STEAM-Engine, is the name of a machine which derives its moving power from the elasticity and condensibility of the steam of boiling water. It is the most valuable present which the arts of life have ever received from the philosopher. The mariner's compass, the telescope, gunpowder, and other most useful servants to human weakness and ingenuity, were the productions of chance, and we do not exactly know to whom we are indebted for them; but the steam-engine was, in the very beginning, the result of reflection, and the production of a very ingenious mind; and every improvement it has received, and every alteration in its construction and principles, were also the results of philosophical study.

The steam-engine was beyond all doubt invented by the marquis of Worcester during the reign of Charles II. This nobleman published in 1663 a small book entitled A CENTURY OF INVENTIONS; giving some obscure and enigmatical account of a hundred discoveries or contrivances of his own, which he extols as of great importance to the public. He appears to have been a person of much knowledge and great ingenuity: but his description or accounts of these inventions seem not so much intended to instruct the public, as to raise wonder; and his encomiums on their utility and importance

(b) We earnestly recommend this subject to the consideration of the philosopher. The laws which regulate the formation of elastic vapour, or the general phenomena which it exhibits, give us that link which connects chemistry with mechanical philosophy. Here we see chemical affinities and mechanical forces set in immediate opposition to each other, and the one made the indication, characteristic, and measure of the other. We have not the least doubt that they make but one science, the Science of Universal Mechanics; nor do we despair of seeing the phenomena of solution, precipitation, crystallization, fermentation, nay animal and vegetable secretion and assimilation, successfully investigated, as cases of local motion, and explained by the agency of central forces. Some thing of this kind, and that not inconsiderable, was done when Dr Cullen first showed how the double affinities might be illustrated by the assistance of numbers. Dr Black gave to this hint (for it was little more) that elegant precision which characterizes all his views. Mr Kirwan has greatly promoted this study by his numerous and ingenious examples of its application; and the most valuable passages of the writings of Mr Lavoisier, are those where he traces with logical precision the balancings of force which appear in the chemical phenomena. It is from the familiar balancings and consequent measurements, which may be observed and obtained in the present case, that we are to hope for admission into this almost unbounded science of contemplation. We have another link equally interesting and promising, viz. the production of heat by friction. This also highly deserves the consideration of the mathematical philosopher. ance are to a great degree extravagant, resembling more the puff of an advertising tradesman than the puristic communications of a gentleman. The marquis of Worcester was indeed a projector, and very importunate and mysterious withal in his applications for public encouragement. His account, however, of the steam-engine, although by no means fit to give us any distinct notions of its structure and operation, is exact as far as it goes, agreeing precisely with what we now know of the subject. It is No 68. of his inventions. His words are as follow: "This admirable method which I propose of raising water by the force of fire has no bounds if the vessels be strong enough: for I have taken a cannon, and having filled it three fourths full of water, and flint up its muzzle and touch-hole, and exposed it to the fire for 24 hours, it burst with a great explosion. Having afterwards discovered a method of fortifying vessels internally, and combined them in such a way that they filled and acted alternately, I have made the water spout in an uninterrupted stream 40 feet high; and one vessel of rarefied water raised 40 of cold water. The person who conducted the operation had nothing to do but turn two cocks; so that one vessel of water being consumed, another begins to force, and then to fill itself with cold water, and so on in succession."

It does not appear that the noble inventor could ever interest the public by these accounts. His character as a projector, and the many failures which persons of this turn of mind daily experience, probably prejudiced people against him, and prevented all attention to his projects. It was not till towards the end of the century, when experimental philosophy was prosecuted all over Europe with uncommon ardour, that these notions again engaged attention. Captain Savary, a person also of great ingenuity and ardent mind, saw the reality and practicability of the marquis of Worcester's project. He knew the great expansive power of steam, and had discovered the inconceivable rapidity with which it is reconverted into water by cold; and he soon contrived a machine for raising water, in which both of these properties were employed. He says, that it was entirely his own invention. Dr Defagulliers infers that he only copied the marquis's invention, and charges him with gross plagiarism, and with having bought up and burned the copies of the marquis's book, in order to secure the honour of the discovery to himself. This is a very grievous charge, and should have been substantiated by very distinct evidence. Defagulliers produces none such; and he was much too late to know what happened at that time. The argument which he gives is a very foolish one, and gave him no title to consider Savary's experiment as a falsehood; for it might have happened precisely as Savary relates, and not as it happened to Defagulliers. The fact is, that Savary obtained his patent of invention after a hearing of objections, among which the discovery of the marquis of Worcester was not mentioned: and it is certain that the account given in the Century of Inventions could instruct no person who was not sufficiently acquainted with the properties of steam to be able to invent the machine himself.

Captain Savary obtained his patent after having actually erected several machines, of which he gave a description in a book entitled The Miner's Friend, published in 1696, and in another work published in 1699. Much about this time Dr Papin, a Frenchman and fellow of the Royal Society, invented a method of dissolving bones and other animal solids in water, by confining them in clole vessels, which he called DIGESTERS, so as to acquire a great degree of heat. For it must be observed in this place, that it had been discovered long before (in 1684) by Dr Hooke, the most inquisitive experimental philosopher of that inquisitive age, that water could not be made to acquire above a certain temperature in the open air; and that as soon as it begins to boil, its temperature remains fixed, and an increase of heat only produces a more violent ebullition, and a more rapid waste. But Papin's experiments made the elastic power of steam very familiar to him: and when he left England and settled as professor of mathematics at Marpurg, he made many awkward attempts to employ this force in mechanics, and even for raising water. It appears that he had made experiments with this view in 1698, by order of Charles, landgrave of Hesse. For this reason the French affect to consider him as the inventor of the steam-engine. He indeed published some account of his invention in 1707; but he acknowledges that Captain Savary had also, and without any communication with him, invented the same thing. Whoever will take the trouble of looking at the description which he has given of these inventions, which are to be seen in the Acta Eruditorum Lipsiae, and in Leupold's Theatrum Machinarum, will see that they are most awkward, absurd, and impracticable. His conceptions of natural operations were always vague and imperfect, and he was neither philosopher nor mechanician.

We are thus anxious about the claim of those gentlemen, because a most respectable French author, Mr Bofut, says in his Hydrodynamique, that the first notion of the steam-engine was certainly owing to Dr Papin, who had not only invented the digester, but had in 1695 published a little performance describing a machine for raising water, in which the pistons are moved by the vapour of boiling water alternately dilated and condensed. Now the fact is, that Papin's first publication was in 1707, and his piston is nothing more than a float on the surface of the water, to prevent the waste of steam by condensation; and the return of the piston is not produced, as in the steam engine, by the condensation of the steam, but by admitting the air and a column of water to press it back into its place. The whole contrivance is so awkward, and so unlike any distinct notions of the subject, that it cannot do credit to any person. We may add, that much about the fame time Mr Amontons contrived a very ingenious but intricate machine, which he called ton's fire-a fire-wheel. It consisted of a number of buckets placed in the circumference of a wheel, and communicating with each other by very intricate circuitous passages. One part of this circumference was exposed to the heat of a furnace, and another to a stream or cistern of cold water. The communications were so disposed, that the steam produced in the buckets on one side of the wheel drove the water into buckets on the other side, so that one side of the wheel was always much heavier than the other; and it must therefore turn round, and may execute some work. The death of the inventor, and the intricacy of the machine, caused it to be neglected. Another member of the Parisian academy of sciences (Mr Delalandes) also presented to the academy a project of a steam-wheel, where the impulsive force of the va- pour was employed; but it met with no encouragement. The English engineers had by this time so much improved Savary's first invention that it supplanted all others. We have therefore no hesitation in giving the honour of the first and complete invention to the marquis of Worcester; and we are not disposed to refuse Captain Savary's claim to originality as to the construction of the machine, and even think it probable that his own experiments made him see the whole independent of the marquis's account.

Captain Savary's engine, as improved and simplified by himself is as follows.

A (fig. 6.) represents a strong copper boiler properly built up in a furnace. There proceeds from its top a large steam-pipe B, which enters into the top of another strong vessel R called the receiver. This pipe has a cock at C called the steam cock. In the bottom of the receiver is a pipe F, which communicates sidewise with the rising pipe KGH. The lower end H of this pipe is immersed in the water of the pit or well, and its upper part K opens into the cistern into which the water is to be delivered. Immediately below the pipe of communication F there is a valve G, opening when pressed from below, and shutting when pressed downwards. A similar valve is placed at I, immediately above the pipe of communication. Lastly, there is a pipe ED which branches off from the rising pipe, and enters into the top of the receiver. This pipe has a cock D called the injection-cock. The mouth of the pipe ED has a nozzle f pierced with small holes, pointing from a centre in every direction. The keys of the two cocks C and D are united, and the handle g h is called the regulator.

Let the regulator be so placed that the steam-cock C is open and the injection-cock D is shut; put water into the boiler A, and make it boil strongly. The steam coming from it will enter the receiver, and gradually warm it, much steam being condensed in producing this effect. When it has been warmed so as to condense no more, the steam proceeds into the rising pipe; the valve G remains shut by its weight; the steam lifts the valve I, and gets into the rising pipe, and gradually warms it. When the workman feels this to be the case, or hears the rattling of the valve I, he immediately turns the steam-cock so as to shut it, the injection-cock still remaining shut (at least we may suppose this for the present). The apparatus must now cool, and the steam in the receiver collapses into water. There is nothing now to balance the pressure of the atmosphere; the valve I remains shut by its weight; but the air incumbent on the water in the pit presses up this water through the suction-pipe HG, and causes it to lift the valve G, and flow into the receiver R, and fill it to the top, if not more than 20 or 25 feet above the surface of the pit water.

The steam cock is now opened. The steam which, during the cooling of the receiver, has been accumulating in the boiler, and acquiring a great elasticity by the action of the fire, now rushes in with great violence, and, pressing on the surface of the water in the receiver, causes it to shut the valve G and open the valve I by its weight alone, and it now flows into the rising pipe, and would stand on a level if the elasticity of the steam were no more than what would balance the atmospheric pressure. But it is much more than this, and therefore it presses the water out of the receiver into the rising pipe, and will even cause it to come out at K, if the elasticity of the steam is sufficiently great. In order to ensure this, the boiler has another pipe in its top, covered with a safety-valve V, which is kept down by a weight W suspended on a fleelyard LM. This weight is so adjusted that its pressure on the safety-valve is somewhat greater than the pressure of a column of water VK as high as the point of discharge K. The fire is so regulated that the steam is always issuing a little by the loaded valve V. The workman keeps the steam-valve open till he hears the valve I rattle. This tells him that the water is all forced out of the receiver, and that the steam is now following it. He immediately turns the regulator which turns the steam-cock, and now, for the first time, opens the injection-cock. The cold water trickles at first through the holes of the nozzle f, and falling down through the steam, begins to condense it; and then its elasticity being less than the prelude of the water in the pipe KEFDf, the cold water spouts in all directions through the nozzle, and, quick as thought, produces a complete condensation. The valve G now opens again by the prelude of the atmosphere on the water of the pit, and the receiver is soon filled with cold water. The injection-cock is now shut, and the steam-cock opened, and the whole operation is now repeated; and so on continually.

This is the simple account of the process, and will serve to give the reader an introductory notion of the operation; but a more minute attention must be paid to many particulars before we can see the properties and defects of this ingenious machine.

The water is driven along the rising pipe by the elasticity of the steam. This must in the boiler, and this must in every part of the machine, exert a prelude on every inch square inch of the vessels equal to that of the upright column of water. Suppose the water to be raised 100 feet, about 25 of this may be done in the suction-pipe; that is, the upper part of the receiver may be about 25 feet above the surface of the pit-water. The remaining 75 must be done by forcing, and every square inch of the boiler will be squeezed out by a prelude of more than 30 pounds. This very moderate height therefore requires very strong vessels; and the marquis of Worcester was well aware of the danger of their bursting. A copper boiler of six feet diameter must be nine-tenths of an inch thick to be just in equilibrium with this prelude: and the soldered joint will not be able to withstand it, especially in the high temperature to which the water must be heated in order to produce steam of sufficient elasticity. By consulting the table of the elasticity of steam deduced from our experiments mentioned in the preceding article, we see that this temperature must be at least 283° of Fahrenheit's thermometer. In this heat soft folder is just ready to melt, and has no tenacity; even spelter folder is considerably weakened by it. Accordingly, in a machine erected by Dr Desaguliers, the workman having loaded the safety-valve a little more than usual to make the engine work more briskly, the boiler burst with a dreadful explosion, and blew up the furnace and adjoining parts of the building as if it had been gunpowder. Mr Savary succeeded pretty well in raising moderate quantities of water to small heights, but could make nothing of deep mines. Many attempts were made, on the marquis's quis's principle, to strengthen the vessels from within by radiated bars and by hoops, but in vain. Very small boilers or evaporators were then tried, kept red hot, or nearly so, and supplied with a slender stream of water trickling into them; but this afforded no opportunity of making a collection of steam during the refrigeration of the receiver, so as to have a magazine of steam in readiness for the next forcing operation; and the working of such machines was always an employment of great danger and anxiety.

The only situation in which this machine could be employed with perfect safety, and with some effect, was where the whole lift did not exceed 30 or 35 feet. In this case the greatest part of it was performed by the suction-pipe, and a very manageable pressure was sufficient for the rest. Several machines of this kind were erected in England about the beginning of this century. A very large one was erected at a salt-work in the south of France. Here the water was to be raised no more than 18 feet. The receiver was capacious, and it was occasionally supplied with steam from a small salt-pan constructed on purpose with a cover. The entry of the steam into the receiver merely allowed the water to run out of it by a large valve, which was opened by the hand, and the condensation was produced by the help of a small forcing pump also worked by the hand. In so particular a situation as this (and many such may occur in the endless variety of human wants), this is a very powerful engine; and having few moving and rubbing parts, it must be of great durability. This circumstance has occasioned much attention to be given to this first form of the engine, even long after it was supplanted by those of a much better construction. A very ingenious attempt was made very lately to adopt this construction to the uses of the miners. The whole depth of the pit was divided into lifts of 15 feet, in the same manner as is frequently done in pump-machines. In each of these was a suction-pipe 14 feet long, having above it a small receiver like R, about a foot high, and its capacity somewhat greater than that of the pipe. This receiver had a valve at the head of the suction-pipe, and another opening outwards into the little cistern, into which the next suction-pipe above dipped to take in water. Each of these receivers sent up a pipe from its top, which all met in the cover of a large vessel above ground, which was of double the capacity of all the receivers and pipes. This vessel was close on all sides. Another vessel of equal capacity was placed immediately above it, with a pipe from its bottom passing through the cover of the lower vessel and reaching near to its bottom. This upper vessel communicates with the boiler, and constitutes the receiver of the steam-engine. The operation is as follows: The lower vessel is full of water. Steam is admitted into the upper vessel, which expels the air by a valve, and fills the vessel. It is then condensed by cold water. The pressure of the atmosphere would cause it to enter by all the suction-pipes of the different lifts, and press on the surface of the water in the lower receiver, and force it into the upper one. But because each suction-pipe dips in a cistern of water, the air presses this water before it, raises it into each of the little receivers which it fills, and allows the spring of the air (which was formerly in them, but which now passes up into the lower receiver) to force the water out of the lower receiver into the upper one. When this has been completed, the steam is again admitted into the upper receiver. This allows the water to run back into the lower receiver, and the air returns into the small receivers in the pit, and allows the water to run out of each into its proper cistern. By this means the water of each pipe has been raised 15 feet. The operation may thus be repeated continually.

The contrivance is ingenious, and similar to those which are to be met with in the hydraulics of Schottus, Sturmius, and other German writers. But the operation must be exceedingly slow; and we imagine that the expense of steam must be great, because it must fill a very large and very cold vessel, which must waste a great portion of it by condensation. We see by some late publications of the very ingenious Mr Blackey, that he is still attempting to maintain the reputation of this machine by some contrivances of this kind; but we imagine that they will be ineffectual, except in some very particular situations.

For the great defect of the machine, even when we occasions can secure it against all risk of bursting, is the prodigious waste of steam, and consequently of fuel. Daily experience shows, that a few scattered drops of cold water are sufficient for producing an almost instantaneous condensation of a great quantity of steam. Therefore when the steam is admitted into the receiver of Savary's engine, and comes into contact with the cold top and cold water, it is condensed with great rapidity; and the water does not begin to subside till its surface has become so hot that it condenses no more steam. It may now begin to yield to the pressure of the incumbent steam; but as soon as it descends a little, more of the cold surface of the receiver comes into contact with the steam, and condenses more of it, and the water can descend no farther till this addition of cold surface is heated up to the state of evaporation. This rapid condensation goes on all the while the water is descending. By some experiments frequently repeated by the writer of this article, it appears that no less than \( \frac{1}{2} \)ths of the whole steam is uselessly condensed in this manner, and not more than \( \frac{1}{2} \)th is employed in allowing the water to descend by its own weight; and he has reason to think that the portion thus wasted will be considerably greater, if the steam be employed to force the water out of the receiver to any considerable height.

Observe, too, that all this waste must be repeated in every succeeding stroke; for the whole receiver must be cooled again in order to fill itself with water.

Many attempts have been made to diminish this waste; but all to little purpose, because the very filling of the receiver with cold water occasions its sides to condense a prodigious quantity of steam in the succeeding stroke. Mr Blackey has attempted to lessen this by using two receivers. In the first was oil; and into this only the steam was admitted. This oil passed to and fro between the two receivers, and never touched the water except in a small surface. But this hardly produced a sensible diminution of the waste: for it must now be observed, that there is a necessity for the first cylinder's being cooled to a considerable degree below the boiling point; otherwise, though it will condense much steam, and allow the water to rise into the receiver, there will be a great diminution of the height of suction, unless the vessel be much cooled. This appears plainly by inspecting the table of elasticity. Thus, if the vessel be cooled no lower than 180°, we should lose one half of the pressure of the atmosphere; if cooled to 120, we should still lose \( \frac{1}{4} \)th. The inspection of this table is of great use for understanding and improving this noble machine; and without a constant recollection of the elasticity of steam corresponding to its actual heat, we shall never have a notion of the niceties of its operation.

The rapidity with which the steam is condensed is really astonishing. Experiments have been made on steam-vessels of fix feet in diameter and seven feet high; and it has been found, that about four ounces of water, as warm as the human blood, will produce a complete condensation in less than a second; that is, will produce all the condensation that it is capable of producing, leaving an elasticity about one-fifth of the elasticity of the air. In another experiment with the same steam-vessel, no cold water was allowed to get into it, but it was made to communicate by a long pipe four inches in diameter with another vessel immersed in cold water. The condensation was so rapid that the time could not be measured: it certainly did not exceed half a second. Now this condensation was performed by a very trifling surface of contact. Perhaps we may explain it a little in this way: When a mass of steam, in immediate contact with the cold water, is condensed, it leaves a void, into which the adjoining steam instantly expands; and by this very expansion its capacity for heat is increased, or it grows cold, that is, abstracts the heat from the steam situated immediately beyond it. And in this expansion and refrigeration it is itself partly condensed or converted into water, and leaves a void, into which the circumjacent steam immediately expands, and produces the same effect on the steam beyond it. And thus it may happen that the abstraction of a small quantity of heat from an inconsiderable mass of steam may produce a condensation which may be very extensive. Did we know the change made in the capacity of steam for heat by a given change of bulk, we should be able to tell exactly what would be the effect of this local actual condensation. But experiment has not as yet given us any precise notions on this subject. We think that this rapid condensation to a great distance by a very moderate actual abstraction of heat is a proof that the capacity of steam for heat is prodigiously increased by expansion. We say a very moderate actual abstraction of heat, because very little heat is necessary to raise four ounces of blood-warm water to a boiling temperature, which will unfit it for condensing steam. The remarkable phenomenon of snow and ice produced in the Hungarian machine, when the air condensed in the receiver is allowed to blow through the cock (see PNEUMATICS), shows this to be the case in moist air, that is, in air holding water in a state of chemical solution. We see something very like it in a thunder-storm. A small black cloud sometimes appears in a particular spot, and in a very few seconds spreads over many hundred acres of sky, that is, a precipitation of water goes on with that rapid diffusion. We imagine that this increase of capacity or demand for heat, and the condensation that must ensue if this demand is not supplied, is much more remarkable in pure watery vapours, and that this is a capital distinction of their constitution from vapours dissolved in air (A).

The reader must now be so well acquainted with what passes in the steam-vessel, and with the exterior results from it, as readily to comprehend the propriety of the changes which we shall now describe as having been made in the construction and principle of the steam-engine.

Of all places in England the tin-mines of Cornwall attempted flood most in need of hydraulic assistance; and Mr Sa, to improve vary was much engaged in projects for draining them, the steam- by his steam-engine. This made its construction and principles well known among the machinists and engine- engineers of that neighbourhood. Among these were a Mr Newcomen, an ironmonger or blacksmith, and Mr Cawley a glazier at Dartmouth in Devonshire, who had dabbled much with this machine. Newcomen was a person of some reading, and was in particular acquainted with the person, writings, and projects of his countryman Dr Hooke. There are to be found among Hooke's papers, in the possession of the Royal Society, some notes of observations, for the use of Newcomen his countryman, on Papin's boasted method of transmitting to a great distance the action of a mill by means of pipes. Papin's project was to employ the mill to work two air-pumps of great diameter. The cylinders of these pumps were to communicate by means of pipes with equal cylinders furnished with pistons, in the neighbourhood of a distant mine. These pistons were to be connected, by means of levers, with the piston-rods of the mine. Therefore, when the piston of the air-pump at the mill was drawn up by the mill, the corresponding piston at the side of the mine would be pressed down by the atmosphere, and thus would raise the piston-rod in the mine, and draw the water. It would appear from these notes, that Dr Hooke had dissuaded Mr Newcomen from erecting a machine on this principle, of which he had exposed the fallacy in several discourses before the Royal Society. One passage is remarkable. "Could he (meaning Papin) make a speedy vacuum under your second piston, your work is done."

It is highly probable that, in the course of this speculation, it occurred to Mr Newcomen that the vacuum he so much wanted might be produced by steam, and that this gave rise to his new principle and construction of the steam-engine. The specific desideratum was in Newcomen's mind; and therefore, when Savary's engine appeared, and became known in his neighbourhood many years after, he would readily catch at the help which it promised.

Savary, however, claims the invention as his own; but Switzer, who was personally acquainted with both, is positive that Newcomen was the inventor. By his principles (as a Quaker) being averse from contention, he was contented to share the honour and the profits with Savary, whose acquaintance at court enabled him to procure the patent in 1705, in which all the three were associated. Posterity has done justice to the modest inventor, and the machine is universally called NEWCOMEN'S

(A) But if it has been found that the condensation requires more cold water than what is allowed above, and it is suspected that the rapidity of condensing a large volume of steam by the cold surface of a vessel is overrated. MEN'S ENGINE. Its principle and mode of operation may be clearly conceived as follows.

