by the weight of the liquid: which provision nevertheless would have diminished the wear and tear of the touching surfaces, and secured much longer the perfection of the instrument. This property would be particularly desirable in cocks which convey a fluid from a great height; and still more so in those used for containing steam or any other fluid under a _high_ pressure. I can hardly persuade myself that I have stood so long alone in my ideas upon this subject; but not having seen any thing _published_ on the subject, under a name implying the above mentioned property, I venture to give this as my invention--which indeed it is, even should other persons have pursued and embodied the same idea.

Fig. 9, 10 and 11 of Plate 17, represents one of the forms of this equilibrium Cock. It consists of a square plug case or chamber _a b_, with a hole _c d_ bored transversely through it, exactly across its centre: and to this chamber is fixed by the flanches _e f_, the bifurcated water-passage _g h_, forming one body at _i_. The plug of this instrument admits of various forms and proportions; of which I have shewn two in the figures 9 and 11. The first _m n_, receives the fluid through the two openings _c d_, which correspond, in one position of the plug, with the double water-passage before mentioned. And further, the plug itself is bored lengthwise in its under end _n_, so as to form the spout of the cock: or otherwise (see fig. 9) this spout is taken in a double form from the _outer_ surface of the plug at _b a_, so as to present two streams, thus producing, I think, an instrument of somewhat greater solidity. All that seems important is, that whatever be the pressure of the fluid from without, it be made _equal_ on both sides of the plug, so as to occasion no friction between it and the chamber. The principle is indeed so effectual, that one might distribute steam pressure of the greatest strength or even gunpowder pressure, without _much_ resistance to the operator, and without injuring the mechanism by oft repeated action.

OF
A MACHINE
_To communicate and suspend Motion_.

In Plate 19, figs. 3 and 4, shew this mechanism in two directions. It is composed of two wheels _C D_, cut (or cast) into teeth of a peculiar kind, that both _geer_ with one another, and at the same time, include the chord or round strap _A B_, by which they are driven. These teeth can be better represented by a figure than in words; and will I suppose be understood from figures 3 and 4: They are divided, on the rim of each wheel by a _space_ too small to admit a tooth of the other wheel: but then, _every-other_ tooth is cut away in a sloping direction on each side of the wheel, from the bottom of the tooth to its top on the opposite side: so that while these teeth are working in each other they offer two grooves, in the form of a V, which coming together surround the chord and press it in four points, either to drive the wheels by the cord, or to pull the chord by the wheels, according to the use it may be wished to make of this mechanism. In fig. 4 the cord is seen at _A B_, passing among the teeth of the wheels; and in fig. 3 it is shewn at _C_, as a mere circle, in the centre of a lozenge formed by the teeth whose points _now_ geer together. Fig. 5 is a sketch belonging to this subject, which shews something of the manner of using this _round strap_ as a _mover_: for by carrying it (either in a horizontal or vertical plane) _by a line slightly curved_, from one machine to another, it will drive them all and give the means of stopping any _one_ at pleasure. Suppose then, _A B C D_ fig. 5, to be four machines placed as above mentioned. If I wish to stop the machine _B_, I merely draw back the pressure wheel _E_, and the cord ceases to lay hold on the machine as shewn by the dotted line: but when I want to _set it on_ again, I do it by bringing back the wheel _E_ to its present position. And thus at a small expence, I could _geer_ a considerable factory, in a way which I think as durable as it appears economical. The principal objection, perhaps, is that this cord is liable to wear out soon, by such incessant action; but then the pressure on it needs not be great; and of friction properly speaking there is _very_ little: Besides which, the cords would be made of a peculiar texture, perhaps of leather, sewed edge to edge and covered like a whip, _by one of the machines I shall bring forward hereafter_.

It so happens that many of my Inventions are of a generic nature, and thus apply to cases which, appearing different, have nevertheless some common properties. The _rule of contraries_ especially applies to many of them,--of which this is an example. It offers a good method of driving a boat through a tunnel, or other confined space, either by the force of steam or any convenient power. To this end a rope laid along the side of such canal, and fixed at each end, or at several intermediate points, might be led between a pair of wheels like those above described; which duly turned, would drive the boat the distance required with the least possible expence of _power_, and _without_ the defect of agitating the water.--But I must not anticipate too much on my intended subjects.

OF
A MACHINE
_To set on, and suspend, rapid Motions_.