I have represented this Mechanism in figs. 5 and 6, Plate 31: where A B shew the crank-shaft of a steam-engine, working by means of slide-valves, the place of the excentric being at a b, in a line with the pulling-bar e f. Instead, then, of the usual connecting frame between the excentric at a b, and the valve-lever at g, I use for the above purpose, a lever e f terminated by an arc o, furnished (in the present instance) with five teeth, and connected by the joint e with the valve-lever g, in the usual manner. In the arc, which terminates this lever to the right, are the five teeth above-mentioned; and, they geer in the ten teeth of the wheel c d, which will be seen (in fig. 6) to be on the same shaft with the spur-wheel m, itself driven by the spur-wheel n, of twice the diameter. This wheel c d, therefore, makes two revolutions for one of the crank-shaft: and, supposing it to turn in the direction of the arrow, it will first of all draw upward the arc o, producing no effect on the valve-lever at g; but, when the tooth r is arrived at p (the tooth p being then arrived at the entrance of the curve q), the wheel c d will begin to draw the arc o along with it, round it’s own centre; and, the teeth of the arc being kept in it’s teeth by the similar curve q, the valve-bar will be drawn from g to h, in the course of one quarter of a revolution of the crank-shaft A B. But, now, the tooth r of the arc o will be found at s: and, therefore, the further revolution of the wheel c d will carry the arc o downward toward t, until the tooth r has reached the point t; that is, until the wheel c d has made another half-revolution, and the shaft A B another quarter; when, as before, the arc o, conducted by the curve t r, will again drive back the lever e f, till it comes into it’s present position: after which, their motions will be regularly continued. It is, then, evident, that the slide-valves are thus opened and shut, each during one quarter of a turn of the crank-shaft A B; and thus they remain stationary during another quarter, and that, in two positions of said shaft diametrically opposite to each other. And thus have we a simple mean, adaptable to every engine, of giving it much of the advantage of the hand-geering system, while preserving all that of the slide-valve principle. And, were it desired to lengthen the interregnum of the opening motion, it would be done by making the wheel c d smaller, and the ratio of n to m (see fig. 6) larger in the same proportion.

I observe here, however, that care should be taken not to make the valve motions too rapid, nor the intervals between them too long; for, I consider one of the best properties of this motion to be, that it acts like an excentric; that is, slowly at first, most rapidly afterwards, and finishes as slowly as it began; which is a precious quality in all reciprocating machines.

Finally, I would remark, that the two last rounds in the rack of the arc o might be rather larger than the intermediate ones, and turn, moreover, on pins, so as to suffer less friction when rolling on the conducting curves q and t. There might also be a plate or cap rivetted or screwed over all the teeth, so as to strengthen each one, by the force of the whole, as is shewn in fig. 1, Plate 29; from which, as before observed, this Mechanism is deduced.

The foregoing completes the Third Section of my work: and gives an article beyond the twenty, first intended:—which I thought important enough to claim this distinction. I now beg leave to add a remark or two on the text and plates of this, and the Second Part, by way of clearing up some obscurities, that might otherwise embarrass my readers.

And, first, in fig. 1, of Plate 21, the receiving vessel M, erroneously appears to form part of the wheel D E; but is, in reality, placed before it, as in all similar cases.—And, further, a small deviation of the circular lines, in Plate 22, has set the plate and it’s description, in page 192, at variance; the difference between the lines o p and C q being not “imperceptible,” as there stated. I wish, then, that the dotted radius A o p, in the said fig. 2, may be carried (or supposed) halfway between p and C. Finally, in page 200, line 8, the 24th Plate is incorrectly called the 25th.