Let A (fig. 7.) represent a great boiler properly built in a furnace. At a small height above it is a cylinder CBBC of metal, bored very truly and smoothly. The boiler communicates with this cylinder by means of the throat or steam-pipe NQ. The lower aperture of this pipe is shut by the plate N, which is ground very flat, so as to apply very accurately to the whole circumference of the orifice. This plate is called the regulator or steam-cock, and it turns horizontally round an axis b a which passes through the top of the boiler, and is nicely fitted to the socket, like the key of a cock, by grinding. The upper end of this axis is furnished with a handle b T.

A piston P is suspended in this cylinder, and made air-tight by a packing of leather or soft rope, well filled with tallow; and, for greater security, a small quantity of water is kept above the piston. The piston-rod PD is suspended by a chain which is fixed to the upper extremity F of the arched head FD of the great lever or WORKING BEAM HK, which turns on the gudgeon O. There is a similar arched head EG at the other end of the beam. To its upper extremity E is fixed a chain carrying the pump-rod XL, which raises the water from the mine. The load on this end of the beam is made to exceed considerably the weight of the piston P at the other extremity.

At some small height above the top of the cylinder is a cistern W, called the INJECTION CISTERN. From this descends the INJECTION PIPE ZSR, which enters the cylinder through its bottom, and terminates in a small hole R, or sometimes in a nozzle pierced with many smaller holes diverging from a centre in all directions. This pipe has at S a cock called the INJECTION COCK, fitted with a handle V.

At the opposite side of the cylinder, a little above its bottom, there is a lateral pipe, turning upwards at the extremity, and there covered by a clack-valve f, called the SHIFTING VALVE, which has a little dish round it to hold water for keeping it air-tight.

There proceeds also from the bottom of the cylinder a pipe d e g h (passing behind the boiler), of which the lower end is turned upwards, and is covered with a valve h. This part is immersed in a cistern of water Y, called the HOT WELL, and the pipe itself is called the REDUCTION PIPE. Lastly, the boiler is furnished with a safety-valve called the PUPPET CLACK (which is not represented in this sketch for want of room), in the same manner as Savary's engine. This valve is generally loaded with one or two pounds on the square inch, so that it allows the steam to escape when its elasticity is one-tenth greater than that of common air. Thus all risk of bursting the boiler is avoided, and the pressure outwards is very moderate; to allo is the heat. For, by inspecting the table of vaporous elasticity, we see that the heat corresponding to 32 inches of elasticity is only about 216° degrees of Fahrenheit's thermometer.

These are all the essential parts of the engine, and are here drawn in the most simple form, till our knowledge of their particular offices shall show the propriety of the peculiar forms which are given to them. Let us now see how the machine is put in motion, and what is the nature of its work.

The water in the boiler being supposed to be in a state of strong ebullition, and the steam issuing by the safety-valve, let us consider the machine in a state of rest, having both the steam-cock and injection cock shut. The resting position or attitude of the machine must be such as appears in sketch, the pump rods preponderating, and the great piston being drawn up to the top of the cylinder. Now open the steam cock by turning the handle T of the regulator. The steam from the work-boiler will immediately rush in, and flying all over the cylinder, will mix with the air. Much of it will be condensed by the cold surface of the cylinder and piston, and the water produced from it will trickle down the sides, and run off by the eduction-pipe. This condensation and waste of steam will continue till the whole cylinder and piston be made as hot as boiling water. When this happens, the steam will begin to open the shifting-valve f, and issue through the pipe; slowly at first and very cloudy, being mixed with much air. The blast at f will grow stronger by degrees, and more transparent, having already carried off the greatest part of the common air which filled the cylinder. We supposed that the air was boiling briskly, so that the steam was issuing by the safety-valve which is in the top of the boiler, and through every crevice. The opening of the steam-cock puts an end to this at once, and it has sometimes happened that the cold cylinder abstracts the steam from the boiler with such astonishing rapidity, that the prelude of the atmosphere has burst up the bottom of the boiler. We may here mention an accident of which we were witnesses, which also shows the immense rapidity of the condensation. The boiler was in a frail shed at the side of the engine-house; a flood of snow from the top of the house fell down and broke through the roof of the shed, and was scattered over the head of the boiler, which was of an oblong or oval shape. In an instant the sides of it were squeezed together by the pressure of the atmosphere.

When the manager of the engine perceives that not only the blast at the shifting valve is strong and steady, but that the boiler is now fully supplied with steam of a proper strength, appearing by the renewal of the discharge at the safety-valve, he shuts the steam-cock, and opens the injection-cock S by turning its handle V. The pressure of the column of water in the injection-pipe ZS immediately forces some water through the spout R. This coming in contact with the pure vapour which now fills the cylinder, condenses it, and thus makes a partial void, into which the more distant steam immediately expands, and by expanding collapses (as has been already observed). What remains in the cylinder no longer balances the atmospherical preasure on the surface of the water in the injection cistern, and therefore the water spouts rapidly through the hole R by the joint action of the column ZS, and the unbalanced preasure of the atmosphere; at the same time the shifting-valve f, and the eduction-valve h, are shut by the unbalanced pressure of the atmosphere. The velocity of the injection water must therefore rapidly increase, and the jet will dash (if single) against the bottom of the piston, and be scattered through the whole capacity of the cylinder. In a very short space of time, therefore, the condensation of the steam becomes universal, and the elasticity of what remains is almost nothing. The whole pressure of the atmosphere is exerted in the upper surface of the piston, while there is hardly any on its underside. Therefore, if the load on the outer end E of the working beam is inferior to this pressure, it must yield to it. The piston P must descend, and the pump piston L must ascend, bringing along with it the water of the mine, and the motion must continue till the great piston reaches the bottom of the cylinder; for it is not like the motion which would take place in a cylinder of air rarefied to the same degree. In this last case, the impelling force would be continually diminished, because the capacity of the cylinder is diminished by the descent of the piston, and the air in it is continually becoming more dense and elastic. The piston would stop at a certain height, where the elasticity of the included air, together with the load at E, would balance the atmospherical pressure on the piston. But when the contents of the cylinder are pure vapour, and the continued stream of injected cold water keeps down its temperature to the same pitch as at the beginning, the elasticity of the remaining steam can never increase by the descent of the piston, nor exceed what corresponds to this temperature. The impelling or accelerating force therefore remains the same, and the descent of the piston will be uniformly accelerated, if there is not an increase of resistance arising from the nature of the work performed by the other end of the beam. This circumstance will come under consideration afterwards, and we need not attend to it at present. It is enough for our present purpose to see, that if the cylinder has been completely purged of common air before the steam-cock was shut, and if none has entered since, the piston will descend to the very bottom of the cylinder. And this may be frequently observed in a good steam-engine, where every part is air-tight. It sometimes happens, by the pit-pump drawing air, or some part of the communication between the two strains giving way, that the piston comes down with such violence as to knock out the bottom of the cylinder with the blow.

The only observation which remains to be made on the motion of the piston in descending is, that it does not begin at the instant the injection is made. The piston was kept at the top by the preponderancy of the outer end of the working beam, and it must remain there till the difference between the elasticity of the steam below it and the pressure of the atmosphere exceeds this preponderancy. There must therefore be a small space of time between the beginning of the condensation and the beginning of the motion. This is very small, not exceeding the third or the fourth part of a second; but it may be very distinctly observed by an attentive spectator. He will see, that the instant the injection cock is opened, the cylinder will sensibly rise upwards a little by the pressure of the air on its bottom. Its whole weight is not nearly equal to this pressure; and instead of its being necessary to support it by a strong floor, we must keep it down by strong joints loaded by heavy walls. It is usual to frame these joints into the posts which carry the axis of the working-beam, and are therefore loaded with the whole strain of the machine. This rising of the cylinder shows the instantaneous commencement of the condensation; and it is not till after this has been distinctly observed that the piston is seen to start, and begin to descend.

When the manager sees the piston as low as he thinks proper, he shuts the injection-cock, and opens the steam-cock. The steam has been accumulating above the water in the boiler during the whole time of the piston's descent, and is now rushing violently through the puppet clack. The moment, therefore, that the steam-cock is opened, it rushes violently into the cylinder, having an elasticity greater than that of the air. It therefore immediately blows open the snifing valve, and allows (at least) the water which had come in by the former injection, and what arose from the condensed steam, to descend by its own weight through the eduction pipe d e g h to open the valve h, and to run out into the hot well. And we must easily see that this water is boiling hot; for while lying in the bottom of the cylinder, it will condense steam till it acquires this temperature, and therefore cannot run down till it condenses no more. There is still a waste of steam at its first admission, in order to heat the inside of the cylinder and the injected water to the boiling temperature: but the space being small, and the whole being already very warm, this is very soon done; and when things are properly constructed, little more steam is wanted than what will warm the cylinder; for the eduction pipe receives the injection water even during the descent of the piston, and it is therefore removed pretty much out of the way of the steam.

This first puff of the entering steam is of great service; it drives out of the cylinder the vapour which it finds there. This is seldom pure watery vapour: all pure water contains a quantity of air in a state of chemical union. The union is but feeble, and a boiling heat is sufficient for disengaging the greatest part of it by increasing its elasticity. It may also be disengaged by simply removing the external pressure of the atmosphere. This is clearly seen when we expose a glass of water in an exhausted receiver. Therefore the small space below the piston contains watery vapour mixed with all the air which had been disengaged from the water in the boiler by ebullition, and all that was separated from the injection water by the diminution of external pressures. All this is blown out of the cylinder by the first puff of steam. We may observe in this place, that waters differ exceedingly in the quantity of air which they hold in a state of solution. All spring water contains much of it: and water newly brought up from deep mines contains a great deal more, because the solution was aided in these situations by great pressures. Such waters sparkle when poured into a glass. It is therefore of great consequence to the good performance of a steam-engine to use water containing little air, both in the boiler and in the injection-cistern. The water of running brooks is preferable to all others, and the freer it is from any saline impregnation it generally contains steam-leafs air. Such engines as are so unfortunately situated, that they are obliged to employ the very water which they have brought up from great depths, are found contain greatly inferior in their performance to others. The little air collected below the piston greatly diminishes the accelerating force, and the expulsion of such a quantity requires a long-continued blast of the best steam at the beginning of every stroke. It is advisable to keep such water in a large shallow pond for a long while before using it.

Let us now consider the state of the piston. It is evident that it will start or begin to rise the moment piston rises, the steam-cock is opened; for at that instant the excess of atmospheric pressure, by which it was kept down in opposition to the preponderancy of the outer end of the beam, is diminished. The piston is therefore dragged upwards, and it will rise even although the steam which is admitted be not so elastic as common air. Suppose the mercury in the barometer to stand at 30 inches, and that the preponderancy at the outer end of the beam is \( \frac{1}{4} \)th of the pressure of the air on the piston, the piston will not rise if the elasticity of the steam is not equal to 30—\( \frac{1}{8} \), that is, to 26.7 inches nearly; but if it is just this quantity, the piston will rise as fast as this steam can be supplied through the steam-pipe, and the velocity of its ascent depends entirely on the velocity of this supply. This observation is of great importance; and it does not seem to have occurred to the mathematicians, who have paid most attention to the mechanism of the motion of this engine. In the mean time, we may clearly see that the entry of the steam depends chiefly on the counter weight at E: for suppose there was none, steam no stronger than air would not enter the cylinder at all; and if the steam be stronger, it will enter only by the excess of its strength. Writers on the steam-engine (and even some of great reputation) familiarly speak of the steam giving the piston a push: But this is scarcely possible. During the rise of the piston the snifting valve is never observed to blow; and we have not heard any well-attested accounts of the piston-chains ever being slackened by the upward pressure of the steam, even at the very beginning of the stroke. During the rising of the piston the steam is (according to the common conception and manner of speaking) sucked in, in the same way that air is sucked into a common syringe or pump when we draw up the piston; for in the steam-engine the piston is really drawn up by the counter weight. But it is still more sucked in, and requires a more copious supply, for another reason. As the piston descended only in consequence of the inside of the cylinder's being sufficiently cooled to condense the steam, this cooled surface must again be presented to the steam during the rise of the piston, and must condense steam a second time. The piston cannot rise another inch till the part of the cylinder which the piston has already quitted has been warmed up to the boiling point, and steam must be expended in this warming. The inner surface of the cylinder is not only of the heat of boiling water while the piston rises, but is also perfectly dry; for the film of water left on it by the ascending piston must be completely evaporated, otherwise it will be condensing steam. That the quantity thus wasted is considerable, appears by the experiments of Mr Beighton. He found that five pints of water were boiled off in a minute, and produced 16 strokes of an engine whose cylinder contained 113 gallons of 282 inches each; and he thence concluded that steam was 2886 times rarer than water. But in no experiment made with scrupulous care on the expansion of boiling water does it appear that the density of steam exceeds \( \frac{1}{10,000} \)th of the density of water. Defaguiers says that it is above 14,000 times rarer than water. We have frequently attempted to measure the weight of steam which filled a very light vessel, which held 1,260 grains of water, and found it always less than one grain; so that we have no doubt of its being much more than 10,000 times rarer than water. This being the case, we may safely suppose that the number of gallons of steam, instead of being 16 times 113, were nearly five times as much; and that only \( \frac{5}{6} \)th was employed in allowing the piston to rise, and the remaining \( \frac{1}{6} \)ths were employed to warm the cylinder. But no distinct experiment shews so great an expansion of water when converted into steam at 212°. Mr Watt never found it under the pressure of the air more than 1800 times rarer than water.

The moving force during the ascent of the piston must be considered as resulting chiefly, if not solely, from the preponderating weight of the pit piston-rods. The office of this is to return the steam-piston to the top of the cylinder, where it may again be pressed down by the air, and make another working stroke by raising the pump-rods. But the counter-weight at E has another service to perform in this use of the engine; namely, to return the pump pistons into their places at the bottom of their respective working barrels, in order that they also may make a working stroke. This requires force independent of the friction and inertia of the moving parts; for each piston must be pushed down through the water in the barrel, which must rise through the piston with a velocity whose proportion to the velocity of the piston is the same with that of the bulk of the piston to the bulk of the perforation through which the water rises through the piston. It is enough at present to mention this in general terms: we shall consider it more particularly afterwards, when we come to calculate the performance of the engine, and to deduce from our acquired knowledge maxims of construction and improvement.

From this general consideration of the ascent of the piston, we may see that the motion differs greatly from the descent. It can hardly be supposed to accelerate, even if the steam in the cylinder were in a moment annihilated. For the resistance to the descent of the piston is the same with the weight of the column of water, which would cause it to flow through the box of the pump piston with the velocity with which it really rises through it, and must therefore increase as the square of that velocity increases; that is, as the square of the velocity of the piston increases. Independent of friction, therefore, the velocity of descent through the water must soon become a maximum, and the motion become uniform. We shall see by and by, that in such a pump as is generally used this will happen in less than the tenth part of a second. The friction of the pump will diminish this velocity a little, and retard the time of its attaining uniformity. But, on the other hand, the supply of steam which is necessary for this motion, being susceptible of no acceleration from its previous motion, and depending entirely on the briskness of the ebullition, an almost instantaneous stop is put to acceleration.

Accordingly, any person who observes with attention the working of a steam-engine, will see that the rise of the piston and descent of the pump-rods is extremely uniform, whereas the working stroke is very sensibly accelerated. Before quitting this part of the subject, and after leaving it should afterwards escape our recollection, we may observe, that the counter-weight is different during the two motions of the pump-rods. While the machine is making a working stroke, it is lifting not only the co-pump-rods. hunn of water in the pump, but the absolute weight of the pistons and piston-rods also; but while the pump-rods are descending, there is a diminution of the counter-weight by the whole weight lost by the immersion of the rod in water. The wooden rods which are generally used, soaked in water, and joined by iron straps, are heavier, and but a little heavier, than water, and they are generally about one-third of the bulk of the water in the pumps.

These two motions complete the period of the operation; and the whole may be repeated by shutting the steam-cock and opening the injection-cock whenever the piston has attained the proper height. We have been very minute in our attention to the different circumstances, that the reader may have a distinct notion of the state of the moving forces in every period of the operation. It is by no means sufficient that we know in general that the injection of cold water makes a void which allows the air to press down the piston, and that the readmission of the steam allows the piston to rise again. This lumping and flowery way of viewing it has long prevented even the philosopher from seeing the defects of the construction, and the methods of removing them.

We now see the great difference between Savary's and Newcomen's engine in respect of principle. Savary's was really an engine which raised water by the force of steam; but Newcomen's raises water entirely by the pressure of the atmosphere, and steam is employed merely as the most expeditious method of producing a void, into which the atmospheric pressure may impel the first mover of his machine. The elasticity of the steam is not the first mover.

We see also the great superiority of this new machine. We have no need of steam of great and dangerous elasticity; and we operate by means of very moderate heats, and consequently with much smaller quantities of fuel; and there is no bounds to the power of this machine. How deep ever a mine may be, a cylinder may be employed of such dimensions that the pressure of the air on its piston may exceed in any degree the weight of the column of water to be raised. And lastly, this form of the machine renders it applicable to almost every mechanical purpose; because a skillful mechanic can readily find a method of converting the reciprocating motion of the working beam into a motion of any kind which may suit his purpose. Savary's engine could hardly admit of such an immediate application, and seems almost restricted to raising water.

Inventions improve by degrees. This engine was first offered to the public in 1705. But many difficulties occurred in the execution, which were removed one by one; and it was not till 1712 that the engine seemed to give confidence in its efficacy. The most exact and unremitting attention of the manager was required, to the precise moment of opening and shutting the cocks; and neglect might frequently be ruinous, by beating out the bottom of the cylinder, or allowing the piston to be wholly drawn out of it. Stops were contrived to prevent both of these accidents; then strings were used to connect the handles of the cocks with the beam, so that they should be turned whenever it was in certain positions. These were gradually changed and improved into detents and catches of different shapes; at last, in 1717, Mr Beighton, a very ingenious and well-informed artist, simplified the whole of these subordinate movements, and brought the machine into the form in which it has continued, without the smallest material change, to the present day. We shall now describe one of these improved engines, copying almost exactly the drawings and description given by Boffet in his Hydrodynamique; these being by far the most accurate and perspicuous of any that have been published.

Fig. 8. No 1. is a perspective view of the boiler cylinder, and all the parts necessary for turning the cock. Fig. 8. No 2. is a vertical section of the same; and the Beighton fame pieces of both are marked with the fame letters of reference.

The rod X of the piston P is suspended from the arch of the working-beam, as was represented in the preceding sketch (fig. 7.). An upright bar of timber FG is also seen hanging by a chain. This is suspended from a concentric arch of the beam, as may be seen also in the sketch at φλ. The bar is called the plug-beam; and it must rise and fall with the piston, but with a slower motion. The use of this plug-beam is to give motion to the different pieces which turn the cocks.

The steam-pipe K is of one piece with the bottom of the cylinder, and rises within it an inch or two, to prevent any of the cold injection water from falling into the boiler. The lower extremity Z of the steam-pipe penetrates the head of the boiler, projecting a little way. A flat plate of brass, in shape resembling a racket or battledore, called the regulator, applies itself exactly to the whole circumference of the steam-pipe, and completely excludes the steam from the cylinder. Being moveable round an upright axis, which is represented by the dotted lines at the side of the steam-pipe in the profile, it may be turned aside by the handle i, No 1. The profile shows in the section of this plate a protuberance in the middle. This rests on a strong flat spring, which is fixed below it athwart the mouth of the steam-pipe. This spring presses it strongly towards the steam-pipe, causing it to apply very close; and this knob slides along the spring, while the regulator turns to the right or left.

We have said that the injection-water is furnished from a cistern placed above the cylinder. When the cistern cannot be supplied by pipes from some more elevated source, its water is raised by the machine itself. A small lifting pump i k (fig. 7.), called the jack-head or jacquette, is worked by a rod γ, suspended from a concentric arch μ near the outer end of the working beam. This forces a small portion of the pit water along the rising pipe i LM into the injection cistern.

In fig. 8. No 1. and 2. the letters QM 3' represent the pipe which brings down the water from the injection cistern. This pipe has a cock at R to open or shut the passage of this water. It spouts through the jet 3', and dashing against the bottom of the piston, it is dispersed into drops, and scattered through the whole capacity of the cylinder, so as to produce a rapid condensation of the steam.

An upright post A may be observed in the perspective view of the cylinder, &c. This supports one end B of a horizontal iron axis BC. The end C is supported by a similar post, of which the place only is marked by the dotted lines A, that the pieces connected ted with this axis may not be hid by it. A kind of stirrup \(a b c d\) hangs from this axis, supported by the hooks \(a\) and \(d\). This stirrup is crossed near the bottom by a round bolt or bar \(e\), which passes through the eyes or rings that are at the ends of the horizontal fork \(h f g\), whose long tail \(h\) is double, receiving between its branches the handle \(i\) of the regulator. It is plain from this construction, that when the stirrup is made to vibrate round the horizontal axis \(BC\), on which it hangs freely by its hooks, the bolt \(e\) must pull or push the long fork \(h f g\) backwards and forwards horizontally, and by so doing will move the regulator round its axis by means of the handle \(i\). Both the tail of the fork and the handle of the regulator are pierced with several holes, and a pin is put through them which unites them by a joint. The motion of the handle may be increased or diminished by choosing for the joint a hole near to the axis or remote from it; and the exact position at which the regulator is to stop on both sides is determined by pins fixed in the horizontal bar on which the end of the handle appears to rest.