I shall conclude this Part, by an observation or two on the reception my System of Toothed Wheels, as described in this work, has met with—not intending to speak of the local difficulties I experienced at a former period. But, here, the interests of truth force me to break silence. The necessity I stood under of bringing out this work in Parts, has, at least, had one advantage: it has given me an opportunity of watching the workings of prejudice—not to say of envy,—and thus of neutralizing, in some degree, the effects of either: from which, however, I claim nothing but the right of making my labours the more extensively useful, by making them better known. I have, then, to say that, among a few other objections to the System, this error has come from so respectable a quarter, that it would be unjust to Science, and injurious to truth, to let it pass unrefuted. It has been said, that “my wheels are a Chinese Invention;” and this proof has been adduced of it—namely, a sugar-mill, from China, having it’s cylinders fluted in a spiral direction. Now, the fact is, it would have been difficult to give a better proof that the wheels are NOT a “Chinese Invention;” for two inventions are then only alike when they produce the same effect, by similar means. But here the effects intended are totally different. A sugar-mill acts in or near the plane of the centres; and one of it’s cylinders is not intended to drive the other independently of pressure between them. This is so true, that the rollers of many sugar-mills are not fluted at all. Besides this, my wheels exert no pressure in that direction; and if they did, they would not be cog-wheels. In a word, their action is at right angles to the former, and has an object of quite a distinct nature. These, then, are by no means the same machine; and, therefore, mine is not a “Chinese Invention.”

Here, however, I beg not to be misunderstood! I should feel no regret at appearing on the mechanical stage, a few hundred years after so ancient and astonishing a nation as the Chinese! But, in this case, truth did not permit me to sanction, by my silence, this flagrant error.

Finally, an opinion exists, somewhere, that these wheels will never be generally used, from the difficulty of making them; and this opinion has been expressed, apparently, with no very amiable feeling. But, amiable or hateful, the opinion is highly erroneous! It is so far from fact, that, in a competent manufactory, they can be made more cheaply than others now are; and many persons are already calling for them from every quarter; nor is any thing wanted to insure their immediate prevalence but a common degree of commercial energy.

OF
A CUTTING ENGINE,
For large Bevil Wheels and Models, on the Patent Principle.

One of the most prominent subjects of this essay, if not the most important, is the System of Toothed Wheels, with which the second and third Parts were introduced, and which still claims a share of my readers’ attention. As hinted a few pages backward, it seems not enough for me to exhibit and describe the System, but I must defend it against repeated objections, on pain of seeing it’s utility delayed, and the public deprived of it’s real and solid advantages. I am far from wishing to impeach the motives of those who still nourish or express dissent, when they deign to bring reasons for so doing; but the mere opinion—“it won’t do”—expressed by a man of reputation, may impede, for a time, the progress of an useful discovery, and thus produce a public evil. This, then, is a result I am anxious to avert; as the present System has many points of excellence, against which no insuperable objection can be brought. Had I not declined, already, to name either the friends or enemies of the System, I might here appeal to persons who highly approve of it; and, indeed, who use it daily with manifest advantage. But, I forbear. If, by means of the Engines already given, and that I am going to offer, it is proved, that the difficulty of making these wheels is trifling, compared with their utility, one important point will be gained: I shall not hear it repeated, “that the System cannot succeed, because of the difficulties of it’s execution.”

The present Cutting Engine is shewn in figs. 1, 2, 3, of Plate 32. It’s immediate use is to form the teeth of wooden models, for casting. These are previously built as usual, and lagged with bay-wood, of sufficient thickness to furnish the teeth, and leave a small thickness of that wood behind or under them.—A B, in fig. 2, represents a wheel of this kind, ready for cutting;—mounted correctly on the centre pin C D, which latter is so formed as to be fixable in any position on the table or bench E F. Under the wheel A B, there is a kind of index a b, put upon the said centre pin C D, which, by means of the clamp and screw b c d, can be occasionally connected with the wheel A B so as to turn it, when it is itself turned by the means hereafter to be mentioned. To proceed with the description: G is a slide, moving horizontally on the bench E F, as seen at f e fig. 3; this slide being the basis of the headstock G H, which contains the perpendicular slide H I, itself the support of the cutter-frame K L, so constructed as to turn on it’s bolt above I, and take any proper position over the edge of the wheel or model A B. This slide, then, with it’s appurtenances H I K L, moves along the bench E F, as seen in fig. 3 at f e: and what gives it this motion, is, the screw g, furnished, purposely, with a left-handed thread, working in the half-nut contained in the small frame h, which contains also a jointed cap, that can be lifted off in an instant, and the screw set at liberty. Moreover, the second use of this screw g, is to be thus disengaged from it’s nut, and lifted up to about i, where it serves to push back the slide G towards the wheel, without that loss of time it would occasion if pushed back by the working of the screw. The letters M N, shew another important part of the Machine, applying to the cutting-process. It is an inclined plane, sloped to the same degree as the bottom of the teeth of the wheel. (See the line a k.) This inclined plane, then, is fastened, in any proper place, on the bench E F, by the wedge N, just like the puppet of a common turning lathe; and it passes through an opening in the slide G I, or rather suffers this to pass over it, as better seen at M, fig. 3. Furthermore, the slide I (fig. 2), after gliding down this inclined plane M G, will have to be raised between each cutting: and that is the office of the workman’s hand acting on the lever O P, through the iron frame Q M, which is shewn at fig. 3, in another direction; and marked with the letters Q l m. In fine, the slide G carries on each side of the Machine a pulling bar n, connected with the said slide, and with a smaller sliding piece o, the use of which is to hold a pin (seen in the figure, but leaving no room for a letter of indication), which turns the wheel A B, by the plate p, as the slide G recedes, and the cutter-system I K L descends on the inclined plane before-mentioned. Having thus adverted to all the important parts of the Machine, we turn to fig. 1, for the purpose of shewing what the plate (whose edge is seen at o p) means; and the effect it is intended to produce.

In that figure, let B A c be the section of any wheel it is desired to cut on this principle. The width of the face of such wheel is shewn by the line a b; and a c is called the projection of that face, on the base of the cone of which the wheel A B is a portion; it’s summit being at C. The line e d, shews one of the spiral teeth with which the wheel is to be furnished; and I make it by this uniform process: The pitch of the wheel, whatever it be, is set off from e to f: and that pitch is divided into eight parts, (shewn here as four on account of their smallness) while the width of the face f d, is divided into nine parts, shewn here (for the same reason) by four and a half divisions. This latter division is more numerous than the former, that the principle may be a little overdone; or that the teeth may overlap each other by ¹⁄₉ of the pitch: To which purpose, beginning the spiral line e d at e, I move in the second circular line from e to the second radial line C i, and draw that diagonal which forms the first part of the curved line e d. From this second point, I go to the third circular line, taking also the third radial line, and drawing the diagonal. This I do until arrived at the fifth circular line, when I find myself likewise at the fifth radial line C d f. These four spaces thus gone over, represent the eight parts into which this part of the face a b would have been divided, had the figure been larger: and there remains a small division near d, equal to one half the others, through which the curve e d is prolonged by a similar process; and this latter portion is what the successive teeth overlap each other, as before stated.

Now, it will be seen below, that the needful circular motion is given to this wheel, by a movement that takes place in a direction parallel to the base a c B of this figure. The curve e d, must, therefore, be transferred from the surface of the cone, to this base a c B. To do this, I place a point of the compasses at A, and trace, with the openings A a, A c, &c., the six quadrants included in the space a c g h, which are now the projections, on the base, of the circular lines a b f d on the surface of the said cone. Here, a slight difficulty should be obviated: strictly speaking, this projection would be horizontal, and, of course, invisible in this position of the wheel. But I have supposed the figure a c g h, turned ninety degrees downward, round the horizontal line a B, so as to make one representation suffice; and also to shew the connection of the lines a b g h, with those f d a b. The curve k l, is thus a copy of that e d, only shortened in the proportion of a b to a c—that is, of the side of the cone a C, to the half-base a A.

To secure, then, the coincidence of the pitch, as set off on the circumferences a f and a g, we must divide a similar portion of both into an equal number of parts, e f; and treat them, on the lines a c g h, as we did on those a b d f; by which means we shall get the curve k l, the projection of that e d. And this curve k l, must be made part of a plate k l m n (about ¹⁄₁₀ of an inch in thickness), the use of which is as follows:

This Plate k l m n, is no other than that marked o p in fig. 2; and it is there fixed to the index a b, directed to the central pin C D, as it is in fig. 1 to the centre A—insomuch, that the pin shewn in fig. 2 near o, acting on the sloping curve k l, will turn that index (and with it the wheel) by the very motion which draws back the slide G (fig. 2), and lets down the slide I on it’s inclined plane G M.