This alternate motion of the regulator to the right and left is produced as follows: There is fixed to the axis \(BC\) a piece of iron \(o k l\), called the \(Y\), on account of its resemblance to that letter of the alphabet inverted. The stalk \(o\) carries a heavy lump \(p\) of lead or iron; and a long leather strap \(q p r\) is fastened to \(p\) by the middle, and the two ends are fastened to the beam above it, in such a manner that the lump may be alternately caught and held up to the right and left of the perpendicular. By adjusting the length of the two parts of the strap, the \(Y\) may be stopped in any desired position. The two claws \(k\) and \(l\) spread out from each other, and from the line of the stalk, and they are of such length as to reach the horizontal bolt \(e\), which crosses the stirrup below, but not to reach the bottom of the fork \(h f g\). Now suppose the stirrup hanging perpendicularly, and the stalk of the \(Y\) also held perpendicular; carry it a little outward from the cylinder, and then let it go. It will tumble farther out by its weight, without affecting the stirrup till the claw \(l\) strikes on the horizontal bolt \(e\), and then it pushes the stirrup and the fork towards the cylinder, and opens the regulator. It sets it in motion with a smart jerk, which is an effectual way of overcoming the cohesion and friction of the regulator with the mouth of the steam-pipe. This push is adjusted to a proper length by the strap \(q p\), which stops the \(Y\) when it has gone far enough. If we now take hold of the stalk of the \(Y\), and move it up to the perpendicular, the width between its claws is such as to permit this motion, and something more, without affecting the stirrup. But when pulled still nearer to the cylinder, it tumbles towards it by its own weight, and then the claw \(k\) strikes the bolt \(e\), and drives the stirrup and fork in the opposite direction, till the lump \(p\) is caught by the strap \(r p\), now stretched to its full length, while \(q p\) hangs slack. Thus by the motion of the \(Y\) the regulator is opened and shut. Let us now see how the motion of the \(Y\) is produced by the machine itself. To the horizontal axis \(BC\) are attached two spanners or handles \(m\) and \(n\). The spanner \(m\) passes through a long slit in the plug-beam, and is at liberty to move upwards or downwards by its motion round the axis \(BC\). A pin \(\pi\) which goes through the plug-beam catches hold of \(m\) when the beam rises along with the piston; and the pin is so placed, that when the beam is within an inch or two of its highest rise, the pin has lifted \(m\) and thrown the stalk of the \(Y\) past the perpendicular. It therefore tumbles over with great force, and gives a smart blow to the fork, and immediately shuts the regulator. By this motion the spanner \(m\) is removed out of the neighbourhood of the plug-beam. But the spanner \(n\), moving along with it in the same direction, now comes into the way of the pins of the plug-beam. Therefore, when the piston descends again by the condensation of the steam in the cylinder, a pin marked \(\varphi\) in the side of the plug-beam catches hold of the tail of the spanner \(n\), and by pressing it down raises the lump on the stalk of the \(Y\) till it passes the perpendicular, and it then falls down, outwards from the cylinder, and the claw \(l\) again drives the fork in the direction \(h i\), and opens the steam valve. This opening and shutting of the steam valve is executed in the precise moment that is proper, by placing the pins \(\pi\) and \(\varphi\) at a proper height of the plug-beam. For this reason, it is pierced through with a great number of holes, that the places of these pins may be varied at pleasure. This, and a proper curvature of the spanners \(m\) and \(n\), make the adjustment as nice as we please.

The injection-cock \(R\) is managed in a similar manner. On its key may be observed a forked arm \(s t\), like a crab's claw; at a little distance above it is the gudgeon or axis \(u\) of a piece \(y u z\), called the hammer or the F, from its resemblance to that letter. It has a lump of metal \(y\) at one end, and a spear \(u s\) projects from its middle, and passes between the claws \(s\) and \(t\) of the arm of the injection-cock. The hammer \(y\) is held up by a notch in the under side of a wooden lever \(DE\), moveable round the centre \(D\), and supported at a proper height by a spring \(E\), made fast to the joist above it.

Suppose the injection-cock shut, and the hammer in the position represented in the figure. A pin \(\beta\) of the plug-frame rises along with the piston, and catching hold of the detent \(DE\), raises it, and disengages the hammer \(y\) from its notch. This immediately falls down, and strikes a board \(L\) put in the way to stop it. The spear \(u s\) takes hold of the claw \(t\), and forces it aside towards \(x\), and opens the injection-cock. The piston immediately descends, and along with it the plug-frame. During its descent the pin \(\beta\) meets with the tail \(u z\) of the hammer, which is now raised considerably above the level, and brings it down along with it, raising the lump \(y\), and gradually shutting the injection-cock, because the spear takes hold of the claw \(s\) of its arm. When the beam has come to its lowest situation, the hammer is again engaged in the notch of the detent \(DE\), and supported by it till the piston again reaches the top of the cylinder.

In this manner the motions of the injection-cock are also adjusted to the precise moment that is proper for them. The different pins are so placed in the plug-frame, that the steam-cock may be completely shut before the injection-cock is opened. The inherent motion of the machine will give a small addition to the ascent of the piston without expending steam all the while; and by leaving the steam rather less elastic than before, the subsequent descent of the piston is promoted. There was a considerable propriety in the gradual shutting ting of the injection-cock. For after the first dash of the cold water against the bottom of the piston, the condensation is nearly complete, and very little more water is needed; but a continual accession of some is absolutely necessary for completing the condensation, as the capacity of the cylinder diminishes, and the water warms which is already injected.

In this manner the motion of the machine will be repeated as long as there is a supply of steam from the boiler, and of water from the injection cistern, and a discharge procured for what has been injected. We proceed to consider how far these conditions also are provided by the machine itself.

The injection cistern is supplied with water by the jackhead pump, as we have already observed. From this source all the parts of the machine receive their respective supplies. In the first place, a small branch 13, 13, is taken off from the injection pipe immediately below the cistern, and conducted to the top of the cylinder, where it is furnished with a cock. The spout is so adjusted, that no more runs from it than what will keep a constant supply of a foot of water above the piston to keep it tight. Every time the piston comes to the top of the cylinder, it brings this water along with it, and the surplus of its evaporation and leakage runs off by a waste pipe 14, 14. This water necessarily becomes almost boiling hot, and it was thought proper to employ its surplus for supplying the waste of the boiler. This was accordingly practised for some time. But Mr Beighton improved this economical thought, by supplying the boiler from the education-pipe, 2, 2, the water of which must be still hotter than that above the piston. This contrivance required attention to many circumstances, which the reader will understand by considering the perspective and profile. The education-pipe comes out of the bottom of the cylinder at 1 with a perpendicular part, which bends sidewise below, and is flat at the extremity 1. A deep cup 5 communicates with it, holding a metal valve nicely fitted to it by grinding, like the key of a cock. To secure its being always air-tight, a flender stream of water trickles into it from a branch 6 of the waste-pipe from the top of the cylinder. The education-pipe branches off at 2, and goes down to the hot well, where it turns up, and is covered with a valve. In the perspective view may be observed an upright pipe 4, 4, which goes through the head of the boiler, and reaches to within a few inches of its bottom. This pipe is called the feeder, and rises about three or four feet above the boiler. It is open at both ends, and has a branch 3, 3, communicating with the bottom of the cup 5, immediately above the metal valve, and also a few inches below the level of the entry 2 of the education-pipe. This communicating branch has a cock by which its passage may be diminished at pleasure. Now suppose the steam in the boiler to be very strong, it will cause the boiling water to rise in the feeding-pipe above 3, and coming along this branch, to rise also in the cup 5, and run over. But the height of this cup above the surface of the water in the boiler is such, that the steam is never strong enough to produce this effect. Therefore, on the contrary, any water that may be in the cup 5 will run off by the branch 3, 3, and go down into the boiler by the feeding-pipe.

These things being understood, let us suppose a quantity of injected water lying at the bottom of the cylinder. It will run into the education-pipe, fill the crooked branch 1, 1, and open the valve in the bottom of the cup (its weight being supported by a wire hanger from a flender spring), and it will fill the cup to the level of the entry 2 of the education pipe, and will then triviant flow along 3, 3, and supply the boiler by the feeder 4, 4. What more water runs in at 1 will now go along the education-pipe 2, 2, to the hot well. By properly adjusting the cock on the branch 3, 3, the boiler may be supplied as fast as the waste in steam requires. This is a most ingenious contrivance, and does great honour to Mr Beighton. It is not, however, of much importance. The small quantity which the boiler requires may be immediately taken even from a cold cistern, without sensibly diminishing the production of steam: for the quantity of heat necessary for raising the sensible heat of cold water to the boiling temperature is small, when compared with the quantity of heat which must then be combined with it in order to convert the water into steam. For the heat expended in boiling off a cubic foot of water is about fix times as much as would bring it to a boiling heat from the temperature of 55°. No difference can be observed in the performance of such engines, and of those which have their boilers supplied from a brook. It has, however, the advantage of being purged of air; and when an engine must derive all its supplies from pit water, the water from the education-pipe is vastly preferable to that from the top of the cylinder.

We may here observe, that many writers (among them the Abbé Bosfut), in their descriptions of the steam engine, have drawn the branch of communication 3, 3, from the feeding-pipe to a part of the crooked pipe 1, 1, lying below the valve in the cup 5. But this is quite erroneous; for, in this case, when the injection is made into the cylinder, and a vacuum produced, the water from the boiler would immediately rush up through the pipes 4, 3, and spout up into the cylinder: so would the external air coming in at the top of the feeder.

This contrivance has also enabled us to form some judgment of the internal state of the engine during the performance. Mr Beighton paid a minute attention to the situation of the water in the feeders and education-pipe of an engine, which seems to have been one of the best which has yet been erected. It was lifting a co. of the culm of water whose weight was four-sevenths of the pressure of the air on its piston, and made 16 strokes, of six feet each, in a minute. This is acknowledged by all to be a very great performance of an engine of this form. He concluded that the elasticity of the steam in the cylinder was never more than one-tenth greater or less than the elasticity of the air. The water in the feeder never rose more than three feet and a half above the surface of the boiling water, even though it was now lighter by \( \frac{1}{7} \)th than cold water. The education pipe was only four feet and a half long (vertically), and yet it always discharged the injection water completely, and allowed some to pass into the feeder. This could not be if the steam was much more than one-tenth weaker than air. By grasping this pipe in his hand during the rise of the piston, he could guess very well whereabouts the surface of the hot water in it rested during the motion, and he never found it supported so high as four feet. Therefore the steam in the cylinder had at least eight-ninths of the elasticity of the air. Mr Buat, in his examination of an engine which is erected at Montrelaix, in France, by an English engineer, and has always been considered as the pattern in that country, finds it necessary to suppose a much greater variation in the strength of the steam, and says, that it must have been one-fifth stronger and one-fifth weaker than common air. But this engine has not been nearly so perfect. Its lift was not more than one-half the pressure of the atmosphere, and it made but nine strokes in a minute.—At W is a valve covering the mouth of a small pipe, and surrounded with a cup containing water to keep it air-tight. This allows the air to escape which had been extricated from the water of last injection. It is driven out by the first strong puff of steam which is admitted into the cylinder, and makes a noise in its exit. The valve is therefore called the snifting-valve.

To finish our description, we observe, that besides the safety valve 9 (called the PUPPET CLACK), which is loaded with about 3 pounds on the square inch (though the engine will work very well with a load of 1 or 2 pounds), there is another DISCHARGER 10,10, having a clack at its extremity supported by a cord. Its use is to discharge the steam without doors, when the machine gives over working. There is also a pipe SI near the bottom of the boiler, by which it may be emptied when it needs repairs or cleansing.

There are two small pipes 11,11, and 12,12, with cocks called GAGE PIPES. The first descends to within two inches of the surface of the water in the boiler, and the second goes about 2 inches below that surface. If both cocks emit steam, the water is too low, and requires a recruit. If neither give steam, it is too high, and there is not sufficient room above it for a collection of steam. Lastly, there is a filling pipe Q, by which the boiler may be filled when the machine is to be let to work.

The engine has continued in this form for many years. The only remarkable change introduced has been the manner of placing the boiler. It is no longer placed below the cylinder, but at one side, and the steam is introduced by a pipe from the top of the boiler into a flat box immediately below the cylinder. The use of this box is merely to lodge the regulator, and give room for its motions. This has been a very considerable improvement. It has greatly reduced the height of the building. This was formerly a tower. The wall which supported the beam could hardly be built with sufficient strength for withstanding the violent shocks which were repeated without ceasing; and the buildings seldom lasted more than a very few years. But the boiler is now set up in an adjoining shed, and the gudgeons of the main beam rest on the top of upright posts, which are framed into the joists which support the cylinder. Thus the whole moving parts of the machine are contained in one compact frame of carpentry, and have little or no connection with the flight walls of the building, which is merely a cage to hold the machine, and protect it from the weather.

It is now time to inquire what is to be expected from this machine, and to ascertain the most advantageous proportion between the moving power and the load that is to be laid on the machine.

It may be considered as a great pulley, and is indeed sometimes so constructed, the arches at the ends of the working beam being completed to a circle. It must be unequally loaded that it may move. It is loaded, during the working stroke, by the pressure of the atmosphere on the piston side, and by the column of water to be raised and the pump-gear on the pump side.—During the returning stroke it is loaded, on the piston side, by a small part of the atmospheric pressure, and on the pump side by the pump-gear acting as a counter weight. The load during the working stroke must therefore consist of the column of water to be raised and this counter weight. The performance of the machine is to be measured only by the quantity of water raised in a given time to a given height. It varies, therefore, in the joint proportion of the weight of the column of water in the pumps, and the number of strokes made by the machine in a minute. Each stroke consists of two parts, which we have called the working and the returning stroke. It does not, therefore, depend simply on the velocity of the working stroke and the quantity of water raised by it. If these were all that is to be attended to, we know that the weight of the column of water should be nearly \( \frac{1}{7} \)ths of the pressure of the atmosphere, this being the proportion which gives the maximum in the common pulley. But the time of the returning stroke is a necessary part of the whole time elapsed, and therefore the velocity of the returning stroke equally merits attention. This is regulated by the counter weight. The number of strokes per minute does not give an immediate proof of the goodness of the engine. A small load of water and a great counter weight will ensure this, because these conditions will produce a brisk motion in both directions.—The proper adjustment of the pressure of the atmosphere on the piston, the column of water to be raised, and the counter weight, is a problem of very great difficulty; and mathematicians have not turned much of their attention to the subject, although it is certainly the most interesting question that practical mechanics affords them.

Mr Boffut has solved it very shortly and simply, upon Mr Boffut's this supposition, that the working and returning stroke, solution, should be made in equal times. This, indeed, is generally aimed at in the erection of these machines, and they are not reckoned to be well arranged if it be otherwise. We doubt of the propriety of the maxim. Supposing, however, this condition for the present, we may compute the loadings of the two ends of the beam as follows. Let a be the length of the inner arm of the working beam, or that by which the great piston is supported. Let b be the outer arm carrying the pump rods, and let W be a weight equivalent to all the load which is laid on the machine. Let c^a be the area of the piston ; let H be the height of a column of water having c^a for its base, and being equal in weight to the pressure exerted by the steam on the under side of the piston ; and let h be the pressure of the atmosphere on the same area, or the height of a column of water of equal weight. It is evident that both strokes will be performed in equal times, if \( h\ c^a - W\ b \) be equal to \( (h-H)\ c^a + W\ b \). The first of these quantities is the energy of the machine during the working stroke, and the second expresses the similar energy during the returning stroke. This equation gives us \( W = \frac{2h c^a - H c^a}{2b} = \frac{(2h - H) c^a}{2b} \). If we suppose the arms of the lever equal and H = h, we have \( W = c^2 \frac{h}{2} \); that is, the whole weight of the outer end of the beam should be half the pressure of the air on the great piston. This is nearly the usual practice; and the engineers express it by saying, that the engine is loaded with seven or eight pounds on the square inch. This has been found to be nearly the most advantageous load. This way of expressing the matter would do well enough, if the maxim were not founded on erroneous notions, which hinder us from seeing the state of the machine, and the circumstances on which its improvement depends. The piston bears a pressure of 15 pounds, it is said, on the square inch, if the vacuum below it be perfect; but as this is far from being the case, we must not load it above the power of its vacuum, which very little exceeds eight pounds. But this is very far from the truth. When the cylinder is tight, the vacuum is not more than \( \frac{7}{8} \)th deficient, when the cylinder is cooled by the injection to the degree that is every day practicable, and the piston really bears during its descent a pressure very near to 14 pounds on the inch. The load must be diminished, not on account of the imperfect vacuum, but to give the machine a reasonable motion. We must consider not only the moving force, but also the quantity of matter to be put in motion. This is so great in the steam-engine, that even if it were balanced, that is, if there were suspended on the piston arm a weight equal to the whole column of water and the counter weight, the full pressure of the atmosphere on the steam piston would not make it move twice as fast as it does.

This equation by Mr Boffut is moreover essentially faulty in another respect. The W in the first member is not the same with the W in the second. In the first it is the column of water to be raised, together with the counter weight. In the second it is the counter weight only. Nor is the quantity H the same in both cases, as is most evident. The proper equation for ensuring the equal duration of the two strokes may be had in the following manner. Let it be determined by experiment what portion of the atmospheric pressure is exerted on the great piston during its descent. This depends on the remaining elasticity of the steam. Suppose it \( \frac{9}{10} \)ths: this we may express by a h, a being \( \frac{9}{10} \)ths. Let it also be determined by experiment what portion of the atmospheric pressure on the piston remains unbalanced by the steam below it during its ascent. Suppose this \( \frac{7}{10} \)th, we may express this by b h. Then let W be the weight of the column of water to be raised, and c the counter weight. Then, if the arms of the beam are equal, we have the energy during the working stroke \( = a h - W - c \), and during the returning stroke it is \( = c - b h \). Therefore \( c - b h = a h - W - c \); and \( c = \frac{h(a+b)-W}{2} \); which, on the above supposition of the values of a and b, gives us \( c = \frac{h-W}{2} \). We shall make some use of this equation afterwards; but it affords us no information concerning the most advantageous proportion of h and W, which is the material point.

We must consider this matter in another way: And that we may not involve ourselves in unnecessary difficulties, let us make the case as simple as possible, and suppose the arms of the working-beam to be of equal length.

We shall first consider the adjustment of things at the outer end of the beam.

Since the sole use of the steam is to give room for the adjustment of the atmospheric pressure by its rapid condensation, it is admitted into the cylinder only to allow things at the piston to rise again, but without giving it any impulsion of the pulse. The pump-rods must therefore be returned to beam con the bottom of the working barrels, by means of a preponderancy at the outer end of the beam. It may be the weight of the pump-rods themselves, or may be considered as making part of this weight. A weight at the end of the beam will not operate on the rods which are suspended there by chains, and it must therefore be attached to the rods themselves, but above their respective pump-barrels, so that it may not lose part of its efficacy by immersion in the water. We may consider the whole under the notion of the pump-gear, and call it p. Its office is to depress the pump-rods with sufficient velocity, by overcoming the resistances arising from the following causes.

1. From the inertia of the beams and all the parts of the apparatus which are in motion during the descent of the pump-rods. 2. From the loss of weight sustained by the immersion of the pump-rods in water. 3. From the friction of all the pistons and the weight of the plug-frame. 4. From the resistance to the piston's motion, arising from the velocity which must be generated in the water in passing through the descending pistons.

The sum of all these resistances is equal to the pressure of some weight (as yet unknown), which we may call m.

When the pump-rods are brought up again, they bring along with them a column of water, whose weight we may call w.

It is evident that the load which must be overcome by the pressure of the atmosphere on the steam piston consists of w and p. Let this load be called L, and the pressure of the air be called P.

If p be = L, no water will be raised; if p be = 0, the rods will not descend: therefore there is some intermediate value of p which will produce the greatest effect.

In order to discover this, let g be the fall of a heavy body in a second.

The descending mass is p: but it does not descend with its full weight; because it is overcoming a set of resistances which are equivalent to a weight m, and the moving force is \( p - m \). In order to discover the space through which the rods will descend in a second, when urged by the force \( p - m \) (supposed constant, notwithstanding the increase of velocity, and consequently of m), we must institute this proportion \( p : p - m = g : g(p-m) \).

\( p \)

The fourth term of this analogy is the space required.

Let t be the whole time of the descent in seconds. Then \( t^2 : t^2g(p-m) : t^2g(p-m) \). This last term is the whole descent or length of the stroke accomplished in the time t.

The weight of the column of water, which has now got above the piston, is w = L - p. This must be lifted in the next working stroke through the space \( \frac{t^2 g (p-m)}{p} \). Therefore the performance of the engine must be \( \frac{t^2 g (p-m) (L-p)}{p} \).

That this may be the greatest possible, we must consider p as the variable quantity, and make the fluxion of the fraction \( \frac{p-m}{p} \times \frac{L-p}{L} = 0 \).

This will be found to give us \( p = \sqrt{Lm} \); that is, the counter weight or preponderancy of the outer end of the beam is \( = \sqrt{Lm} \).

This gives us a method of determining m experimentally. We can discover by actual measurement the quantity L in any engine, it being equal to the unbalanced weights on the beam and the weight of the water in the pumps. Then \( m = \frac{p^2}{L} \).

Also we have the weight of the column of water \( = L - p, = L - \sqrt{Lm} \).

When therefore we have determined the load which is to be on the outer end of the beam during the working stroke, it must be distributed into two parts, which have the proportion of \( \sqrt{Lm} \) to \( L - \sqrt{Lm} \). The first is the counter weight, and the second is the weight of the column of water.

If m is a fraction of L, such as an aliquot part of it; that is, if

\[ m = \frac{L}{1}, \frac{L}{4}, \frac{L}{9}, \frac{L}{16}, \frac{L}{25}, \text{ &c.} \] \[ p = \frac{L}{1}, \frac{L}{2}, \frac{L}{3}, \frac{L}{4}, \frac{L}{5}, \text{ &c.} \]

The circumstance which is commonly obtruded on us by local considerations is the quantity of water, and the depth from which it is to be raised; that is, w; and it will be convenient to determine every thing in conformity to this.

We saw that \( w = L - \sqrt{Lm} \). This gives us \( L = \pm \sqrt{wm + \frac{m^2}{4} + \frac{m}{2} + w} \), and the counter weight \[ p = \sqrt{wm + \frac{m^2}{4} + \frac{m}{2}}. \]

Having thus ascertained that distribution of the load on the outer end of the beam which produces the greatest effect, we come now to consider what proportion of moving force we must apply, so that it may be employed to the best advantage, or so that any expense of power may produce the greatest performance. It will be so much the greater as the work done is greater, and the power employed is less; and will therefore be properly measured by the quotient of the work done divided by the power employed.

The work immediately done is the lifting up the weight L. In order to accomplish this, we must employ a pressure P, which is greater than L. Let it be \( = L + y \); also let s be the length of the stroke.

If the mass L were urged along the space s by the force L + y, it would acquire a certain velocity, which we may express by \( \sqrt{\frac{s}{y}} \); but it is impelled only by the force y, the rest of P being employed in balancing L. The velocities which different forces generate by impelling a body along the same space are as the square roots of the forces. Therefore \( \sqrt{L+y} : \sqrt{y} = \sqrt{s} : \sqrt{\frac{s\ y}{L+y}} \). The fourth term of this analogy expresses the velocity of the piston at the end of the stroke. The quantity of motion produced will be had by multiplying this velocity by the mass L. This gives \( \frac{L \times \sqrt{s\ y}}{\sqrt{L+y}} \); and this divided by the power expended, or by \( L + y \), gives us the measure of the performance; namely, \[ \frac{L \sqrt{s\ y}}{L+y \times \sqrt{L+y}} \]

That this may be a maximum, consider y as the variable quantity, and make the fluxion of this formula \( = 0 \). This will give us \( y = \frac{L}{2} \).

Now P = L + y, \( = L + \frac{L}{2}, = \frac{3}{2} L \). Therefore the whole load on the outer end of the beam, consisting of the water and the counter weight, must be two-thirds of the prelude of the atmosphere on the steam piston.

We have here supposed that the expenditure is the atmospheric prelude; and so it is if we consider it mechanically. But the expenditure of which we are sensible, and which we are anxious to employ to the best advantage, is fuel. Supposing this to be employed with the same judgment in all cases, we are almost entitled, by what we now know of the production of steam, to say that the steam produced is proportional to the fuel expended. But the steam requisite for merely filling the cylinder is proportional to the area of the piston, and therefore to the atmospheric prelude. The result of our investigation therefore is still just; but the steam wasted by condensation on the sides of the cylinder does not follow this ratio, and this is more than what is necessary for merely filling it. This deranges our calculations, and is in favour of large cylinders; but this advantage must be in a great measure compensated by a similar variation in the production of the steam; for in similar boilers of greater dimensions the fuel is less advantageously employed, because the surface to which the fuel is applied does not increase in the ratio of the capacity, just as the surface of the cylinder which wastes the steam. The rule may therefore be confided in as pretty exact.

It is a satisfactory thing to observe these results agree very well with the most successful practice. By many tests agree changes and trials engineers have established maxims of with the construction, which are probably not very far from the most useful. It is a pretty general maxim, that the load of water should be one-half of the atmospheric pressure. They call this loading the engine with 7\( \frac{1}{2} \) pounds on the inch, and they say that so small a load is necessary on account of the imperfect vacuum. But we have now seen that it is necessary for giving a reasonable velocity of motion. Since, in this practice, w is made \( \frac{1}{3} \) or \( \frac{1}{4} \)ths of P, and L should be \( \frac{1}{3} \)ths of P, and L is \( = w + p \); it follows, that the counter weight should be 1/4th of P; and we have found this to be nearly the case in several very good engines.

It must be remarked, that in the preceding investigation we introduced a quantity M to express the resistances to the motion of the engine. This was done in order to avoid a very troublesome investigation. The resistances are of such a nature as to vary with the velocity, and most of them as the square of the velocity. This is the case with the resistance arising from the motion of the water through the pistons of the pumps, and that arising from the friction in the long lift during the working stroke. Had we taken the direct method, which is similar to the determination of the motion through a medium which resists in the duplicate ratio of the velocity, we must have used a very intricate exponential calculus, which few of our readers would have the patience to look at.

But the greatest part of the quantity m supposes a motion already known, and its determination depends on this motion. We must now show how its different component parts may be computed.

1. What arises from the inertia of the moving parts is by far the most considerable portion of it. To obtain it, we must find a quantity of matter which, when placed at the end of the beam, will have the same momentum of inertia with that of the whole moving parts in their natural places. Therefore (in the returning stroke) add together the weight of the great piston with its rod and chains; the pit pump-rods, chains, and any weight that is attached to them; the arch-heads and iron-work at the ends of the beam, and 1/8ths of the weight of the beam itself; also the plug-beam with its arch-head and chain, multiplied by the square of its distance from the axis, and divided by the square of half the length of the beam; also the jack-head pump-rod, chain, and arch-head, multiplied by the square of its distance from the axis, and divided by the square of the half length of the beam. These articles added into one sum may be called M, and may be supposed to move with the velocity of the end of the beam. Suppose this beam to have made a six-foot stroke in two seconds, with an uniformly accelerated motion. In one second it would have moved 1 1/2 feet, and would have acquired the velocity of three feet per second. But in one second gravity would have produced a velocity of 32 feet in the same mass. Therefore the accelerating force, which has produced the velocity of three feet, is nearly 1/17th of the weight. Therefore \( \frac{M}{11} \) is the first constituent of m in the above investigation. If the observed velocity is greater or less than three feet per second, this value must be increased or diminished in the same proportion.

The second cause of resistance, viz. the immersion of the pump rods in water, is easily computed, being the weight of the water which they displace.

The third cause, the friction of the pistons, &c. is almost insignificant, and must be discovered by experiment.

The fourth cause depends on the structure of the pumps. These pumps, when made of a proper strength, can hardly have the perforation of the piston more than a fourth part of the area of the working-barrel; and the velocity with which the water passes through it is increased at least 1/4th by the contraction (see Pump). The velocity of the water is therefore five times greater than that of the piston. A piston 12 inches diameter, and moving one foot per second, meets with a resistance equal to 20 pounds; and this increases as the square of the diameter and as the square of the velocity. If the whole depth of the pit be divided into several lifts, this resistance must be multiplied by the number of lifts, because it obtains in each pump.

Thus we make up the value of m; and we must acknowledge that the method is still indirect, because it supposes the velocity to be known.

We may obtain it more easily in another way, but still with this circumstance of being indirect. We found that \( p \) was equal to \( \sqrt{Lm} \), and consequently \( m = \frac{p^2}{L} \).

Now in any engine L and p can always be had; and unless p deviates greatly from the proportion which we determined to be the best, the value of m thus obtained will not be very erroneous.

It was farther presumed in this investigation, that the Observations both up and down were uniformly accelerated; but this cannot be the case when the resistances increase with the velocity. This circumstance makes very little change in the working-stroke, and therefore the theorem which determines the best relation of P to L may be confided in. The resistances which vary with the velocity in this case are a mere trifle when compared with the moving power y. These resistances are, 1st, The straining of the water at the entry and at the standing valve of each pump: This is about 37 pounds for a pump 12 inches diameter, and the velocity one foot per second, increasing in the duplicate ratio of the diameter and velocity. And, 2d, The friction of the water along the whole lift: This for a pump of the same size and with the same velocity, lifting 20 fathoms, is only about 2 1/2 pounds, and varies in the simple proportion of the diameter and the depth, and in the duplicate proportion of the velocity. The resistance arising from inertia is greater than in the returning stroke; because the M in this case must contain the momentum of the water both of the pit-pumps and the jackhead-pump: but this part of the resistance does not affect the uniform acceleration. We may therefore confide in the propriety of the formula \( y = \frac{L}{2} \). And we may obtain the velocity of this stroke at the end of a second with great accuracy as follows. Let 2g be the velocity communicated by gravity in a second, and the velocity at the end of the first second of the steam piston's descent will be somewhat less than \( \frac{y}{M} 2g \); where M expresses the inertia of all the parts which are in motion during the decent of the steam piston, and therefore includes L. Compute the two resistances just mentioned for this velocity. Call this r. Then \( \frac{y - \frac{1}{2}r}{M} 2g \) will give another velocity infinitely near the truth.

But the case is very different in the returning stroke, and the proper ratio of p to L is not ascertained with the same certainty: for the moving force p is not so great in proportion to the resistance m; and therefore the acceleration of the motion is considerably affected by it, and the motion itself is considerably retarded, and in a very moderate time it becomes sensibly uniform: for it is precisely similar to the motion of a heavy body falling falling through the air, and may be determined in the manner laid down in the article RESISTANCE of Fluids, viz. by an exponential calculus. We shall content ourselves here with saying, that the resistances in the present case are so great that the motion would be to all sense uniform before the pistons have descended one-third of their stroke, even although there were no other circumstance to affect it.

But this motion is affected by a circumstance quite unconnected with any thing yet considered, depending on conditions not mechanical, and so uncertain, that we are not yet able to ascertain them with any precision; yet they are of the utmost importance to the good performance and improvement of the engine, and therefore deserve a particular consideration.

The counter weight has not only to push down the pump rods, but also to drag up the great piston. This it cannot do unless the steam be admitted into the cylinder. If the steam be no stronger than common air, it cannot enter the cylinder except in consequence of the piston's being dragged up. If common air were admitted into the cylinder, some force would be required to drag up the piston, in the same manner as it is required to draw up the piston of a common syringe; for the air would rush through the small entry of the cylinder in the same manner as through the small nozzle of the syringe. Some part of the atmospheric pressure is employed in driving in the air with sufficient velocity to fill the syringe, and it is only with the remainder that the admitted air presses on the under surface of the syringe. Therefore some of the atmospheric pressure on its upper surface is not balanced. This is felt by the hand which draws it up. The same thing must happen in the steam engine, and some part of the counter weight is expended in drawing up the steam piston. We could tell how much is thus expended if we knew the density of the steam; for this would tell us the velocity with which its elasticity would cause it to fill the cylinder. If we suppose it 12 times rarer than air, which it certainly is, and the piston rises to the top of the cylinder in two seconds, we can demonstrate that it will enter with a velocity not less than 1400 feet per second, whereas 500 feet is enough to make it maintain a density \( \frac{7}{9} \)ths of that of steam in equilibrium with the air. Hence it follows, that its elasticity will not be less than \( \frac{3}{8} \)ths of the elasticity of the air, and therefore not more than \( \frac{1}{3} \)th of counter weight will be expended in drawing up the steam-piston.

But all this is on the supposition that there is an unbounded supply of steam of undiminished elasticity. This is by no means the case. Immediately before opening the steam-cock, the steam was filling through the safety-valve and all the crevices in the top of the boiler, and (in good engines) was about \( \frac{1}{10} \)th stronger or more elastic than air. This had been gathering during something more than the descent of the piston, viz. in about three seconds. The piston rises to the top in about two seconds; therefore about twice and a half as much steam as fills the dome of the boiler is now shared between the boiler and cylinder. The dome is commonly about six times more capacious than the cylinder. If therefore no steam is condensed in the cylinder, the density of the steam, when the piston has reached the top, must be about \( \frac{1}{5} \)ths of its former density, and still more elastic than air. But as much steam is condensed by the cold cy-

linder, its elasticity must be less than this. We cannot tell how much less, both because we do not know how much is thus condensed, and because by this diminution of its pressure on the surface of the boiling water, it must be more copiously produced in the boiler; but an attentive observation of the engine will give us some information. The moment the steam-cock is opened we have a strong puff of steam through the inititing valve. At this time, therefore, it is still more elastic than air; but after this, the inititing valve remains shut during the whole rise of the piston, and no steam any longer issues through the safety-valve or crevices; nay, the whole dome of the boiler may be observed to sink.

These facts give abundant proof that the elasticity of the steam during the ascent of the piston is greatly diminished, and therefore much of the counter weight is expended in dragging up the steam piston in opposition to the unbalanced part of the atmospheric pressure. The motion of the returning stroke is therefore so much decreased by this foreign and inappreciated circumstance, that it would have been quite useless to engage in the intricate exponential investigation, and we must fit down contented with a less perfect adjustment of the counter weight and weight of water.—Any person who attends to the motion of a steam-engine will perceive that the descent of the pump-rods is so far from being accelerated, that it is nearly uniform, and frequently it is sensibly retarded towards the end. We learn by the way, that it is of the utmost importance not only to have a quick production of steam, but also a very capacious dome, or empty space above the water in the boiler. In engines where this space was but four or five times the capacity of the cylinder, we have always observed a very sensible check given to the descent of the pump-rods after having made half their stroke. This obliges us to employ a greater counter weight, which diminishes the column of water, or retards the working stroke; it also obliges us to employ a stronger steam, at the risk of bursting the boiler, and increases the expense of fuel.

It would be a most desirable thing to get an exact knowledge of the elasticity of the steam in the cylinder; and this is by no means difficult. Take a long glass tube exactly calibred, and close at the farther end. Put in the cylinder a small drop of some coloured fluid into it, so as to stand at the middle nearly.—Let it be placed in a long box filled with water to keep it of a constant temperature. Let the open end communicate with the cylinder, with a cock between. The moment the steam-cock is opened, open the cock of this instrument. The drop will be pushed towards the close end of the tube, while the steam in the cylinder is more elastic than the air, and it will be drawn the other way while it is less elastic, and, by a scale properly adapted to it, the elasticity of the steam corresponding to every position of the piston may be discovered. The same thing may be done more accurately by a barometer properly constructed, so as to prevent the oscillations of the mercury.

It is equally necessary to know the state of the cylinder during the descent of the steam-piston. We have hitherto supposed P to be the full pressure of the atmosphere on the area of the piston, supposing the vacuum below it to be complete. But the inspection of our table of elasticity shows that this can never be the case, because the cylinder is always of a temperature far above 32°. We have made many attempts to discover its tem- temperature. We have employed a thermometer in close contact with the side of the cylinder, which soon acquired a steady temperature: this was never less than 145°. We have kept a thermometer in the water which lies on the piston: this never sunk below 135°. It is probable that the cylinder within may be cooled somewhat lower; but for this opinion we cannot give any very satisfactory reason. Suppose it cooled down to 120°; this will leave an elasticity which would support three inches of mercury. We cannot think, therefore, that the unbalanced prelure of the atmosphere exceeds that of 27 inches of mercury, which is about 13 1/2d pounds on a square inch, or 10 1/2 on a circular inch. And this is the value which we should employ in the equation \( P = L + \gamma \). This question may be decided in the same way as the other, by a barometer connected with the inside of the cylinder.

And thus we shall learn the state of the moving forces in every moment of the performance, and the machine will then be as open to our examination as any water or horse mill; and till this be done, or something equivalent, we can only guess at what the machine is actually performing, and we cannot tell in what particulars we can lend it a helping hand. We are informed that Messrs Watt and Boulton have made this addition to some of their engines; and we are persuaded that, from the information which they have derived from it, they have been enabled to make the curious improvements from which they have acquired so much reputation and profit.

There is a circumstance of which we have as yet taken no notice, viz. the quantity of cold water injected. Here we confess ourselves unable to give any precise instructions. It is clear at first sight that no more than is absolutely necessary should be injected. It must generally be supplied by the engine, and this expends part of its power. An excess is much more hurtful by cooling the cylinder and piston too much, and therefore wasting steam during the next rise of the piston. But the determination of the proper quantity requires a knowledge, which we have not yet acquired, of the quantity of heat contained in the steam in a latent form. As much water must be injected as will absorb all this without rising near to the boiling temperature. But it is of much more importance to know how far we may cool the cylinder with advantage; that is, when will the loss of steam, during the next rise of the piston, compensate for the diminution of its elasticity during its present descent? Our table of elasticities shows us, that by cooling the cylinder to 120°, we will leave an elasticity equal to one-tenth of the whole power of the engine; if we cool it only to 140, we leave an elasticity of one-fifth; if we cool it to a blood-heat, we leave an elasticity of one-twentieth. It is extremely difficult to choose among these varieties. Experience, however, informs us, that the best engines are those which use the smallest quantities of injection water. We know an exceedingly good engine having a cylinder of 32 inches and a fix feet stroke, which works with something less than one-fifth of a cubic foot of water at each injection; and we imagine that the quantity should be nearly in the proportion of the capacity of the cylinder. Desaguliers observed, that a very good engine, with a cylinder of 32 inches, worked with 300 inches of water at each injection, which does not much exceed one-sixth of a cubic foot. Mr Watt's observations, by means of the barometer, must have given him much valuable information in this particular, and we hope that he will not always withhold them from the public.

We have gone thus far in the examination, in order This exa- seemingly to ascertain the motion of the engine when mination, loaded and balanced in any known manner, and in or- though not der to discover that proportion between the moving satisfac- power and the load which will produce the greatest tion to the the attention quantity of work. The result has been very unsatis- principal factory, because the computation of the returning stroke acknowledged to be beyond our abilities. But it has circumstances given us the opportunity of directing the reader's attention to the leading circumstances in this inquiry. By knowing the internal state of the cylinder in machines of very different goodnets, we learn the connection be- between the state of the steam and the performance of the machine; and it is very possible that the result of a full examination may be, that in situations where fuel is expensive, it may be proper to employ a weak steam which will expend less fuel, although less work is per- formed by it. We shall see this confirmed in the clear- est manner in some particular employments of the new engines invented by Watt and Boulton.

In the mean time, we see that the equation which we gave from the celebrated Abbé Boslut, is in every re- spect erroneous even for the purpose which he had in view. We also see that the equation which we substi- tuted in its place, and which was intended for determi- ning that proportion between the counter-weight and the moving force, and the load which would render the working stroke and returning stroke of equal duration, is also erroneous, because these two motions are extrem- ely different in kind, the one being nearly uniform, and the other nearly uniformly accelerated. This being supposed true, it should follow that the counter-weight should be reduced to one-half; and we have found this to be very nearly true in some good engines which we have examined.

We shall add but one observation more on this head. The practical engineers have almost made it a maxim, that the two motions are of equal duration. But the only reason which we have heard for the maxim, is that it is awkward to see an engine go otherwise. But we doubt exceedingly the truth of this maxim; and, without being able to give any accurate determination, we think that the engine will do more work if the working stroke be made slower than the returning stroke. Suppose the engine so constructed that they are made in equal times; an addition to the counter-weight will accelerate the returning stroke and retard the working stroke. But as the counter-weight is but small in pro- portion to the unbalanced portion of the atmospheric prelure, which is the moving force of the machine, it is evident that this addition to the counter-weight must bear a much greater proportion to the counter-weight than it does to the moving force, and must therefore accelerate the returning stroke much more than it retards the working stroke, and the time of both strokes taken together must be diminished by this addition and the performance of the machine improved; and this must be the case as long as the machine is not extravagantly loaded. The best machine which we have seen, in re- spect of performance, raises a column of water whose weight is very nearly two-thirds of the prelure of the atmosphere atmosphere on the piston, making 11 strokes of six feet each per minute, and the working stroke was almost twice as low as the other. This engine had worked pumps of 12 inches, which were changed for pumps of 14 inches, all other things remaining the same. In its former state it made from 12 and a half to 13 and a half strokes per minute, the working stroke being considerably lower than the returning stroke. The load was increased, by the change of the pumps, nearly in the proportion of three to four. This had retarded the working stroke; but the performance was evidently increased in the proportion of \(3 \times 13\) to \(4 \times 11\), or of 39 to 44. About 300 pounds were added to the counter-weight, which increased the number of strokes to more than 12 per minute. No sensible change could be observed in the time of the working stroke. The performance was therefore increased in the proportion of 39 to 48. We have therefore no hesitation in saying, that the feebly equality of the two strokes is a sacrifice to fancy. The engineer who observes the working stroke to be slow, fears that his engine may be thought feeble and unequal to its work; a similar notion has long milled him in the construction of water-mills, especially of overhot mills; and even now he is submitting with hesitation and fear to the daily correction of experience.

It is needless to engage more deeply in scientific calculations in a subject where so many of the data are so very imperfectly understood.

We venture to recommend as a maxim of construction (supposing always a large boiler and plentiful supply of pure steam unmixed with air), that the load of work be not less than 10 pounds for every square inch of the piston, and the counter-weight to proportioned that the time of the returning stroke may not exceed two-thirds of that of the working stroke. A serious objection may be made to this maxim, and it deserves mature consideration. Such a load requires the utmost care of the machine, that no admission be given to the common air; and it precludes the possibility of its working, in case the growth of water, or deepening the pit, should make a greater load absolutely necessary. These considerations must be left to the prudence of the engineer. The maxim now recommended relates only to the best actual performance of the engine.

Before quitting this machine, it will not be amiss to give some easy rules, sanctioned by successful practice, for computing its performance. These will enable any artist, who can go through simple calculations, to suit the size of his engine to the task which it is to perform.

The circumstance on which the whole computation must be founded is the quantity of water which must be drawn in a minute, and the depth of the mine; and the performance which may be expected from a good engine is at least 12 strokes per minute of six feet each, working against a column of water whose weight is equal to half of the atmospheric pressure on the steam-piston, or rather to 7.64 pounds on every square inch of its surface.

It is most convenient to estimate the quantity of water in cubic feet, or its weight in pounds, recollecting that a cubic foot of water weighs 62\( \frac{1}{2} \) pounds. The depth of the pit is usually reckoned in fathoms of six feet, and the diameter of the cylinder and pump is usually reckoned in inches.

Let Q be the quantity of water to be drawn per minute in cubical feet, and f the depth of the mine in fathoms; let c be the diameter of the cylinder, and p that of the pump; and let us suppose the arms of the beam to be of equal length.

1st. To find the diameter of the pump, the area of the piston in square feet is \(p^2 \times \frac{0.7854}{144}\). The length of the column drawn in one minute is 12 times 6 or 72 feet, and therefore its solid contents is \(p^2 \times \frac{72 \times 0.7854}{144}\) cubical feet, or \(p^2 \times 0.3927\) cubical feet. This must be equal to Q; therefore \(p^2\) must be \( \frac{Q}{0.3927} \) or nearly \( \frac{Q}{2.5} \). Hence this practical rule: Multiply the cubic feet of water which must be drawn in a minute by 2.5, and extract the square root of the product: this will be the diameter of the pump in inches.

Thus suppose that 58 cubic feet must be drawn every minute; 58 multiplied by 2.5 gives 145, of which the square root is 12, which is the required diameter of the pump.

2. To find the proper diameter of the cylinder.

The piston is to be loaded with 7.64 pounds on every square inch. This is equivalent to fix pounds on a circular inch very nearly. The weight of a cylinder of water an inch in diameter and a fathom in height is \(2 \frac{1}{3}\) pounds, or nearly two pounds. Hence it follows that \(6c^2\) must be made equal to \(2f p^2\), and that \(c^2\) is equal to \( \frac{2f p^2}{6} \), or to \( \frac{f p^2}{3} \).

Hence the following rule: Multiply the square of the diameter of the pump piston (found as above) by the fathoms of lift, and divide the product by 3; the square root of the quotient is the diameter of the cylinder.

Suppose the pit to which the foregoing pump is to be applied is 24 fathoms deep; then \( \frac{24 \times 144}{3} \) gives 1152, of which the square root is 34 inches very nearly.

This engine, constructed with care, will certainly do the work.

Whatever is the load of water proposed for the engine, let 10 be the pounds on every circular inch of the steam piston, and make \(c^2 = p^2 \times \frac{2f}{m}\), and the square root will be the diameter of the steam piston in inches.

To free the practical engineer as much as possible from all trouble of calculation, we subjoin the following Table of the Dimensions and Power of the Steam Engine, drawn up by Mr Beighton in 1717, and fully verified by practice since that time. The measure is in English ale gallons of 282 cubic inches. Mr Beighton's table of the dimensions and power of the steam-engine.