We may remark, lastly, that as the present Machine is adapted to large models, it is not, now, provided with a dividing-plate, although the means of so doing are self-evident. On the contrary, the division dots are seen on the edge of the wheel A B, as is likewise one dot, near b, on the clamp b c, from which a given distance is set off to each of the dots on the wheel, so as to give the pitch required. By these means, then, the wheel is divided and cut, in good, if not in exquisite divisions; and all the teeth take their shape from the Plate o p (or k l m n of fig. 1), and are thus good, in that respect also.

To recapitulate the steps of this process—The workman stands behind the Machine, near E; and, working the screw with his right hand, draws back the slide G, (the power then turning the cutter r very swiftly) by which means, the slide I glides down the inclined plane M, and the cutter, impinging on the sloping face of the wheel, cuts it to the depth r a; the shape of the tooth (by the turning of the wheel) being the spiral form e d of fig. 1. It may be added, that the lifting lever O permits this descent of the bar Q M, because it is suffered to fall lower than now represented. Thus, when the slide G is arrived near h, the tooth is finished; and the cutter leaves the wheel at a: after which, the cutter-frame and slide I K L are raised by means of the lever O—the screw g taken out of it’s steps, and the slide G pushed back by it, until the vertical slide I rests again on the inclined plane M, as it at first did. Nothing, now, remains to prepare for cutting a new tooth, but to change the division-dot, by the application of the gauge or compasses, from b to the next point on the wheel; to do which, of course, the clamp b c must be loosened and refastened by the thumb-screw d. I would just notice the 4th figure—to say, it is a sketch of one quarter of a bevil wheel; intended merely to shew the form and position of these teeth, and the general appearance of the System.

Finally, my readers will please to advert to what has been already said on the forms of these teeth, and their uses: and recollect especially what was observed on the epicycloid, as applied to them. It will easily be perceived, that to put that form on one of these teeth would be an almost hopeless attempt!—and, happily, it is not necessary. We can, however, by using the cutter r with various slopes, and going several times through each space, cut facets on the teeth, quite near enough to the theoretical form to make them work well together; and, as before observed, nothing is wanting to make the teeth perfect, but to run them together with the wheels placed in due position.

OF
A CENTRIFUGAL DASH-WHEEL,
For Bleachers, Dyers, &c.

The third figure, in Plate 33, is a sketch of the common Wash or Dash-wheel. The pieces of calico (or other goods) are put into it through the round holes, dotted in the figure; and, by the revolution of the wheel from right to left, are carried up from a to b, or nearly so; from whence they drop by their weight to about the point c, where they meet the angle formed by the circumference of the wheel and one of the four arms or partitions, by which it is divided. If the wheel go too fast, the line of falling becomes more like the curve b d, and the goods strike the circumference too high, and in an oblique direction;—whence the blow is reduced, and the washing becomes imperfect. If, on the other hand, the wheel move too slowly, the pieces slide down the ascending partition (a) before it comes to the vertex, and thus only fall from the axis to the lowest point of the wheel;—whence, also, an inefficient stroke. Thus, do these wheels require a moderate velocity: and they are reckoned to do their work best when making from 22 to 24 turns, and giving, of course, four times that number of strokes per minute.

The produce of these wheels is thus circumscribed by a natural cause that cannot be altered—namely, by the law of falling bodies; and my Invention has in view to elude the shackles which confine this process, and to produce a much greater effect in the same space,—the same time,—and with the same expence of workmanship.

To this end (see figs. 2 and 4, of the same Plate) I place two, four, or more boxes a, b, c, d, on as many wheels e f, toothed on my Patent principle; the latter, in the present case, being about two feet in diameter, and the boxes, in length, three quarters of that diameter: and of any convenient width, according to the size of the pieces. The wheels e f are mounted on the strong shafts C D, which run, below, in the wheel E; and by which, also, they are turned round the common centre, by means of the vertical wheel F. Further, in the centre, and between the wheels e f, I place the bevil wheel i, of half the diameter, in which the main shaft runs loosely, and which is itself fixed to the upper frame work, so as not to turn at all. The three Patent teeth at e i f shew that these wheels are to geer into each other on that principle: and it is likewise seen that this whole mechanism is included in a set of rails, of an octagonal form, for the purpose of preserving the men from danger, while in the act of charging and discharging the boxes. And here it is worthy of some remark, that this process must be easier, and more quickly performed, with these open boxes, than through holes made in the vertical side of a Dash-wheel, on the usual principle.

To account, now, for the sloping position of the shafts C D, and the consequent slope of the boxes, they are thus placed, in order that the goods may not drag too much on the bottoms of the boxes, when passing from one end of them to the other. Instead of this, they are, in fact, thrown, by the centrifugal force, from the inner angle h (fig. 2) to some point k up that side of the box which is then outwards; where they strike, and then fall into the contiguous angle under k, to be again projected thence, after one revolution round the common centre; for, it should here be remembered, that, by the given proportion of the wheels, the circulating wheels e f turn on their own axes exactly one half round, for every whole revolution round the common centre A B.

To elucidate this still further, I have outlined, at A fig. 1, the central wheel i, of fig. 2, together with one of the excentric wheels B, and the lines a b, a b, &c., representing the boxes, are supposed to be wires with the balls b b, &c. sliding on them, as is usual in some experiments on the Whirling Machine—(See “Ferguson’s Lectures,”) Of these wires, I have given the true directions in 12 positions of the wheel B: the epicycloid b b b, &c., shewing the steps by which the ball b is brought toward the common centre, during three quarters of the revolution; and also the position of the wire on which it slides: where it is evident that the ball b has a tendency to preserve it’s station, at the first end of the wire, until the latter takes the position b b c, when it forms (or nearly) a tangent to the curve, and is, at the same time, at right angles to the radius of motion, A b d. From this moment, then, the ball is free to leave the centre, and to fly off in a tangent with the velocity with which the curve itself is generated at that point. We might, thus, during the rest of it’s flight, seek it somewhere in the line b f g; but, as the wire continues to change it’s position, and must turn half round on it’s own axis, by the time it arrives at B b, or describes a quarter-circle on the common centre, it will again overtake the ball—and, giving it a curvilinear direction, will finally carry it to it’s other extremity, at or near the point B—where it’s motion first began: and thus shall we give as many strokes to the ball, as half turns to the wheel B; or, in other words, as many dashes to the cloth, as we give turns to the boxes, round the common centre.

By this process, then, substituted for that of the common Dash-wheel, we can increase almost indefinitely, the number of passages of the cloth from one end of the boxes to the other; and the force of the dash will be as the squares of those numbers; since (as Ferguson expresses it) “a double centrifugal force balances a quadruple power of gravity.” If, then, with four boxes we turn this machine 60 times in a minute, we shall have 240 strokes in that time, instead of about 90 given by a common Dash-wheel; and this difference might be more than doubled, if so desired: for should, then, the stroke be found too severe, the boxes might be shortened, so as to lessen it’s violence, though preserving all it’s frequency.

There are two other objects that present enough analogy to this Washing process, to be here mentioned. The first is the operation of Fulling, as applied to woollen cloths in general. That process, I fear, is not performed at present in the best manner possible; and I feel persuaded that the centrifugal motion might be applied to it with advantage—whether as to quantity of produce, or perfection of effect: and having thus said, I shall leave the idea to the riper judgment of my manufacturing readers.

The second object I shall just introduce is, that of Kneading Dough, for bread, by the same centrifugal agency. It is well known, that an ingenious baker, of Paris, invented, some time ago, a method of kneading; which consists in letting the lump of dough fall successively from the four sides of a square box, revolving on a horizontal centre. As this idea seems to have succeeded perfectly, I offer the Centrifugal System, as tending to quicken, almost indefinitely, such a process; and I particularly recommend it to the attention of Government, and of all large establishments as a mean of doing well and rapidly, by power, what is frequently done slowly and ineffectually, by the usual methods. Verbum sat.