<table> <tr> <th rowspan="2">Diam. of pump.</th> <th colspan="3">Holds by a fixt stroke.</th> <th colspan="2">Weighs in one yard.</th> <th colspan="2">At 16 strokes per min.</th> <th colspan="2">Ditto in hogheads.</th> <th colspan="2">Ditto per hour.</th> </tr> <tr> <th>Inch.</th> <th>Gall.</th> <th>Gall.</th> <th>Lb. avor.</th> <th>Gall.</th> <th>Hd. Gal.</th> <th>Gall.</th> <th>Hd. Gal.</th> </tr> <tr><td>12</td><td>14.4</td><td>28.8</td><td>146</td><td>462</td><td>7.21</td><td>440.</td></tr> <tr><td>11</td><td>12.13</td><td>24.26</td><td>123.5</td><td>338</td><td>6.20</td><td>369.33</td></tr> <tr><td>10</td><td>10.02</td><td>20.04</td><td>102</td><td>320</td><td>5.5</td><td>304.48</td></tr> <tr><td>9</td><td>8.12</td><td>16.24</td><td>82.7</td><td>259.8</td><td>4.7</td><td>247.7</td></tr> <tr><td>8½</td><td>7.26</td><td>14.52</td><td>73.9</td><td>232.3</td><td>3.43</td><td>221.15</td></tr> <tr><td>8</td><td>6.41</td><td>12.82</td><td>65.3</td><td>205.2</td><td>3.16</td><td>195.22</td></tr> <tr><td>7½</td><td>6.01</td><td>12.02</td><td>61.2</td><td>192.3</td><td>3.2</td><td>182.13</td></tr> <tr><td>7¾</td><td>5.66</td><td>11.32</td><td>57.6</td><td>181.1</td><td>2.55</td><td>172.30</td></tr> <tr><td>7</td><td>4.91</td><td>9.82</td><td>50.0</td><td>157.7</td><td>2.31</td><td>149.40</td></tr> <tr><td>6½</td><td>4.23</td><td>8.46</td><td>43.0</td><td>135.3</td><td>2.9</td><td>128.54</td></tr> <tr><td>6</td><td>3.61</td><td>7.2</td><td>36.7</td><td>115.5</td><td>1.52</td><td>110.1</td></tr> <tr><td>5½</td><td>3.13</td><td>6.2</td><td>31.8</td><td>99.2</td><td>1.36</td><td>94.30</td></tr> <tr><td>5</td><td>2.51</td><td>5.0</td><td>25.5</td><td>85.3</td><td>1.7</td><td>66.61</td></tr> <tr><td>4½</td><td>2.02</td><td>4.04</td><td>20.5</td><td>64.6</td><td>1.1</td><td>66.60</td></tr> <tr><td>4</td><td>1.6</td><td>3.2</td><td>16.2</td><td>51.2</td><td>0.51</td><td>48.51</td></tr> </table>

The depth to be drawn in yards.

<table> <tr> <th>Diameter of cylinder in inches.</th> <th>15</th> <th>20</th> <th>25</th> <th>30</th> <th>35</th> <th>40</th> <th>45</th> <th>50</th> <th>60</th> <th>70</th> <th>80</th> <th>90</th> </tr> <tr><td>18½</td><td>21½</td><td>24</td><td>26½</td><td>28</td><td>30</td><td>32</td><td>34</td><td>37</td><td>40</td><td>43½</td><td></td><td></td></tr> <tr><td>17</td><td>19½</td><td>22</td><td>25</td><td>26½</td><td>28</td><td>29½</td><td>31</td><td>34</td><td>37</td><td>39½</td><td></td><td></td></tr> <tr><td>15½</td><td>18</td><td>20</td><td>22</td><td>23</td><td>25</td><td>27</td><td>28</td><td>31</td><td>34</td><td>36</td><td>38</td><td></td></tr> <tr><td>14</td><td>16½</td><td>18</td><td>20</td><td>21</td><td>23</td><td>24</td><td>25</td><td>28</td><td>30</td><td>33</td><td>35</td><td></td></tr> <tr><td>13½</td><td>15</td><td>17</td><td>19</td><td>20</td><td>21</td><td>23</td><td>24</td><td>26</td><td>28</td><td>31</td><td>32</td><td></td></tr> <tr><td>12½</td><td>14</td><td>16</td><td>18</td><td>19</td><td>20</td><td>21</td><td>23</td><td>25</td><td>27</td><td>29</td><td>30</td><td></td></tr> <tr><td>12</td><td>14</td><td>15½</td><td>17½</td><td>18½</td><td>19</td><td>21</td><td>22</td><td>24</td><td>26</td><td>28</td><td>29½</td><td></td></tr> <tr><td>11</td><td>13</td><td>15</td><td>16½</td><td>18</td><td>19</td><td>20</td><td>21</td><td>23</td><td>25</td><td>27</td><td>28</td><td></td></tr> <tr><td>10½</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>18</td><td>19</td><td>20</td><td>22</td><td>24</td><td>25</td><td>27</td><td></td></tr> <tr><td>10</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>18</td><td>19</td><td>20</td><td>22</td><td>23</td><td>24</td><td></td></tr> <tr><td>9½</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>17</td><td>19</td><td>20</td><td>22</td><td>23</td><td></td></tr> <tr><td>9</td><td>10</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>17</td><td>19</td><td>20</td><td>21</td><td></td></tr> <tr><td>8½</td><td>10</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>17</td><td>19</td><td>20</td><td>21</td><td></td></tr> <tr><td>8</td><td>10</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>17</td><td>19</td><td>20</td><td>21</td><td></td></tr> <tr><td>7½</td><td>9</td><td>10</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>17</td><td>19</td><td>20</td><td></td></tr> <tr><td>7</td><td>9</td><td>10</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>17</td><td>19</td><td>20</td><td></td></tr> </table>

The first part of the table gives the size of the pump suited to the growth of water. The second gives the size of the cylinder suited to the load of water. If the depth is greater than any in this table, take its fourth part, and double the diameter of the cylinder. Thus if 150 hogheads are to be drawn in an hour from the depth of 100 fathoms, the last column of part first gives for 149.40 a pump of seven inches bore. In a line with this, under the depth of 50 yards, which is one-fourth of 100 fathoms, we find 20½, the double of which is 41 inches for the diameter of the cylinder.

It is almost impossible to give a general rule for strokes of different lengths, &c. but any one who professes the ability to erect an engine, should surely know as much arithmetic as will accommodate the rule now given to any length of stroke.

We venture to say, that no ordinary engineer can tell à priori the number per minute which an engine will give. We took 12 strokes of fixt feet each for a standard, which a careful engineer may easily accomplish, and which an employer has a right to expect, the engine being loaded with water to half the pressure of the atmosphere: if the load be less, there is some fault—an improper counter weight, or too little boiler, or leaks, &c. &c.

Such is the state in which Newcomen's steam-engine had continued in use for 60 years, neglected by the philosopher, although it is the most curious object which human ingenuity has yet offered to his contemplation, and abandoned to the efforts of the unlettered artif. Its use has been entirely confined to the raising of water. Mr Keane Fitzgerald indeed published in the Philosophical Transactions a method of converting its reciprocating motion into a continued rotary motion by employing the great beam to work a crank or a train of wheel-work. As the real action of the machine is confined to its working stroke, to accomplish this, it became necessary to connect with the crank or wheeled work a very large and heavy fly, which should accumulate in itself the whole prelude of the machine during its time of action, and therefore continue in motion, and urge forward the working machinery, while the steam-engine was going through its inactive returning stroke. This will be the case, provided that the resistance exerted by the working machine during the whole period of the working and returning stroke of the steam-engine, together with the friction of both, does not exceed the whole pressure exerted by the steam-engine during its working stroke; and provided that the momentum of the fly, arising from its great weight and velocity, be very great, so that the resistance of the work during one returning stroke of the steam-engine do not make any very sensible diminution of the velocity of the fly. This is evidently possible and easy. The fly may be made of any magnitude; and being exactly balanced round its axis, it will soon acquire any velocity consistent with the motion of the steam-engine. During the working stroke of the engine it is uniformly accelerated, and by its acquired momentum it produces in the beam the movement of the returning stroke; but in doing this, its momentum is shared with the inert matter of the steam-engine, and consequently its velocity diminished, but not entirely taken away. The next working stroke therefore, by pressing on it afresh, increases its remaining velocity by a quantity nearly equal to the whole that it acquired during the first stroke. We say nearly, but not quite equal, because the time of the second working stroke must be shorter than that of the first, on account of the velocity already in the machine. In this manner the fly will be more and more accelerated every succeeding stroke, because the prelude of the engine during the working stroke does more than restore to the fly the momentum which it lost in producing the returning movement of the steam-engine. Now suppose the working part of the machine to be added. The acceleration of the fly during each working stroke of the steam-engine will be less than it was before, because the impelling pressure is now partly employed in driving the working machine, and because the fly will lose more of its momentum during the returning stroke of the steam-engine, part of it being expended in driving the working machine. It is evident, therefore, that a time will come come when the successive augmentation of the fly's velocity will cease; for, on the one hand, the continual acceleration diminishes the time of the next working stroke, and therefore the time of action of the accelerating power. The acceleration must diminish in the same proportion; and on the other hand, the resistance of the working machine generally, though not always, increases with its velocity. The acceleration ceases whenever the addition made to the momentum of the fly during a working stroke of the steam-engine is just equal to what it looses by driving the machine, and by producing the returning movement of the steam engine.

This must be acknowledged to be a very important addition to the engine, and though sufficiently obvious, it is ingenious, and requires considerable skill and address to make it effective (b).

The movement of the working machine, or mill of whatever kind, must be in some degree hobbiling or unequal. But this may be made quite insensible, by making the fly exceedingly large, and disposing the greatest part of its weight in the rim. By these means its momentum may be made so great, that the whole force required for driving the mill and producing the returning movement of the engine may bear a very small proportion to it. The diminution of its velocity will then be very trifling.

No counter weight is necessary here, because the returning movement is produced by the inertia of the fly. A counter weight may, however, be employed, and should be employed, viz. as much as will produce the returning movement of the steam-engine. It will do this better than the same force accumulated in the fly; for this force must be accumulated in the fly by the intervention of rubbing parts, by which some of it is lost; and it must be afterwards returned to the engine with a similar loss. But, for the same reason, it would be improper to make the counter weight able to drive the mill during the returning stroke.

By this contrivance Mr Fitzgerald hoped to render the steam-engine of most extensive use; and he, or others associated with him, obtained a patent excluding all others from employing the steam-engine for turning a crank. They also published proposals for erecting mills of all kinds driven by steam-engines, and stated very fairly their powers and their advantages. But their proposals do not seem to have acquired the confidence of the public; for we do not know of any mill ever having been erected under this patent.

The great obstacle to this extensive use of the steam-engine is the prodigious expense of fuel. An engine having a cylinder of four feet diameter, working night and day, consumes about 3400 chaldron (London) of good coals in a year.

This circumstance limits the use of steam-engines exceedingly. To draw water from coal-pits, where they can be stocked with unsaleable small coal, they are of universal employment; also for valuable mines, for supplying a great and wealthy city with water, and a few other purposes where a great expense can be borne, they are very proper engines; but in a thousand cases, where their unlimited powers might be vastly serviceable, the enormous expense of fuel completely excludes them. We cannot doubt but that the attention of engineers was much directed to every thing that could promise a diminution of this expense. Every one had his particular notion for the construction of his furnace, and some were undoubtedly more successful than others. But science was not yet sufficiently advanced: It was not till Dr Black had made his beautiful discovery of latent heat, that we could know the intimate relation between the heat expended in boiling off a quantity of water and the quantity of steam that is produced.

Much about the time of this discovery, viz. 1763, Mr James Watt, established in Glasgow in the commercial line, was amusing himself with repairing a working model of the steam-engine which belonged to the philosophical apparatus of the university. Mr Watt was a person of a truly philosophical mind, eminently conversant in all branches of natural knowledge, and the pupil and intimate friend of Dr Black. In the course of the above-mentioned amusement many curious facts in the production and condensation of steam occurred to him; and among others, that remarkable fact which is always appealed to by Dr Black as the proof of the immense quantity of heat which is contained in a very minute quantity of water in the form of elastic steam. When a quantity of water is heated several degrees above the boiling point in a close digester, if a hole be opened, the steam rushes out with prodigious violence, and the heat of the remaining water is reduced, in the course of three or four seconds, to the boiling temperature. The water of the steam which has escaped amounts only to a very few drops; and yet these have carried off with them the whole excess of heat from the water in the digester.

Since then a certain quantity of steam contains so great a quantity of heat, it must expend a great quantity of fuel; and no construction of furnace can prevent this. Mr Watt therefore set his invention to work to discover methods of husbanding this heat. The cylinder of his little model was heated almost in an instant, so that it could not be touched by the hand. It could not be otherwise, because it condensed the vapour by abstracting its heat. But all the heat thus communicated to the cylinder, and wafted by it on surrounding bodies, contributed nothing to the performance of the engine,

(b) We do not recollect at present the date of this proposal of Mr Fitzgerald; but in 1781 the Abbé Arnal, canon of Alais in Languedoc, entertained a thought of the same kind, and proposed it for working lighters in the inland navigations; a scheme which has been successfully practised (we are told) in America. His brother, a major of engineers in the Austrian service, has carried the thing much farther, and applied it to manufactures; and the Aulic Chamber of Mines at Vienna has patronized the project: (See Journal Encyclopedique, 1781). But these schemes are long posterior to Mr Fitzgerald's patent, and are even later than the erection of several machines driven by steam-engines which have been erected by Messrs Watt and Boulton. We think it our duty to state these particulars, because it is very usual for our neighbours on the continent to assume the credit of British inventions. engine, and must be taken away at every injection, and again communicated and wafted. Mr Watt quickly understood the whole process which was going on within the cylinder, and which we have considered so minutely, and saw that a very considerable portion of the steam must be wafted in warming the cylinder. His first attempts were made to ascertain how much was thus wafted, and he found that it was not less than three or four times as much as would fill the cylinder and work the engine. He attempted to diminish this waste by using wooden cylinders. But though this produced a sensible diminution of the waste, other reasons forced him to give them up. He then casted his metal cylinders in a wooden case with light wood ashes between. By this, and using no more injection than was absolutely necessary for the condensation, he reduced the waste almost one half. But by using too small a quantity of cold water, the inside of the cylinder was hardly brought below the boiling temperature; and there consequently remained in it a steam of very considerable elasticity, which robbed the engine of a proportional part of the atmospheric pressure. He saw that this was unavoidable as long as the condensation was performed in the cylinder. The thought struck him to attempt the condensation in another place. His first experiment was made in the simplest manner. A globular vessel communicated by means of a long pipe of one inch diameter with the bottom of his little cylinder of four inches diameter and 30 inches long. This pipe had a stop-cock, and the globe was immersed in a vessel of cold water. When the piston was at the top, and the cylinder filled with strong steam, he turned the cock. It was scarcely turned, nay he did not think it completely turned, when the sides of his cylinder (only strong tin-plate) were crushed together like an empty bladder. This surprised and delighted him. A new cylinder was immediately made of brass sufficiently thick, and nicely bored. When the experiment was repeated with this cylinder, the condensation was so rapid, that he could not say that any time was expended in it. But the most valuable discovery was, that the vacuum in the cylinder was, as he hoped, almost perfect. Mr Watt found, that when he used water in the boiler purged of air by long boiling, nothing that was very sensibly inferior to the pressure of the atmosphere on the piston could hinder it from coming quite down to the bottom of the cylinder. This alone was gaining a great deal, for in most engines the remaining elasticity of the steam was not less than one-eighth of the atmospheric pressure, and therefore took away one-eighth of the power of the engine.

Having gained this capital point, Mr Watt found many difficulties to struggle with before he could get the machine to continue its motion. The water produced from the condensed steam, and the air which was extricated from it, or which penetrated through unavoidable leaks, behaved to accumulate in the condensing vessel, and could not be voided in any way similar to that adopted in Newcomen's engine. He took another method: He applied pumps to extract both, which were worked by the great beam. The contrivance is easy to any good mechanic; only we must observe, that the piston of the water-pump must be under the surface of the water in the condenser, that the water may enter the pump by its own weight, because there is no atmospherical pressure there to force it in. We must also observe, that a considerable force is necessarily expended here, because, as there is but one stroke for rarefying the air, and this rarefaction must be nearly complete, the air-pump must be of large dimensions, and its piston must act against the whole pressure of the atmosphere. Mr Watt, however, found that this force could be easily spared from his machine, already so much improved in respect of power.

Thus has the steam-engine received a very considerable improvement. The cylinder may be allowed to remain very hot; nay, boiling hot, and yet the condensation be completely performed. The only elastic steam that now remains is the small quantity in the pipe of communication. Even this small quantity Mr Watt at last got rid of, by admitting a small jet of cold water up this pipe to meet the steam in its passage to the condenser. This both cooled this part of the apparatus in a situation where it was not necessary to warm it again, and it quickened the condensation. He found at last that the small pipe of communication was of itself sufficiently large for the condensation, and that no separate vessel, under the name of condenser, was necessary. This circumstance shows the prodigious rapidity of the condensation. We may add, that unless this had been the case, his improvement would have been vastly diminished; for a large condenser would have required a much larger air-pump, which would have expended much of the power of the engine. By these means the vacuum below the piston is greatly improved: for it will appear clear to any person who understands the subject, that as long as any part of the condenser is kept of a low temperature, it will abstract and condense the vapour from the warmer parts, till the whole acquires the elasticity corresponding to the coldest part. By the same means much of the waste is prevented, because the cylinder is never cooled much below the boiling temperature. Many engines have been erected by Mr Watt in this form, and their performance gave universal satisfaction.

We have contented ourselves with giving a very slight description without a figure of this improved engine, because we imagine it to be of very easy comprehension, and because it is only a preparation for still greater improvements, which, when understood, will at the same time leave no part of this more simple form unexplained.

During the progress of these improvements Mr Watt made many experiments on the quantity and density of the steam of boiling water. These fully convinced him that although he had greatly diminished the waste of the steam, a great deal yet remained, and that the steam of steam expended during the rise of the piston was at least three times more than what would fill the cylinder. The cause of this was very apparent. In the subsequent descent of the piston, covered with water much below the boiling temperature, the whole cylinder was necessarily cooled and exposed to the air. Mr Watt's fertile genius immediately suggested to him the expedient of employing the elasticity of the steam from the boiler to impel the piston down the cylinder, in place of the pressure of the atmosphere; and thus he restored the engine to its first principles, making it an engine really moved by steam. As this is a new epoch in its history, we shall be more particular in the description; at the fame fame time still restricting ourselves to the essential circumstances, and avoiding every peculiarity which is to be found in the prodigious varieties which Mr Watt has introduced into the machines which he has erected, every individual of which has been adapted to local circumstances, or diversified by the progress of Mr Watt's improvements.

Let A (fig. 9.) represent the boiler. This has received great improvements from his complete acquaintance with the procedure of nature in the production of steam. In some of his engines the fuel has been placed in the midst of the water, surrounded by an iron or copper vessel, while the exterior boiler was made of wood, which transmits, and therefore wastes the heat very slowly. In others, the flame not only plays round the whole outside, as in common boilers, but also runs along several flues which are conducted through the midst of the water. By such contrivances the fire is applied to the water in a most extensive surface, and for a long time, so as to impart to it the greatest part of its heat. So skilfully was it applied in the Albion mills, that although it was perhaps the largest engine in the kingdom, its unconsumed smoke was inferior to that of a very small brew-house. In this second engine of Mr Watt, the top of the cylinder is shut up by a strong metal plate g h, in the middle of which is a collar or box of leathers k l, formed in the usual manner of a jack-head pump, through which the piston rod PD, nicely turned and polished, can move up and down, without allowing any air to pass by its sides. From the dome of the boiler proceeds a large pipe BCIOQ, which, after reaching the cylinder with its horizontal part BC, descends parallel to its side, sending off two branches, viz. IM to the top of the cylinder, and ON to its bottom. At I is a puppet valve opening from below upwards. At L, immediately below this branch, there is a similar valve, also opening from below upwards. The pipe descends to Q, near the bottom of a large cistern c d e f, filled with cold water constantly renewed. The pipe is then continued horizontally along the bottom of this cistern (but not in contact), and terminates at R in a large pump ST. The piston S has clack valves opening upwards, and its rod S s, passing through a collar of leathers at T, is suspended by a chain to a small arch head on the outer arm of the beam. There is a valve R in the bottom of this pump, as usual, which opens when pressed in the direction QR, and shuts against a contrary pressure. This pump delivers its contents into another pump XY, by means of the small pipe X, which proceeds from its top. This second pump has a valve at X, and a clack in its piston Z as usual, and the piston rod Z z is suspended from another arch head on the outer arm of the beam. The two valves I and L are opened and shut by means of spanners and handles, which are put in motion by a plug frame, in the same manner as in Newcomen's engine.

Lastly, there may be observed a crooked pipe a b o, which enters the upright pipe laterally a little above Q. This has a small jet hole at o; and the other end a, which is considerably under the surface of the water of the condensing cistern, is covered with a puppet valve v, whose long stalk v u rises above the water, and may be raised or lowered by hand or by the plug beam. The valves R and X, and the clacks in the pistons S and Z, are opened or shut by the pressure to which they are immediately exposed.

This figure is not an exact copy of any of Mr Watt's engines, but has its parts so disposed that all may come distinctly into view, and exactly perform their various functions. It is drawn in its quietest position, the outer end of the beam preponderating by the counter weight, and the piston P at the top of the cylinder, and the pistons S and Z in their lowest situations.

In this situation let us suppose that a vacuum is (by any means) produced in all the space below the piston, the valve I being shut. It is evident that the valve R will also be shut, as also the valve v. Now let the valve I be opened. The steam from the boiler, as elastic as common air, will rush into the space above the piston, and will exert on it a pressure as great as that of the atmosphere. It will therefore press it down, raise the outer end of the beam, and cause it to perform the same work as an ordinary engine.

When the piston P has reached the bottom of the cylinder, the plug frame shuts the valve I, and opens L. By so doing the communication is open between the top and bottom of the cylinder, and nothing hinders the steam which is above the piston from going along the passage MLON. The piston is now equally affected on both sides by the steam, even though a part of it is continually condensed by a cylinder, and in the pipe IOQ. Nothing therefore hinders the piston from being dragged up by the counter weight, which acts with its whole force, undiminished by any remaining unbalanced elasticity of steam. Here therefore this form of the engine has an advantage (and by no means a small one) over the common engines, in which a great part of the counter weight is expended in overcoming unbalanced atmospheric pressure.

Whenever the piston P arrives at the top of the cylinder, the valve L is shut by the plug frame, and the valves I and v are opened. All the space below the piston is at this time occupied by the steam which came from the upper part of the cylinder. This being a little wafted by condensation, is not quite a balance for the pressure of the atmosphere. Therefore, during the ascent of the piston, the valve R was shut, and it remains so. When, therefore, the valve v is opened, the cold water of the cistern must spout up through the hole o, and condense the steam. To this must be added the coldness of the whole pipe OQS. As fast as it is condensed, its place is supplied by steam from the lower part of the cylinder. We have already remarked, that this successive condensation is accomplished with astonishing rapidity. In the mean time steam from the boiler passes on the upper surface of the piston. It must therefore descend as before, and the engine must perform a second working stroke.

But in the mean time the injection water lies in the bottom of the pipe OQR, heated to a considerable degree by the condensation of the steam; also a quantity of air has been disengaged from it and from the water in the boiler. How is this to be discharged?—This is the office of the pumps ST and XY. The capacity of ST is very great in proportion to the space in which the air and water are lodged. When, therefore, the piston S has got to the top of its course, there must be a vacuum in the barrel of this pump, and the water and air must open the valve R and come into it. When the piston S comes down again in the next returning stroke, this water and air gets through the valve of the piston; and in the next working stroke they are discharged by the piston into the pump XY, and raised by its piston. The air escapes at Y, and as much of the water as is necessary is delivered into the boiler by a small pipe Yg to supply its waste. It is a matter of indifference whether the pistons S and Z rise with the outer or inner end of the beam, but it is rather better that they rise with the inner end. They are otherwise drawn here, in order to detach them from the rest and show them more distinctly.

Such is Mr Watt's second engine. Let us examine its principles, that we may see the causes of its avowed and great superiority over the common engines.

We have already seen one ground of superiority, the full operation of the counter weight. We are authorised by careful examination to say, that in the common engines at least one-half of the counter weight is expended in counteracting an unbalanced prelure of the air on the piston during its ascent. In many engines, which are not the worst, this extends to \( \frac{1}{3} \)th of the whole pressure. This is evident from the examination of the engine at Montrelaix by Boffut. This makes a very great counter weight necessary, which exhausts a proportional part of the moving force,

But the great advantage of Mr Watt's form is the almost total annihilation of the waste of steam by condensation in the cylinder. The cylinder is always boiling hot, and therefore perfectly dry. This must be evident to any person who understands the subject. By the time that Mr Watt had completed his improvements, his experiments on the production of steam had given him a pretty accurate knowledge of its density; and he found himself authorised to say, that the quantity of steam employed did not exceed twice as much as would fill the cylinder, so that not above one-half was unavoidably wasted. But before he could bring the engine to this degree of perfection, he had many difficulties to overcome: He inclosed the cylinder in an outer wooden case at a small distance from it. This diminished the expense of heat by communication to surrounding bodies. Sometimes he allowed the steam from the boiler to occupy this interval. This undoubtedly prevented all dissipation from the inner cylinder; but in its turn it diffused much heat by the outer case, and a very sensible condensation was observed between them. This has occasioned him to omit this circumstance in some of his best engines. We believe it was omitted in the Albion mills.

The greatest difficulty was to make the great piston tight. The old and effectual method, by water lying on it, was inadmissible. He was therefore obliged to have his cylinders most nicely bored, perfectly cylindrical, and finely polished; and he made numberless trials of different soft substances for packing his piston, which should be tight without enormous friction, and which should long remain so, in a situation perfectly dry, and hot almost to burning.

After all that Mr Watt has done in this respect, he thinks that the greatest part of the waste of steam which he still perceives in his engines arises from the unavoidable escape by the sides of the piston during its descent.

But the fact is, that an engine of this construction, of the same dimensions with a common engine, making the same number of strokes of the same extent, does not consume above one-fourth part of the fuel that is consumed by the best engines of the common form. It is also a very fortunate circumstance, that the performance of the engine is not immediately destroyed, nor indeed sensibly diminished, by a small want of tightness in the piston. In the common engine, if air get in, in this way, it immediately puts a stop to the work; but although even a considerable quantity of steam get past the piston during its descent, the rapidity of condensation is such, that hardly any diminution of pressure can be observed.

Mr Watt's penetration soon discovered another most valuable property of this engine. When an engine of the common form is erected, the engineer must make an accurate estimate of the work to be performed, and must proportion his engine accordingly. He must be careful that it be fully able to execute its task; but its power must not exceed its load in any extravagant degree. This would produce a motion which is too rapid, and which, being alternately in opposite directions, would occasion jolts which no building or machinery could withstand. Many engines have been shattered by the pumps drawing air, or a pump-rod breaking; by which accidents the steam-piston descends with such rapidity that every thing gives way. But in most operations of mining, the task of the engine increases, and it must be so constructed at first as to be able to bear this addition. It is very difficult to manage an engine that is much superior to its task; and the easiest way is, to have it almost full loaded, and to work it only during a few hours each day, and allow the pit water to accumulate during its repose. This increases the first cost, and wastes fuel during the inaction of the engine.

But this new engine can at all times be exactly fitted (at least during the working stroke) to the load of work can away that then happens to be on it. We have only to add, that the engine may be equal to twice its task, if the which has admitted above the cylinder be equal to that of pens to be common boiling water; but when once the ebullition on it is fairly commenced, and the whole air expelled from all parts of the apparatus, it is evident, that by damping the fire, steam of half this elasticity may be continually supplied, and the water will continue boiling although its temperature does not exceed 185° of Fahrenheit's thermometer. This appears by inspecting our table of vaporous elasticity, and affords another argument for rendering that table more accurate by new experiments. We hope that Mr Watt will not withhold from the public the knowledge which he has acquired on this subject. It may very possibly result from an accurate investigation, that it would be advisable to work our steam-engines with weak steams, and that the diminution of work may be more than compensated by the diminution of fuel. It is more probable indeed, and it is Mr Watt's opinion, that the contrary is the case, and that it is much more economical to employ great heats. At any rate, the decision of this question is of great importance for improving the engine; and we fee, in the mean time, that the engine can at all times be fitted so as to perform its task with a moderate and manageable motion, and that as the task increases we can increase the power of the engine. But the method now proposed has a great inconvenience. While the steam is weaker than the atmosphere, there is an external force tending to squeeze in the fides and bottom of the boiler. This could not be rectified when the difference is considerable, and common air would rush in through every crevice of the boiler and soon choke the engine: it must therefore be given up.

But the same effect will be produced by diminishing the passage for the steam into the cylinder. For this purpose, the puppet valve by which the steam enters the cylinder was made in the form of a long taper spigot, and it was lodged in a cone of the same shape; consequently the passage could be enlarged or contracted at pleasure by the distance to which the inner cone was drawn up.

In this way several engines were constructed, and the general purpose of suiting the power of the engine to its task was completely answered: but (as the mathematical reader will readily perceive) it was extremely difficult to make this adjustment precise and constant. In a great machine like this going by jerks, it was hardly possible that every successive motion of the valve should be precisely the same. This occasioned very sensible irregularities in the motion of the engine, which increased and became hazardous when the joints worked loose by long use.

Mr Watt's genius, always fertile in resources, found out a complete remedy for all these inconveniences. Making the valve of the ordinary form of a puppet clack, he adjusted the button of its stalk or tail so that it should always open full to the same height. He then regulated the pins of the plug-frame, in such a manner that the valve should shut the moment that the piston had descended a certain proportion (suppose one-fourth, one-third, one-half, &c.) of the cylinder. So far the cylinder was occupied by steam as elastic as common air. In pressing the piston farther down, it behoved the steam to expand, and its elasticity to diminish. It is plain that this could be done in any degree we please, and that the adjustment can be varied in a minute, according to the exigency of the case, by moving the plug pins.

In the mean time, it must be observed, that the pressure on the piston is continually changing, and consequently the accelerating force. The motion therefore will no longer be uniformly accelerated: it will approach much faster to uniformity; nay, it may be retarded, because although the pressure on the piston at the beginning of the stroke may exceed the resistance of the load, yet when the piston is near the bottom the resistance may exceed the pressure. Whatever may be the law by which the pressure on the piston varies, an ingenious mechanic may contrive the connecting machinery in such a way that the chains or rods at the outer end of the beam shall continually exert the same pressure, or shall vary their pressure according to any law he finds most convenient. It is in this manner that the watchmaker, by the form of the fusee, produces an equal pressure on the wheel-work by means of a very unequal action of the main-spring. In like manner, by making the outer arch heads portions of a proper spiral instead of a circle, we can regulate the force of the beam at pleasure.

Thus we see how much more manageable an engine is in this form than Newcomen's was, and also more easily investigated in respect of its power in its various positions. The knowledge of this last circumstance was of mighty consequence, and without it no notion could be formed of what it could perform. This suggested to Mr Watt the use of the barometer communicating with the cylinder; and by the knowledge acquired by these means has the machine been so much improved by its ingenious inventor.

We must not omit in this place one deduction made by Mr Watt from his observations, which may be called a discovery of great importance in the theory of the engine.

Let ABCD (fig. 10.) represent a section of the cylinder of a steam-engine, and EF the surface of its piston. Let us suppose that the steam was admitted of great while EF was in contact with AB, and that as soon as it had pressed it down to the situation EF the steam cock is shut. The steam will continue to press it down, and as the steam expands its pressure diminishes. We Fig. 10. may express its pressure (exerted all the while the piston moves from the situation AB to the situation EF) by the line EF. If we suppose the elasticity of the steam proportional to its density, as is nearly the case with air, we may express the pressure on the piston in any other position, such as KL or DC, by K' and Dc, the ordinates of a rectangular hyperbola F/c, of which AE, AB are the asymptotes, and A the centre. The accumulated pressure during the motion of the piston from EF to DC will be expressed by the area EFcDE, and the pressure during the whole motion by the area ABFcDA.

Now it is well known that the area EFcDE is equal to ABFc multiplied by the hyperbolic logarithm of \( \frac{AD}{AE} = L \cdot \frac{AD}{AE} \), and the whole area ABFcDA is

\[ ABFc \times \left( 1 + L \cdot \frac{AD}{AE} \right). \]

Thus let the diameter of the piston be 24 inches, and the pressure of the atmosphere on a square inch be 14 pounds; the pressure on the piston is 6333 pounds. Let the whole stroke be 6 feet, and let the steam be stopped when the piston has descended 18 inches, or 1.5 feet. The hyperbolic logarithm of \( \frac{6}{1.5} \) is 1.3862943. Therefore the accumulated pressure ABFcDA is \( 6333 \times 2.3862943 = 15114 \) pounds.

As few professional engineers are possessed of a table of hyperbolic logarithms, while tables of common logarithms are or should be in the hands of every person who is much engaged in mechanical calculations, let the following method be practised. Take the common logarithm of \( \frac{AD}{AE} \), and multiply it by 2.3026; the product is the hyperbolic logarithm of \( \frac{AD}{AE} \).

The accumulated pressure while the piston moves from AB to EF is 6333 × 1, or simply 6333 pounds. Therefore the steam while it expands into the whole cylinder adds a pressure of 8781 pounds.

Suppose that the steam had got free admission during the whole descent of the piston, the accumulated pressure would have been 6333 × 4, or 25332 pounds.

Here Mr Watt observed a remarkable result. The steam expended in this case would have been four times greater greater than when it was flopped at one-fourth, and yet the accumulated pressure is not twice as great, being nearly five-thirds. One-fourth of the steam performs nearly three-fifths of the work, and an equal quantity performs more than twice as much work when thus admitted during one-fourth of the motion.

This is a curious and an important information, and the advantage of this method of working a steam-engine increases in proportion as the steam is sooner flopped; but the increase is not great after the steam is rarefied four times. The curve approaches near to the axis, and small additions are made to the area. The expense of such great cylinders is considerable, and may sometimes compensate this advantage.

<table> <tr> <th>Let the steam be stopped at</th> <th>Its performance is mult.</th> </tr> <tr> <td>\( \frac{1}{2} \)</td> <td>-</td> <td>1.7</td> </tr> <tr> <td>\( \frac{1}{3} \)</td> <td>-</td> <td>2.1</td> </tr> <tr> <td>\( \frac{1}{4} \)</td> <td>-</td> <td>2.4</td> </tr> <tr> <td>\( \frac{1}{5} \)</td> <td>-</td> <td>2.6</td> </tr> <tr> <td>\( \frac{1}{6} \)</td> <td>-</td> <td>2.8</td> </tr> <tr> <td>\( \frac{1}{7} \)</td> <td>-</td> <td>3.</td> </tr> <tr> <td>\( \frac{1}{8} \)</td> <td>-</td> <td>3.2</td> </tr> <tr> <td>&amp;c.</td> <td>&amp;c.</td> <td>&amp;c.</td> </tr> </table>

It is very pleasing to observe so many unlooked-for advantages resulting from an improvement made with the sole view of lessening the waste of steam by condensation. While this purpose is gained, we learn how to husband the steam which is not thus wasted. The engine becomes more manageable, and is more easily adapted to every variation in its task, and all its powers are more easily computed.

The active mind of its ingenious inventor did not stop here: It had always been matter of regret that one-half of the motion was unaccompanied by any work. It was a very obvious thing to Mr Watt, that as the steam admitted above the piston preflled it down, so steam admitted below the piston preflled it up with the same force, provided that a vacuum were made on its upper side. This was easily done, by connecting the lower end of the cylinder with the boiler and the upper end with the condenser.

Fig. 11. is a representation of this construction exactly copied from Mr Watt's figure accompanying his specification. Here BB is a section of the cylinder, surrounded at a small distance by the cafe IIII. The section of the piston A, and the collar of leathers which embraces the piston rod, gives a distinct notion of its construction, of the manner in which it is connected with the piston-rod, and how the packing of the piston and collar contributes to make all tight.

From the top of the cylinder proceeds the horizontal pipe. Above the letter D is observed the seat of the steam valve, communicating with the box above it. In the middle of this may be observed a dark shaded circle. This is the mouth of the upper branch of the steam pipe coming from the boiler. Beyond D, below the letter N, is the seat of the upper condensing valve. The bottom of the cylinder is made spherical, fitting the piston, so that they may come into entire contact. Another horizontal pipe proceeds from this bottom. Above the letter E is the seat of the lower steam valve, opening into the valve box. This box is at the extremity of another steam pipe marked C, which branches off from the upper horizontal part, and descends obliquely, coming forward to the eye. The lower part is represented as cut open, to show its interior conformation. Beyond this steam valve, and below the letter F, may be observed the seat of the lower condensing valve. A pipe descends from hence, and at a small distance below unites with another pipe GG, which comes down from the upper condensing valve N. These two eduction-pipes thus united go downwards, and open at L into a rectangular box, of which the end is seen at L. This box goes backward from the eye, and at its farther extremity communicates with the air-pump K, whose piston is here represented in section with its butterfly valves. The piston delivers the water and air laterally into another rectangular box M, darkly shaded, which box communicates with the pump I. The piston-rods of this and of the air-pump are suspended by chains from a small arch head on the inner arm of the great beam. The lower part of the eduction-pipe, the horizontal box L, the air-pump K, with the communicating box M between it and the pump I, are all immersed in the cold water of the condensing cistern. The box L is made flat, broad, and shallow, in order to increase its surface and accelerate the condensation. But that this may be performed with the greatest expedition, a small pipe H, open below (but occasionally flopped by a plug valve), is inserted laterally into the eduction-pipe G, and then divides into two branches; one of which reaches within a foot or two of the upper valve N, and the other approaches as near to the valve F.

As it is intended by this construction to give the piston a strong impulse in both directions, it will not be proper to suspend its rod by a chain from the great beam; for it must not only pull down that end of the beam, but also push it upwards. It may indeed be suspended by double chains like the pistons of the engines for extinguishing fires; and Mr Watt has accordingly done so in some of his engines. But in his drawing from which this figure is copied, he has communicated the force of the piston to the beam by means of a toothed rack OO, which engages or works in the toothed sector QQ on the end of the beam. The reader will understand, without any farther explanation, how the impulse given to the piston in either direction is thus transmitted to the beam without diminution. The fly XX, with its pinion Y, which also works in the toothed arch QQ, may be supposed to be removed for the present, and will be considered afterwards.

We shall take the present opportunity of describing Mr Watt's method of communicating the force of the steam-engine to any machine of the rotary kind. VV represents the rim and arms of a very large and heavy metalline fly. On its axis is the concentric toothed wheel U. There is attached to the end of the great beam a strong and stiff rod TT, to the lower end of which a toothed wheel W is firmly fixed by two bolts, so that it cannot turn round. This wheel is of the same size and in the same vertical plane with the wheel U; and an iron link or strap (which cannot be seen here, because it is on the other side of the two wheels) connects the centres of the two wheels, so that the one cannot quit the other. The engine being in the position represented in the figure, suppose the fly to be turned once round by any external force in the direction of the darts. It is plain, that since the toothed wheels cannot quit each other, being kept together by STEAM ENGINE.

Its principle and mode of operation may be clearly conceived as follows.

Let A (fig. 7.) represent a great boiler properly built in a furnace. At a small height above it is a cylinder CBBC of metal, bored very truly and smoothly. The boiler communicates with this cylinder by means of the throat or steam-pipe NQ. The lower aperture of this pipe is shut by the plate N, which is ground very flat, so as to apply very accurately to the whole circumference of the orifice. This plate is called the regulator or steam-cock, and it turns horizontally round an axis b a which passes through the top of the boiler, and is nicely fitted to the socket, like the key of a cock, by grinding. The upper end of this axis is furnished with a handle b T.

A piston P is suspended in this cylinder, and made air-tight by a packing of leather or soft rope, well filled with tallow; and, for greater security, a small quantity of water is kept above the piston. The piston-rod PD is suspended by a chain which is fixed to the upper extremity F of the arched head FD of the great lever or WORKING BEAM HK, which turns on the gudgeon O. There is a similar arched head EG at the other end of the beam. To its upper extremity E is fixed a chain carrying the pump-rod XL, which raises the water from the mine. The load on this end of the beam is made to exceed considerably the weight of the piston P at the other extremity.

At some small height above the top of the cylinder is a cistern W, called the INJECTION CISTERN. From this descends the INJECTION PIPE ZSR, which enters the cylinder through its bottom, and terminates in a small hole R, or sometimes in a nozzle pierced with many smaller holes diverging from a centre in all directions. This pipe has at S a cock called the INJECTION COCK, fitted with a handle V.

At the opposite side of the cylinder, a little above its bottom, there is a lateral pipe, turning upwards at the extremity, and there covered by a clack-valve f, called the SHIFTING VALVE, which has a little dish round it to hold water for keeping it air-tight.

There proceeds also from the bottom of the cylinder a pipe d e g h (passing behind the boiler), of which the lower end is turned upwards, and is covered with a valve h. This part is immersed in a cistern of water Y, called the HOT WELL, and the pipe itself is called the REDUCTION PIPE. Lastly, the boiler is furnished with a safety-valve called the PUPPET CLACK (which is not represented in this sketch for want of room), in the same manner as Savary's engine. This valve is generally loaded with one or two pounds on the square inch, so that it allows the steam to escape when its elasticity is one-tenth greater than that of common air. Thus all risk of bursting the boiler is avoided, and the pressure outwards is very moderate; to allo is the heat. For, by inspecting the table of vaporous elasticity, we see that the heat corresponding to 32 inches of elasticity is only about 216° degrees of Fahrenheit's thermometer.

These are all the essential parts of the engine, and are here drawn in the most simple form, till our knowledge of their particular offices shall show the propriety of the peculiar forms which are given to them. Let us now see how the machine is put in motion, and what is the nature of its work.

The water in the boiler being supposed to be in a state of strong ebullition, and the steam issuing by the safety-valve, let us consider the machine in a state of rest, having both the steam-cock and injection cock shut. The resting position or attitude of the machine must be such as appears in sketch, the pump rods preponderating, and the great piston being drawn up to the top of the cylinder. Now open the steam cock by turning the handle T of the regulator. The steam from the work-boiler will immediately rush in, and flying all over the cylinder, will mix with the air. Much of it will be condensed by the cold surface of the cylinder and piston, and the water produced from it will trickle down the sides, and run off by the eduction-pipe. This condensation and waste of steam will continue till the whole cylinder and piston be made as hot as boiling water. When this happens, the steam will begin to open the shifting-valve f, and issue through the pipe; slowly at first and very cloudy, being mixed with much air. The blast at f will grow stronger by degrees, and more transparent, having already carried off the greatest part of the common air which filled the cylinder. We supposed that the air was boiling briskly, so that the steam was issuing by the safety-valve which is in the top of the boiler, and through every crevice. The opening of the steam-cock puts an end to this at once, and it has sometimes happened that the cold cylinder abstracts the steam from the boiler with such astonishing rapidity, that the prelude of the atmosphere has burst up the bottom of the boiler. We may here mention an accident of which we were witnesses, which also shows the immense rapidity of the condensation. The boiler was in a frail shed at the side of the engine-house; a flood of snow from the top of the house fell down and broke through the roof of the shed, and was scattered over the head of the boiler, which was of an oblong or oval shape. In an instant the sides of it were squeezed together by the pressure of the atmosphere.

When the manager of the engine perceives that not only the blast at the shifting valve is strong and steady, but that the boiler is now fully supplied with steam of a proper strength, appearing by the renewal of the discharge at the safety-valve, he shuts the steam-cock, and opens the injection-cock S by turning its handle V. The pressure of the column of water in the injection-pipe ZS immediately forces some water through the spout R. This coming in contact with the pure vapour which now fills the cylinder, condenses it, and thus makes a partial void, into which the more distant steam immediately expands, and by expanding collapses (as has been already observed). What remains in the cylinder no longer balances the atmospherical preasure on the surface of the water in the injection cistern, and therefore the water spouts rapidly through the hole R by the joint action of the column ZS, and the unbalanced preasure of the atmosphere; at the same time the shifting-valve f, and the eduction-valve h, are shut by the unbalanced pressure of the atmosphere. The velocity of the injection water must therefore rapidly increase, and the jet will dash (if single) against the bottom of the piston, and be scattered through the whole capacity of the cylinder. In a very short space of time, therefore, the condensation of the steam becomes universal, and the elasticity of what remains is almost nothing. The whole pressure of the atmosphere is exerted in the upper surface of the piston, while there is hardly any on its underside. Therefore, if the load on the outer end E of the working beam is inferior to this pressure, it must yield to it. The piston P must descend, and the pump piston L must ascend, bringing along with it the water of the mine, and the motion must continue till the great piston reaches the bottom of the cylinder; for it is not like the motion which would take place in a cylinder of air rarefied to the same degree. In this last case, the impelling force would be continually diminished, because the capacity of the cylinder is diminished by the descent of the piston, and the air in it is continually becoming more dense and elastic. The piston would stop at a certain height, where the elasticity of the included air, together with the load at E, would balance the atmospherical pressure on the piston. But when the contents of the cylinder are pure vapour, and the continued stream of injected cold water keeps down its temperature to the same pitch as at the beginning, the elasticity of the remaining steam can never increase by the descent of the piston, nor exceed what corresponds to this temperature. The impelling or accelerating force therefore remains the same, and the descent of the piston will be uniformly accelerated, if there is not an increase of resistance arising from the nature of the work performed by the other end of the beam. This circumstance will come under consideration afterwards, and we need not attend to it at present. It is enough for our present purpose to see, that if the cylinder has been completely purged of common air before the steam-cock was shut, and if none has entered since, the piston will descend to the very bottom of the cylinder. And this may be frequently observed in a good steam-engine, where every part is air-tight. It sometimes happens, by the pit-pump drawing air, or some part of the communication between the two strains giving way, that the piston comes down with such violence as to knock out the bottom of the cylinder with the blow.