OF
AN HYDRAULIC LAMP
For the Table.

I call this an Hydraulic Lamp, to distinguish it from the Hydrostatic Lamps, commonly so named: and I think the distinction proper, because this Machine acts in a different manner. It’s principle will be seen in a moment, by turning to the 5th figure, of Plate 33. If, there, we pour oil (or any liquid) into the bent tube A D G at A, the first effect will be to raise it to C, in the rising branch B C; and from C it will trickle down the branch C D, leaving the air, there, to occupy it’s own place. Continuing to pour, slowly, more oil into A the trickling oil in C D will ultimately fill the rising tube E D, expelling the air before it; and, now, the weight to balance the column in A B will be both the columns B C and E D; whence, of course, that column will rise as far above C as C is above B; that is, half-way between C and A. Here, there would be a small deduction to be made, if the height B C were considerable; but, as it is only supposed to be about a foot, the compression of the air in C D, &c., (being about ¹⁄₃ of a foot or ¹⁄₉₀ of an atmosphere) may be neglected. Continuing, then, to pour oil into A, we shall again fill, not the descending tube E F, but the rising tube F G; whose column will thus be to be added to those B C and E D; so that now the column A B will rise to A, and there abide, as long as the mouth G is kept full, or nearly so.

The above is the principle of the Lamp announced in the title; whose effect depends, then, on the number of bends made in the tube A D G, which number (whatever be the form) it would be well to make rather greater than smaller, as the height B C, &c., might be so much the less, compared with the whole height of the column A B; by which means, also, a smaller difference in the level of the column below, would return the oil necessary for the consumption of the wick above.

I have given this idea what I think a better form in fig. 6. Instead of the bent tube A G, of fig. 5, this form supposes a series of air-tight cups, embracing each other; one half of them with their mouths opening upwards, and the other half with theirs opening downwards. They are shewn, by a section only, in this fig. 6; where a b c, c b a, present the under cups, forming one piece with the outer surface of the bottom vessel d a c, c a e: and, while speaking of this part of the Machine, I would just indicate it’s cover d e f g put on like the lid of a snuff-box, and carrying a case or tube f g, the use of which will be mentioned in a moment. To proceed, then, the upper vessel is shewn by the edges of it’s cups seen immediately over the figures 1 2 3, 4 5 6, placed between the letters a b c, &c.—These inverted cups make also one body with the moveable cover shewn between d and e, and to which is soldered the tube h i—which, sliding in the case f g, keeps this inverted vessel steady. Where note: that there is an inner tube soldered into the tube h i, through which alone the oil rises, and which can hardly be made too small, since it has only to supply the consumption of a lamp—namely, a few ounces of oil in a whole evening. We may, finally, take notice of the weight placed under f g, upon the said inverted vessel, and which helps to counterpoise the oil in the rising tube h i; which tube, as before observed, may be as many times higher than the distance a d or e a, as there are rising columns between the cups a b c and those 1 2 3, &c.

I am not wholly prepared to say what portion of the oil it might be best to re-elevate by the pressure of the aforesaid weight f g; but, if it were a considerable part of that contained in the central compartment c c, that column would be shortened in proportion; and the reservoir at i would, doubtless, feel the want of it to preserve it’s level. I think, therefore, it might be well to use, below, a cup or two more than sufficient, so as to raise the main column higher than actually wanted; and to coerce this rising tendency, by a small stop-cock in the rising branch, to be gently opened at the will of the person using the lamp. I cannot say I have exhausted this subject; either in these respects, or as to it’s technical capabilities. But I have fully tried this method of raising oil above it’s level; and used, for some time, a lamp made on this principle, and which is still in my possession: and, at some future time, I intend to bring forward an Hydraulic Machine, founded on the same principles.

OF
A MECHANICAL ESSAY,
To derive Power from expanding Metals.