The only observation which remains to be made on the motion of the piston in descending is, that it does not begin at the instant the injection is made. The piston was kept at the top by the preponderancy of the outer end of the working beam, and it must remain there till the difference between the elasticity of the steam below it and the pressure of the atmosphere exceeds this preponderancy. There must therefore be a small space of time between the beginning of the condensation and the beginning of the motion. This is very small, not exceeding the third or the fourth part of a second; but it may be very distinctly observed by an attentive spectator. He will see, that the instant the injection cock is opened, the cylinder will sensibly rise upwards a little by the pressure of the air on its bottom. Its whole weight is not nearly equal to this pressure; and instead of its being necessary to support it by a strong floor, we must keep it down by strong joints loaded by heavy walls. It is usual to frame these joints into the posts which carry the axis of the working-beam, and are therefore loaded with the whole strain of the machine. This rising of the cylinder shows the instantaneous commencement of the condensation; and it is not till after this has been distinctly observed that the piston is seen to start, and begin to descend.

When the manager sees the piston as low as he thinks proper, he shuts the injection-cock, and opens the steam-cock. The steam has been accumulating above the water in the boiler during the whole time of the piston's descent, and is now rushing violently through the puppet clack. The moment, therefore, that the steam-cock is opened, it rushes violently into the cylinder, having an elasticity greater than that of the air. It therefore immediately blows open the snifing valve, and allows (at least) the water which had come in by the former injection, and what arose from the condensed steam, to descend by its own weight through the eduction pipe d e g h to open the valve h, and to run out into the hot well. And we must easily see that this water is boiling hot; for while lying in the bottom of the cylinder, it will condense steam till it acquires this temperature, and therefore cannot run down till it condenses no more. There is still a waste of steam at its first admission, in order to heat the inside of the cylinder and the injected water to the boiling temperature: but the space being small, and the whole being already very warm, this is very soon done; and when things are properly constructed, little more steam is wanted than what will warm the cylinder; for the eduction pipe receives the injection water even during the descent of the piston, and it is therefore removed pretty much out of the way of the steam.

This first puff of the entering steam is of great service; it drives out of the cylinder the vapour which it finds there. This is seldom pure watery vapour: all pure water contains a quantity of air in a state of chemical union. The union is but feeble, and a boiling heat is sufficient for disengaging the greatest part of it by increasing its elasticity. It may also be disengaged by simply removing the external pressure of the atmosphere. This is clearly seen when we expose a glass of water in an exhausted receiver. Therefore the small space below the piston contains watery vapour mixed with all the air which had been disengaged from the water in the boiler by ebullition, and all that was separated from the injection water by the diminution of external pressures. All this is blown out of the cylinder by the first puff of steam. We may observe in this place, that waters differ exceedingly in the quantity of air which they hold in a state of solution. All spring water contains much of it: and water newly brought up from deep mines contains a great deal more, because the solution was aided in these situations by great pressures. Such waters sparkle when poured into a glass. It is therefore of great consequence to the good performance of a steam-engine to use water containing little air, both in the boiler and in the injection-cistern. The water of running brooks is preferable to all others, and the freer it is from any saline impregnation it generally contains steam-leafs air. Such engines as are so unfortunately situated, that they are obliged to employ the very water which they have brought up from great depths, are found contain greatly inferior in their performance to others. The little air collected below the piston greatly diminishes the accelerating force, and the expulsion of such a quantity requires a long-continued blast of the best steam at the beginning of every stroke. It is advisable to keep such water in a large shallow pond for a long while before using it.

Let us now consider the state of the piston. It is evident that it will start or begin to rise the moment piston rises, the steam-cock is opened; for at that instant the excess of atmospheric pressure, by which it was kept down in opposition to the preponderancy of the outer end of the beam, is diminished. The piston is therefore dragged upwards, and it will rise even although the steam which is admitted be not so elastic as common air. Suppose the mercury in the barometer to stand at 30 inches, and that the preponderancy at the outer end of the beam is \( \frac{1}{4} \)th of the pressure of the air on the piston, the piston will not rise if the elasticity of the steam is not equal to 30—\( \frac{1}{8} \), that is, to 26.7 inches nearly; but if it is just this quantity, the piston will rise as fast as this steam can be supplied through the steam-pipe, and the velocity of its ascent depends entirely on the velocity of this supply. This observation is of great importance; and it does not seem to have occurred to the mathematicians, who have paid most attention to the mechanism of the motion of this engine. In the mean time, we may clearly see that the entry of the steam depends chiefly on the counter weight at E: for suppose there was none, steam no stronger than air would not enter the cylinder at all; and if the steam be stronger, it will enter only by the excess of its strength. Writers on the steam-engine (and even some of great reputation) familiarly speak of the steam giving the piston a push: But this is scarcely possible. During the rise of the piston the snifting valve is never observed to blow; and we have not heard any well-attested accounts of the piston-chains ever being slackened by the upward pressure of the steam, even at the very beginning of the stroke. During the rising of the piston the steam is (according to the common conception and manner of speaking) sucked in, in the same way that air is sucked into a common syringe or pump when we draw up the piston; for in the steam-engine the piston is really drawn up by the counter weight. But it is still more sucked in, and requires a more copious supply, for another reason. As the piston descended only in consequence of the inside of the cylinder's being sufficiently cooled to condense the steam, this cooled surface must again be presented to the steam during the rise of the piston, and must condense steam a second time. The piston cannot rise another inch till the part of the cylinder which the piston has already quitted has been warmed up to the boiling point, and steam must be expended in this warming. The inner surface of the cylinder is not only of the heat of boiling water while the piston rises, but is also perfectly dry; for the film of water left on it by the ascending piston must be completely evaporated, otherwise it will be condensing steam. That the quantity thus wasted is considerable, appears by the experiments of Mr Beighton. He found that five pints of water were boiled off in a minute, and produced 16 strokes of an engine whose cylinder contained 113 gallons of 282 inches each; and he thence concluded that steam was 2886 times rarer than water. But in no experiment made with scrupulous care on the expansion of boiling water does it appear that the density of steam exceeds \( \frac{1}{10,000} \)th of the density of water. Defaguiers says that it is above 14,000 times rarer than water. We have frequently attempted to measure the weight of steam which filled a very light vessel, which held 1,260 grains of water, and found it always less than one grain; so that we have no doubt of its being much more than 10,000 times rarer than water. This being the case, we may safely suppose that the number of gallons of steam, instead of being 16 times 113, were nearly five times as much; and that only \( \frac{5}{6} \)th was employed in allowing the piston to rise, and the remaining \( \frac{1}{6} \)ths were employed to warm the cylinder. But no distinct experiment shews so great an expansion of water when converted into steam at 212°. Mr Watt never found it under the pressure of the air more than 1800 times rarer than water.

The moving force during the ascent of the piston must be considered as resulting chiefly, if not solely, from the preponderating weight of the pit piston-rods. The office of this is to return the steam-piston to the top of the cylinder, where it may again be pressed down by the air, and make another working stroke by raising the pump-rods. But the counter-weight at E has another service to perform in this use of the engine; namely, to return the pump pistons into their places at the bottom of their respective working barrels, in order that they also may make a working stroke. This requires force independent of the friction and inertia of the moving parts; for each piston must be pushed down through the water in the barrel, which must rise through the piston with a velocity whose proportion to the velocity of the piston is the same with that of the bulk of the piston to the bulk of the perforation through which the water rises through the piston. It is enough at present to mention this in general terms: we shall consider it more particularly afterwards, when we come to calculate the performance of the engine, and to deduce from our acquired knowledge maxims of construction and improvement.

From this general consideration of the ascent of the piston, we may see that the motion differs greatly from the descent. It can hardly be supposed to accelerate, even if the steam in the cylinder were in a moment annihilated. For the resistance to the descent of the piston is the same with the weight of the column of water, which would cause it to flow through the box of the pump piston with the velocity with which it really rises through it, and must therefore increase as the square of that velocity increases; that is, as the square of the velocity of the piston increases. Independent of friction, therefore, the velocity of descent through the water must soon become a maximum, and the motion become uniform. We shall see by and by, that in such a pump as is generally used this will happen in less than the tenth part of a second. The friction of the pump will diminish this velocity a little, and retard the time of its attaining uniformity. But, on the other hand, the supply of steam which is necessary for this motion, being susceptible of no acceleration from its previous motion, and depending entirely on the briskness of the ebullition, an almost instantaneous stop is put to acceleration.

Accordingly, any person who observes with attention the working of a steam-engine, will see that the rise of the piston and descent of the pump-rods is extremely uniform, whereas the working stroke is very sensibly accelerated. Before quitting this part of the subject, and after leaving it should afterwards escape our recollection, we may observe, that the counter-weight is different during the two motions of the pump-rods. While the machine is making a working stroke, it is lifting not only the co-pump-rods. hunn of water in the pump, but the absolute weight of the pistons and piston-rods also; but while the pump-rods are descending, there is a diminution of the counter-weight by the whole weight lost by the immersion of the rod in water. The wooden rods which are generally used, soaked in water, and joined by iron straps, are heavier, and but a little heavier, than water, and they are generally about one-third of the bulk of the water in the pumps.

These two motions complete the period of the operation; and the whole may be repeated by shutting the steam-cock and opening the injection-cock whenever the piston has attained the proper height. We have been very minute in our attention to the different circumstances, that the reader may have a distinct notion of the state of the moving forces in every period of the operation. It is by no means sufficient that we know in general that the injection of cold water makes a void which allows the air to press down the piston, and that the readmission of the steam allows the piston to rise again. This lumping and flowery way of viewing it has long prevented even the philosopher from seeing the defects of the construction, and the methods of removing them.

We now see the great difference between Savary's and Newcomen's engine in respect of principle. Savary's was really an engine which raised water by the force of steam; but Newcomen's raises water entirely by the pressure of the atmosphere, and steam is employed merely as the most expeditious method of producing a void, into which the atmospheric pressure may impel the first mover of his machine. The elasticity of the steam is not the first mover.

We see also the great superiority of this new machine. We have no need of steam of great and dangerous elasticity; and we operate by means of very moderate heats, and consequently with much smaller quantities of fuel; and there is no bounds to the power of this machine. How deep ever a mine may be, a cylinder may be employed of such dimensions that the pressure of the air on its piston may exceed in any degree the weight of the column of water to be raised. And lastly, this form of the machine renders it applicable to almost every mechanical purpose; because a skillful mechanic can readily find a method of converting the reciprocating motion of the working beam into a motion of any kind which may suit his purpose. Savary's engine could hardly admit of such an immediate application, and seems almost restricted to raising water.

Inventions improve by degrees. This engine was first offered to the public in 1705. But many difficulties occurred in the execution, which were removed one by one; and it was not till 1712 that the engine seemed to give confidence in its efficacy. The most exact and unremitting attention of the manager was required, to the precise moment of opening and shutting the cocks; and neglect might frequently be ruinous, by beating out the bottom of the cylinder, or allowing the piston to be wholly drawn out of it. Stops were contrived to prevent both of these accidents; then strings were used to connect the handles of the cocks with the beam, so that they should be turned whenever it was in certain positions. These were gradually changed and improved into detents and catches of different shapes; at last, in 1717, Mr Beighton, a very ingenious and well-informed artist, simplified the whole of these subordinate movements, and brought the machine into the form in which it has continued, without the smallest material change, to the present day. We shall now describe one of these improved engines, copying almost exactly the drawings and description given by Boffet in his Hydrodynamique; these being by far the most accurate and perspicuous of any that have been published.

Fig. 8. No 1. is a perspective view of the boiler cylinder, and all the parts necessary for turning the cock. Fig. 8. No 2. is a vertical section of the same; and the Beighton fame pieces of both are marked with the fame letters of reference.

The rod X of the piston P is suspended from the arch of the working-beam, as was represented in the preceding sketch (fig. 7.). An upright bar of timber FG is also seen hanging by a chain. This is suspended from a concentric arch of the beam, as may be seen also in the sketch at φλ. The bar is called the plug-beam; and it must rise and fall with the piston, but with a slower motion. The use of this plug-beam is to give motion to the different pieces which turn the cocks.

The steam-pipe K is of one piece with the bottom of the cylinder, and rises within it an inch or two, to prevent any of the cold injection water from falling into the boiler. The lower extremity Z of the steam-pipe penetrates the head of the boiler, projecting a little way. A flat plate of brass, in shape resembling a racket or battledore, called the regulator, applies itself exactly to the whole circumference of the steam-pipe, and completely excludes the steam from the cylinder. Being moveable round an upright axis, which is represented by the dotted lines at the side of the steam-pipe in the profile, it may be turned aside by the handle i, No 1. The profile shows in the section of this plate a protuberance in the middle. This rests on a strong flat spring, which is fixed below it athwart the mouth of the steam-pipe. This spring presses it strongly towards the steam-pipe, causing it to apply very close; and this knob slides along the spring, while the regulator turns to the right or left.

We have said that the injection-water is furnished from a cistern placed above the cylinder. When the cistern cannot be supplied by pipes from some more elevated source, its water is raised by the machine itself. A small lifting pump i k (fig. 7.), called the jack-head or jacquette, is worked by a rod γ, suspended from a concentric arch μ near the outer end of the working beam. This forces a small portion of the pit water along the rising pipe i LM into the injection cistern.

In fig. 8. No 1. and 2. the letters QM 3' represent the pipe which brings down the water from the injection cistern. This pipe has a cock at R to open or shut the passage of this water. It spouts through the jet 3', and dashing against the bottom of the piston, it is dispersed into drops, and scattered through the whole capacity of the cylinder, so as to produce a rapid condensation of the steam.

An upright post A may be observed in the perspective view of the cylinder, &c. This supports one end B of a horizontal iron axis BC. The end C is supported by a similar post, of which the place only is marked by the dotted lines A, that the pieces connected ted with this axis may not be hid by it. A kind of stirrup \(a b c d\) hangs from this axis, supported by the hooks \(a\) and \(d\). This stirrup is crossed near the bottom by a round bolt or bar \(e\), which passes through the eyes or rings that are at the ends of the horizontal fork \(h f g\), whose long tail \(h\) is double, receiving between its branches the handle \(i\) of the regulator. It is plain from this construction, that when the stirrup is made to vibrate round the horizontal axis \(BC\), on which it hangs freely by its hooks, the bolt \(e\) must pull or push the long fork \(h f g\) backwards and forwards horizontally, and by so doing will move the regulator round its axis by means of the handle \(i\). Both the tail of the fork and the handle of the regulator are pierced with several holes, and a pin is put through them which unites them by a joint. The motion of the handle may be increased or diminished by choosing for the joint a hole near to the axis or remote from it; and the exact position at which the regulator is to stop on both sides is determined by pins fixed in the horizontal bar on which the end of the handle appears to rest.

This alternate motion of the regulator to the right and left is produced as follows: There is fixed to the axis \(BC\) a piece of iron \(o k l\), called the \(Y\), on account of its resemblance to that letter of the alphabet inverted. The stalk \(o\) carries a heavy lump \(p\) of lead or iron; and a long leather strap \(q p r\) is fastened to \(p\) by the middle, and the two ends are fastened to the beam above it, in such a manner that the lump may be alternately caught and held up to the right and left of the perpendicular. By adjusting the length of the two parts of the strap, the \(Y\) may be stopped in any desired position. The two claws \(k\) and \(l\) spread out from each other, and from the line of the stalk, and they are of such length as to reach the horizontal bolt \(e\), which crosses the stirrup below, but not to reach the bottom of the fork \(h f g\). Now suppose the stirrup hanging perpendicularly, and the stalk of the \(Y\) also held perpendicular; carry it a little outward from the cylinder, and then let it go. It will tumble farther out by its weight, without affecting the stirrup till the claw \(l\) strikes on the horizontal bolt \(e\), and then it pushes the stirrup and the fork towards the cylinder, and opens the regulator. It sets it in motion with a smart jerk, which is an effectual way of overcoming the cohesion and friction of the regulator with the mouth of the steam-pipe. This push is adjusted to a proper length by the strap \(q p\), which stops the \(Y\) when it has gone far enough. If we now take hold of the stalk of the \(Y\), and move it up to the perpendicular, the width between its claws is such as to permit this motion, and something more, without affecting the stirrup. But when pulled still nearer to the cylinder, it tumbles towards it by its own weight, and then the claw \(k\) strikes the bolt \(e\), and drives the stirrup and fork in the opposite direction, till the lump \(p\) is caught by the strap \(r p\), now stretched to its full length, while \(q p\) hangs slack. Thus by the motion of the \(Y\) the regulator is opened and shut. Let us now see how the motion of the \(Y\) is produced by the machine itself. To the horizontal axis \(BC\) are attached two spanners or handles \(m\) and \(n\). The spanner \(m\) passes through a long slit in the plug-beam, and is at liberty to move upwards or downwards by its motion round the axis \(BC\). A pin \(\pi\) which goes through the plug-beam catches hold of \(m\) when the beam rises along with the piston; and the pin is so placed, that when the beam is within an inch or two of its highest rise, the pin has lifted \(m\) and thrown the stalk of the \(Y\) past the perpendicular. It therefore tumbles over with great force, and gives a smart blow to the fork, and immediately shuts the regulator. By this motion the spanner \(m\) is removed out of the neighbourhood of the plug-beam. But the spanner \(n\), moving along with it in the same direction, now comes into the way of the pins of the plug-beam. Therefore, when the piston descends again by the condensation of the steam in the cylinder, a pin marked \(\varphi\) in the side of the plug-beam catches hold of the tail of the spanner \(n\), and by pressing it down raises the lump on the stalk of the \(Y\) till it passes the perpendicular, and it then falls down, outwards from the cylinder, and the claw \(l\) again drives the fork in the direction \(h i\), and opens the steam valve. This opening and shutting of the steam valve is executed in the precise moment that is proper, by placing the pins \(\pi\) and \(\varphi\) at a proper height of the plug-beam. For this reason, it is pierced through with a great number of holes, that the places of these pins may be varied at pleasure. This, and a proper curvature of the spanners \(m\) and \(n\), make the adjustment as nice as we please.

The injection-cock \(R\) is managed in a similar manner. On its key may be observed a forked arm \(s t\), like a crab's claw; at a little distance above it is the gudgeon or axis \(u\) of a piece \(y u z\), called the hammer or the F, from its resemblance to that letter. It has a lump of metal \(y\) at one end, and a spear \(u s\) projects from its middle, and passes between the claws \(s\) and \(t\) of the arm of the injection-cock. The hammer \(y\) is held up by a notch in the under side of a wooden lever \(DE\), moveable round the centre \(D\), and supported at a proper height by a spring \(E\), made fast to the joist above it.

Suppose the injection-cock shut, and the hammer in the position represented in the figure. A pin \(\beta\) of the plug-frame rises along with the piston, and catching hold of the detent \(DE\), raises it, and disengages the hammer \(y\) from its notch. This immediately falls down, and strikes a board \(L\) put in the way to stop it. The spear \(u s\) takes hold of the claw \(t\), and forces it aside towards \(x\), and opens the injection-cock. The piston immediately descends, and along with it the plug-frame. During its descent the pin \(\beta\) meets with the tail \(u z\) of the hammer, which is now raised considerably above the level, and brings it down along with it, raising the lump \(y\), and gradually shutting the injection-cock, because the spear takes hold of the claw \(s\) of its arm. When the beam has come to its lowest situation, the hammer is again engaged in the notch of the detent \(DE\), and supported by it till the piston again reaches the top of the cylinder.

In this manner the motions of the injection-cock are also adjusted to the precise moment that is proper for them. The different pins are so placed in the plug-frame, that the steam-cock may be completely shut before the injection-cock is opened. The inherent motion of the machine will give a small addition to the ascent of the piston without expending steam all the while; and by leaving the steam rather less elastic than before, the subsequent descent of the piston is promoted. There was a considerable propriety in the gradual shutting ting of the injection-cock. For after the first dash of the cold water against the bottom of the piston, the condensation is nearly complete, and very little more water is needed; but a continual accession of some is absolutely necessary for completing the condensation, as the capacity of the cylinder diminishes, and the water warms which is already injected.

In this manner the motion of the machine will be repeated as long as there is a supply of steam from the boiler, and of water from the injection cistern, and a discharge procured for what has been injected. We proceed to consider how far these conditions also are provided by the machine itself.

The injection cistern is supplied with water by the jackhead pump, as we have already observed. From this source all the parts of the machine receive their respective supplies. In the first place, a small branch 13, 13, is taken off from the injection pipe immediately below the cistern, and conducted to the top of the cylinder, where it is furnished with a cock. The spout is so adjusted, that no more runs from it than what will keep a constant supply of a foot of water above the piston to keep it tight. Every time the piston comes to the top of the cylinder, it brings this water along with it, and the surplus of its evaporation and leakage runs off by a waste pipe 14, 14. This water necessarily becomes almost boiling hot, and it was thought proper to employ its surplus for supplying the waste of the boiler. This was accordingly practised for some time. But Mr Beighton improved this economical thought, by supplying the boiler from the education-pipe, 2, 2, the water of which must be still hotter than that above the piston. This contrivance required attention to many circumstances, which the reader will understand by considering the perspective and profile. The education-pipe comes out of the bottom of the cylinder at 1 with a perpendicular part, which bends sidewise below, and is flat at the extremity 1. A deep cup 5 communicates with it, holding a metal valve nicely fitted to it by grinding, like the key of a cock. To secure its being always air-tight, a flender stream of water trickles into it from a branch 6 of the waste-pipe from the top of the cylinder. The education-pipe branches off at 2, and goes down to the hot well, where it turns up, and is covered with a valve. In the perspective view may be observed an upright pipe 4, 4, which goes through the head of the boiler, and reaches to within a few inches of its bottom. This pipe is called the feeder, and rises about three or four feet above the boiler. It is open at both ends, and has a branch 3, 3, communicating with the bottom of the cup 5, immediately above the metal valve, and also a few inches below the level of the entry 2 of the education-pipe. This communicating branch has a cock by which its passage may be diminished at pleasure. Now suppose the steam in the boiler to be very strong, it will cause the boiling water to rise in the feeding-pipe above 3, and coming along this branch, to rise also in the cup 5, and run over. But the height of this cup above the surface of the water in the boiler is such, that the steam is never strong enough to produce this effect. Therefore, on the contrary, any water that may be in the cup 5 will run off by the branch 3, 3, and go down into the boiler by the feeding-pipe.