Supposing, then (Plate 34, fig. 1), the tubes A B C to be 20 feet long, their whole expansion will be 0.26 hundredths of an inch. But, as the tubes are placed in the figure, the half tubes A D B D act together on the sphere D, and, both together, drive it in the direction E D, more than as the above expansion, in the proportion of the line E D to that A D. Taking, then, one half only of the above expansion = 0.13 hundredths of an inch, that must be augmented in the ratio of the sine of 60 degrees to radius, or in that of A D to E D. I, therefore, multiply this decimal 0.13 by the fraction ¹⁰⁰⁰⁄₈₆₆, which gives 1300 to be divided by 866, or very nearly 0.15 for the expansion, in the direction E D, occasioned by the two half bars A D B D: and the same is true at the other angles F and G.

Again, to find the expansion (and contraction) of the bars a b c, we must compute their length as compared with the half tubes above-mentioned; and that length is to 10 feet (the half tube A D or B D) as 866 is to 1000 = 11.54 nearly: the expansion of which is thus found:—if 10 feet expand 0.13, what will 11.54?—Answer, 0.15. Now, as the machine acts by the heating of the pipes A B C simultaneously with the cooling of the bars a b c, we must add the former expansion to this contraction, which gives us 0.30, or three tenths of an inch for this combined effect at the three angles of the Machine. And, supposing, now, any pair of bars to act directly against each other, as at H I K; and that, further, the bars be stretched until the angle with the horizon be only 2 degrees, then the vertical motion at I will be to the horizontal (arising from the expansion aforesaid) as 1000 to 35, the sine of 2; that will be, in round numbers, 28 times as great, or 28 times three tenths of an inch = 8.4 inches, which is the stroke of this Machine in these dimensions.

In this calculation, I have not forgotten that the vertical and horizontal motions are nearer alike, when the bars are not drawn so tight at K H; that is, when the joint I is lowered. But it is equally true that, when the joint I rises still more, the difference between these motions is still greater; so that, as a medium effect, I think we may reckon on an eight-inch stroke in the present case.

The question now recurs, of what strength are these strokes? Are they sufficiently powerful to produce a useful effect with so short a motion? This I cannot say from experience; but, from the known strength of iron and steel, their power, in these dimensions, must be very great. A few more observations may occur in the course of the enlarged description we shall give of the Machine itself.

A B C are three pipes of cast iron, well turned at the end, and having conical points of iron, well steeled, let into them, so as to have no tendency to bend. a b c are three steel bars, placed in troughs, so as to be heated or cooled by water poured into the latter. Or, these troughs may be exchanged for tubes, to admit heated or cooled air, according to the means used to cause these mutations. In a word, although I have represented these bars as contained in troughs, I intend to finish my description, on the supposition that they are tubes, because I intend to suppose the Machine worked by air instead of water.

To proceed: at d is an opening under the tube B, into which air enters, and C is an opening on the top of the tube which emits the same air, the three pipes being made to communicate by means of a short junction-pipe at each of the angles D and G. Here, then, the fire-place f g, fig. 2, must be noticed: the use of which is both to heat and cool the Machine; and the following are the means:—This little instrument contains fire in it’s middle compartment, and that fire draws air into the part f, and drives it out of the part g. It also turns on a centre-pin, seen in the figure. This chaffing-dish, then, is placed at i d, and there serves a double purpose. When it’s pipe g conveys heated air into the pipes B A C (and out at C), it heats those pipes and expands them; but, at the same time, the pipe f of this instrument draws cold air through the three tubes a b c, in which are the steel bars that require to be contracted: both which operations conduce alike to the above-described effect. By these means, the weight w is raised, and (for example) water sucked into the pump X. But, turning the fire-place half round, we reverse this effect. The hot air is now drawn, out of the pipes A B C, and cold air drawn through them, by which they are cooled; while the hot air, from the fire, is thrown through the pipe g into the tubes a b c, and passing through the chimneys k l, there heat the bars and expand them,—both which operations concur in letting down the weight E, and thus, in forcing the water of the pump to whatever destination was previously assigned it.

OF
A MACHINE,
For Making Laces, Covering Whips, &c.