These things being understood, let us suppose a quantity of injected water lying at the bottom of the cylinder. It will run into the education-pipe, fill the crooked branch 1, 1, and open the valve in the bottom of the cup (its weight being supported by a wire hanger from a flender spring), and it will fill the cup to the level of the entry 2 of the education pipe, and will then triviant flow along 3, 3, and supply the boiler by the feeder 4, 4. What more water runs in at 1 will now go along the education-pipe 2, 2, to the hot well. By properly adjusting the cock on the branch 3, 3, the boiler may be supplied as fast as the waste in steam requires. This is a most ingenious contrivance, and does great honour to Mr Beighton. It is not, however, of much importance. The small quantity which the boiler requires may be immediately taken even from a cold cistern, without sensibly diminishing the production of steam: for the quantity of heat necessary for raising the sensible heat of cold water to the boiling temperature is small, when compared with the quantity of heat which must then be combined with it in order to convert the water into steam. For the heat expended in boiling off a cubic foot of water is about fix times as much as would bring it to a boiling heat from the temperature of 55°. No difference can be observed in the performance of such engines, and of those which have their boilers supplied from a brook. It has, however, the advantage of being purged of air; and when an engine must derive all its supplies from pit water, the water from the education-pipe is vastly preferable to that from the top of the cylinder.

We may here observe, that many writers (among them the Abbé Bosfut), in their descriptions of the steam engine, have drawn the branch of communication 3, 3, from the feeding-pipe to a part of the crooked pipe 1, 1, lying below the valve in the cup 5. But this is quite erroneous; for, in this case, when the injection is made into the cylinder, and a vacuum produced, the water from the boiler would immediately rush up through the pipes 4, 3, and spout up into the cylinder: so would the external air coming in at the top of the feeder.

This contrivance has also enabled us to form some judgment of the internal state of the engine during the performance. Mr Beighton paid a minute attention to the situation of the water in the feeders and education-pipe of an engine, which seems to have been one of the best which has yet been erected. It was lifting a co. of the culm of water whose weight was four-sevenths of the pressure of the air on its piston, and made 16 strokes, of six feet each, in a minute. This is acknowledged by all to be a very great performance of an engine of this form. He concluded that the elasticity of the steam in the cylinder was never more than one-tenth greater or less than the elasticity of the air. The water in the feeder never rose more than three feet and a half above the surface of the boiling water, even though it was now lighter by \( \frac{1}{7} \)th than cold water. The education pipe was only four feet and a half long (vertically), and yet it always discharged the injection water completely, and allowed some to pass into the feeder. This could not be if the steam was much more than one-tenth weaker than air. By grasping this pipe in his hand during the rise of the piston, he could guess very well whereabouts the surface of the hot water in it rested during the motion, and he never found it supported so high as four feet. Therefore the steam in the cylinder had at least eight-ninths of the elasticity of the air. Mr Buat, in his examination of an engine which is erected at Montrelaix, in France, by an English engineer, and has always been considered as the pattern in that country, finds it necessary to suppose a much greater variation in the strength of the steam, and says, that it must have been one-fifth stronger and one-fifth weaker than common air. But this engine has not been nearly so perfect. Its lift was not more than one-half the pressure of the atmosphere, and it made but nine strokes in a minute.—At W is a valve covering the mouth of a small pipe, and surrounded with a cup containing water to keep it air-tight. This allows the air to escape which had been extricated from the water of last injection. It is driven out by the first strong puff of steam which is admitted into the cylinder, and makes a noise in its exit. The valve is therefore called the snifting-valve.

To finish our description, we observe, that besides the safety valve 9 (called the PUPPET CLACK), which is loaded with about 3 pounds on the square inch (though the engine will work very well with a load of 1 or 2 pounds), there is another DISCHARGER 10,10, having a clack at its extremity supported by a cord. Its use is to discharge the steam without doors, when the machine gives over working. There is also a pipe SI near the bottom of the boiler, by which it may be emptied when it needs repairs or cleansing.

There are two small pipes 11,11, and 12,12, with cocks called GAGE PIPES. The first descends to within two inches of the surface of the water in the boiler, and the second goes about 2 inches below that surface. If both cocks emit steam, the water is too low, and requires a recruit. If neither give steam, it is too high, and there is not sufficient room above it for a collection of steam. Lastly, there is a filling pipe Q, by which the boiler may be filled when the machine is to be let to work.

The engine has continued in this form for many years. The only remarkable change introduced has been the manner of placing the boiler. It is no longer placed below the cylinder, but at one side, and the steam is introduced by a pipe from the top of the boiler into a flat box immediately below the cylinder. The use of this box is merely to lodge the regulator, and give room for its motions. This has been a very considerable improvement. It has greatly reduced the height of the building. This was formerly a tower. The wall which supported the beam could hardly be built with sufficient strength for withstanding the violent shocks which were repeated without ceasing; and the buildings seldom lasted more than a very few years. But the boiler is now set up in an adjoining shed, and the gudgeons of the main beam rest on the top of upright posts, which are framed into the joists which support the cylinder. Thus the whole moving parts of the machine are contained in one compact frame of carpentry, and have little or no connection with the flight walls of the building, which is merely a cage to hold the machine, and protect it from the weather.

It is now time to inquire what is to be expected from this machine, and to ascertain the most advantageous proportion between the moving power and the load that is to be laid on the machine.

It may be considered as a great pulley, and is indeed sometimes so constructed, the arches at the ends of the working beam being completed to a circle. It must be unequally loaded that it may move. It is loaded, during the working stroke, by the pressure of the atmosphere on the piston side, and by the column of water to be raised and the pump-gear on the pump side.—During the returning stroke it is loaded, on the piston side, by a small part of the atmospheric pressure, and on the pump side by the pump-gear acting as a counter weight. The load during the working stroke must therefore consist of the column of water to be raised and this counter weight. The performance of the machine is to be measured only by the quantity of water raised in a given time to a given height. It varies, therefore, in the joint proportion of the weight of the column of water in the pumps, and the number of strokes made by the machine in a minute. Each stroke consists of two parts, which we have called the working and the returning stroke. It does not, therefore, depend simply on the velocity of the working stroke and the quantity of water raised by it. If these were all that is to be attended to, we know that the weight of the column of water should be nearly \( \frac{1}{7} \)ths of the pressure of the atmosphere, this being the proportion which gives the maximum in the common pulley. But the time of the returning stroke is a necessary part of the whole time elapsed, and therefore the velocity of the returning stroke equally merits attention. This is regulated by the counter weight. The number of strokes per minute does not give an immediate proof of the goodness of the engine. A small load of water and a great counter weight will ensure this, because these conditions will produce a brisk motion in both directions.—The proper adjustment of the pressure of the atmosphere on the piston, the column of water to be raised, and the counter weight, is a problem of very great difficulty; and mathematicians have not turned much of their attention to the subject, although it is certainly the most interesting question that practical mechanics affords them.

Mr Boffut has solved it very shortly and simply, upon Mr Boffut's this supposition, that the working and returning stroke, solution, should be made in equal times. This, indeed, is generally aimed at in the erection of these machines, and they are not reckoned to be well arranged if it be otherwise. We doubt of the propriety of the maxim. Supposing, however, this condition for the present, we may compute the loadings of the two ends of the beam as follows. Let a be the length of the inner arm of the working beam, or that by which the great piston is supported. Let b be the outer arm carrying the pump rods, and let W be a weight equivalent to all the load which is laid on the machine. Let c^a be the area of the piston ; let H be the height of a column of water having c^a for its base, and being equal in weight to the pressure exerted by the steam on the under side of the piston ; and let h be the pressure of the atmosphere on the same area, or the height of a column of water of equal weight. It is evident that both strokes will be performed in equal times, if \( h\ c^a - W\ b \) be equal to \( (h-H)\ c^a + W\ b \). The first of these quantities is the energy of the machine during the working stroke, and the second expresses the similar energy during the returning stroke. This equation gives us \( W = \frac{2h c^a - H c^a}{2b} = \frac{(2h - H) c^a}{2b} \). If we suppose the arms of the lever equal and H = h, we have \( W = c^2 \frac{h}{2} \); that is, the whole weight of the outer end of the beam should be half the pressure of the air on the great piston. This is nearly the usual practice; and the engineers express it by saying, that the engine is loaded with seven or eight pounds on the square inch. This has been found to be nearly the most advantageous load. This way of expressing the matter would do well enough, if the maxim were not founded on erroneous notions, which hinder us from seeing the state of the machine, and the circumstances on which its improvement depends. The piston bears a pressure of 15 pounds, it is said, on the square inch, if the vacuum below it be perfect; but as this is far from being the case, we must not load it above the power of its vacuum, which very little exceeds eight pounds. But this is very far from the truth. When the cylinder is tight, the vacuum is not more than \( \frac{7}{8} \)th deficient, when the cylinder is cooled by the injection to the degree that is every day practicable, and the piston really bears during its descent a pressure very near to 14 pounds on the inch. The load must be diminished, not on account of the imperfect vacuum, but to give the machine a reasonable motion. We must consider not only the moving force, but also the quantity of matter to be put in motion. This is so great in the steam-engine, that even if it were balanced, that is, if there were suspended on the piston arm a weight equal to the whole column of water and the counter weight, the full pressure of the atmosphere on the steam piston would not make it move twice as fast as it does.

This equation by Mr Boffut is moreover essentially faulty in another respect. The W in the first member is not the same with the W in the second. In the first it is the column of water to be raised, together with the counter weight. In the second it is the counter weight only. Nor is the quantity H the same in both cases, as is most evident. The proper equation for ensuring the equal duration of the two strokes may be had in the following manner. Let it be determined by experiment what portion of the atmospheric pressure is exerted on the great piston during its descent. This depends on the remaining elasticity of the steam. Suppose it \( \frac{9}{10} \)ths: this we may express by a h, a being \( \frac{9}{10} \)ths. Let it also be determined by experiment what portion of the atmospheric pressure on the piston remains unbalanced by the steam below it during its ascent. Suppose this \( \frac{7}{10} \)th, we may express this by b h. Then let W be the weight of the column of water to be raised, and c the counter weight. Then, if the arms of the beam are equal, we have the energy during the working stroke \( = a h - W - c \), and during the returning stroke it is \( = c - b h \). Therefore \( c - b h = a h - W - c \); and \( c = \frac{h(a+b)-W}{2} \); which, on the above supposition of the values of a and b, gives us \( c = \frac{h-W}{2} \). We shall make some use of this equation afterwards; but it affords us no information concerning the most advantageous proportion of h and W, which is the material point.

We must consider this matter in another way: And that we may not involve ourselves in unnecessary difficulties, let us make the case as simple as possible, and suppose the arms of the working-beam to be of equal length.

We shall first consider the adjustment of things at the outer end of the beam.

Since the sole use of the steam is to give room for the adjustment of the atmospheric pressure by its rapid condensation, it is admitted into the cylinder only to allow things at the piston to rise again, but without giving it any impulsion of the pulse. The pump-rods must therefore be returned to beam con the bottom of the working barrels, by means of a preponderancy at the outer end of the beam. It may be the weight of the pump-rods themselves, or may be considered as making part of this weight. A weight at the end of the beam will not operate on the rods which are suspended there by chains, and it must therefore be attached to the rods themselves, but above their respective pump-barrels, so that it may not lose part of its efficacy by immersion in the water. We may consider the whole under the notion of the pump-gear, and call it p. Its office is to depress the pump-rods with sufficient velocity, by overcoming the resistances arising from the following causes.

1. From the inertia of the beams and all the parts of the apparatus which are in motion during the descent of the pump-rods. 2. From the loss of weight sustained by the immersion of the pump-rods in water. 3. From the friction of all the pistons and the weight of the plug-frame. 4. From the resistance to the piston's motion, arising from the velocity which must be generated in the water in passing through the descending pistons.

The sum of all these resistances is equal to the pressure of some weight (as yet unknown), which we may call m.

When the pump-rods are brought up again, they bring along with them a column of water, whose weight we may call w.

It is evident that the load which must be overcome by the pressure of the atmosphere on the steam piston consists of w and p. Let this load be called L, and the pressure of the air be called P.

If p be = L, no water will be raised; if p be = 0, the rods will not descend: therefore there is some intermediate value of p which will produce the greatest effect.

In order to discover this, let g be the fall of a heavy body in a second.

The descending mass is p: but it does not descend with its full weight; because it is overcoming a set of resistances which are equivalent to a weight m, and the moving force is \( p - m \). In order to discover the space through which the rods will descend in a second, when urged by the force \( p - m \) (supposed constant, notwithstanding the increase of velocity, and consequently of m), we must institute this proportion \( p : p - m = g : g(p-m) \).

\( p \)

The fourth term of this analogy is the space required.

Let t be the whole time of the descent in seconds. Then \( t^2 : t^2g(p-m) : t^2g(p-m) \). This last term is the whole descent or length of the stroke accomplished in the time t.

The weight of the column of water, which has now got above the piston, is w = L - p. This must be lifted in the next working stroke through the space \( \frac{t^2 g (p-m)}{p} \). Therefore the performance of the engine must be \( \frac{t^2 g (p-m) (L-p)}{p} \).

That this may be the greatest possible, we must consider p as the variable quantity, and make the fluxion of the fraction \( \frac{p-m}{p} \times \frac{L-p}{L} = 0 \).

This will be found to give us \( p = \sqrt{Lm} \); that is, the counter weight or preponderancy of the outer end of the beam is \( = \sqrt{Lm} \).

This gives us a method of determining m experimentally. We can discover by actual measurement the quantity L in any engine, it being equal to the unbalanced weights on the beam and the weight of the water in the pumps. Then \( m = \frac{p^2}{L} \).

Also we have the weight of the column of water \( = L - p, = L - \sqrt{Lm} \).

When therefore we have determined the load which is to be on the outer end of the beam during the working stroke, it must be distributed into two parts, which have the proportion of \( \sqrt{Lm} \) to \( L - \sqrt{Lm} \). The first is the counter weight, and the second is the weight of the column of water.

If m is a fraction of L, such as an aliquot part of it; that is, if

\[ m = \frac{L}{1}, \frac{L}{4}, \frac{L}{9}, \frac{L}{16}, \frac{L}{25}, \text{ &c.} \] \[ p = \frac{L}{1}, \frac{L}{2}, \frac{L}{3}, \frac{L}{4}, \frac{L}{5}, \text{ &c.} \]

The circumstance which is commonly obtruded on us by local considerations is the quantity of water, and the depth from which it is to be raised; that is, w; and it will be convenient to determine every thing in conformity to this.

We saw that \( w = L - \sqrt{Lm} \). This gives us \( L = \pm \sqrt{wm + \frac{m^2}{4} + \frac{m}{2} + w} \), and the counter weight \[ p = \sqrt{wm + \frac{m^2}{4} + \frac{m}{2}}. \]

Having thus ascertained that distribution of the load on the outer end of the beam which produces the greatest effect, we come now to consider what proportion of moving force we must apply, so that it may be employed to the best advantage, or so that any expense of power may produce the greatest performance. It will be so much the greater as the work done is greater, and the power employed is less; and will therefore be properly measured by the quotient of the work done divided by the power employed.

The work immediately done is the lifting up the weight L. In order to accomplish this, we must employ a pressure P, which is greater than L. Let it be \( = L + y \); also let s be the length of the stroke.

If the mass L were urged along the space s by the force L + y, it would acquire a certain velocity, which we may express by \( \sqrt{\frac{s}{y}} \); but it is impelled only by the force y, the rest of P being employed in balancing L. The velocities which different forces generate by impelling a body along the same space are as the square roots of the forces. Therefore \( \sqrt{L+y} : \sqrt{y} = \sqrt{s} : \sqrt{\frac{s\ y}{L+y}} \). The fourth term of this analogy expresses the velocity of the piston at the end of the stroke. The quantity of motion produced will be had by multiplying this velocity by the mass L. This gives \( \frac{L \times \sqrt{s\ y}}{\sqrt{L+y}} \); and this divided by the power expended, or by \( L + y \), gives us the measure of the performance; namely, \[ \frac{L \sqrt{s\ y}}{L+y \times \sqrt{L+y}} \]

That this may be a maximum, consider y as the variable quantity, and make the fluxion of this formula \( = 0 \). This will give us \( y = \frac{L}{2} \).

Now P = L + y, \( = L + \frac{L}{2}, = \frac{3}{2} L \). Therefore the whole load on the outer end of the beam, consisting of the water and the counter weight, must be two-thirds of the prelude of the atmosphere on the steam piston.

We have here supposed that the expenditure is the atmospheric prelude; and so it is if we consider it mechanically. But the expenditure of which we are sensible, and which we are anxious to employ to the best advantage, is fuel. Supposing this to be employed with the same judgment in all cases, we are almost entitled, by what we now know of the production of steam, to say that the steam produced is proportional to the fuel expended. But the steam requisite for merely filling the cylinder is proportional to the area of the piston, and therefore to the atmospheric prelude. The result of our investigation therefore is still just; but the steam wasted by condensation on the sides of the cylinder does not follow this ratio, and this is more than what is necessary for merely filling it. This deranges our calculations, and is in favour of large cylinders; but this advantage must be in a great measure compensated by a similar variation in the production of the steam; for in similar boilers of greater dimensions the fuel is less advantageously employed, because the surface to which the fuel is applied does not increase in the ratio of the capacity, just as the surface of the cylinder which wastes the steam. The rule may therefore be confided in as pretty exact.

It is a satisfactory thing to observe these results agree very well with the most successful practice. By many tests agree changes and trials engineers have established maxims of with the construction, which are probably not very far from the most useful. It is a pretty general maxim, that the load of water should be one-half of the atmospheric pressure. They call this loading the engine with 7\( \frac{1}{2} \) pounds on the inch, and they say that so small a load is necessary on account of the imperfect vacuum. But we have now seen that it is necessary for giving a reasonable velocity of motion. Since, in this practice, w is made \( \frac{1}{3} \) or \( \frac{1}{4} \)ths of P, and L should be \( \frac{1}{3} \)ths of P, and L is \( = w + p \); it follows, that the counter weight should be 1/4th of P; and we have found this to be nearly the case in several very good engines.

It must be remarked, that in the preceding investigation we introduced a quantity M to express the resistances to the motion of the engine. This was done in order to avoid a very troublesome investigation. The resistances are of such a nature as to vary with the velocity, and most of them as the square of the velocity. This is the case with the resistance arising from the motion of the water through the pistons of the pumps, and that arising from the friction in the long lift during the working stroke. Had we taken the direct method, which is similar to the determination of the motion through a medium which resists in the duplicate ratio of the velocity, we must have used a very intricate exponential calculus, which few of our readers would have the patience to look at.

But the greatest part of the quantity m supposes a motion already known, and its determination depends on this motion. We must now show how its different component parts may be computed.

1. What arises from the inertia of the moving parts is by far the most considerable portion of it. To obtain it, we must find a quantity of matter which, when placed at the end of the beam, will have the same momentum of inertia with that of the whole moving parts in their natural places. Therefore (in the returning stroke) add together the weight of the great piston with its rod and chains; the pit pump-rods, chains, and any weight that is attached to them; the arch-heads and iron-work at the ends of the beam, and 1/8ths of the weight of the beam itself; also the plug-beam with its arch-head and chain, multiplied by the square of its distance from the axis, and divided by the square of half the length of the beam; also the jack-head pump-rod, chain, and arch-head, multiplied by the square of its distance from the axis, and divided by the square of the half length of the beam. These articles added into one sum may be called M, and may be supposed to move with the velocity of the end of the beam. Suppose this beam to have made a six-foot stroke in two seconds, with an uniformly accelerated motion. In one second it would have moved 1 1/2 feet, and would have acquired the velocity of three feet per second. But in one second gravity would have produced a velocity of 32 feet in the same mass. Therefore the accelerating force, which has produced the velocity of three feet, is nearly 1/17th of the weight. Therefore \( \frac{M}{11} \) is the first constituent of m in the above investigation. If the observed velocity is greater or less than three feet per second, this value must be increased or diminished in the same proportion.

The second cause of resistance, viz. the immersion of the pump rods in water, is easily computed, being the weight of the water which they displace.

The third cause, the friction of the pistons, &c. is almost insignificant, and must be discovered by experiment.

The fourth cause depends on the structure of the pumps. These pumps, when made of a proper strength, can hardly have the perforation of the piston more than a fourth part of the area of the working-barrel; and the velocity with which the water passes through it is increased at least 1/4th by the contraction (see Pump). The velocity of the water is therefore five times greater than that of the piston. A piston 12 inches diameter, and moving one foot per second, meets with a resistance equal to 20 pounds; and this increases as the square of the diameter and as the square of the velocity. If the whole depth of the pit be divided into several lifts, this resistance must be multiplied by the number of lifts, because it obtains in each pump.

Thus we make up the value of m; and we must acknowledge that the method is still indirect, because it supposes the velocity to be known.

We may obtain it more easily in another way, but still with this circumstance of being indirect. We found that \( p \) was equal to \( \sqrt{Lm} \), and consequently \( m = \frac{p^2}{L} \).

Now in any engine L and p can always be had; and unless p deviates greatly from the proportion which we determined to be the best, the value of m thus obtained will not be very erroneous.

It was farther presumed in this investigation, that the Observations both up and down were uniformly accelerated; but this cannot be the case when the resistances increase with the velocity. This circumstance makes very little change in the working-stroke, and therefore the theorem which determines the best relation of P to L may be confided in. The resistances which vary with the velocity in this case are a mere trifle when compared with the moving power y. These resistances are, 1st, The straining of the water at the entry and at the standing valve of each pump: This is about 37 pounds for a pump 12 inches diameter, and the velocity one foot per second, increasing in the duplicate ratio of the diameter and velocity. And, 2d, The friction of the water along the whole lift: This for a pump of the same size and with the same velocity, lifting 20 fathoms, is only about 2 1/2 pounds, and varies in the simple proportion of the diameter and the depth, and in the duplicate proportion of the velocity. The resistance arising from inertia is greater than in the returning stroke; because the M in this case must contain the momentum of the water both of the pit-pumps and the jackhead-pump: but this part of the resistance does not affect the uniform acceleration. We may therefore confide in the propriety of the formula \( y = \frac{L}{2} \). And we may obtain the velocity of this stroke at the end of a second with great accuracy as follows. Let 2g be the velocity communicated by gravity in a second, and the velocity at the end of the first second of the steam piston's descent will be somewhat less than \( \frac{y}{M} 2g \); where M expresses the inertia of all the parts which are in motion during the decent of the steam piston, and therefore includes L. Compute the two resistances just mentioned for this velocity. Call this r. Then \( \frac{y - \frac{1}{2}r}{M} 2g \) will give another velocity infinitely near the truth.

But the case is very different in the returning stroke, and the proper ratio of p to L is not ascertained with the same certainty: for the moving force p is not so great in proportion to the resistance m; and therefore the acceleration of the motion is considerably affected by it, and the motion itself is considerably retarded, and in a very moderate time it becomes sensibly uniform: for it is precisely similar to the motion of a heavy body falling falling through the air, and may be determined in the manner laid down in the article RESISTANCE of Fluids, viz. by an exponential calculus. We shall content ourselves here with saying, that the resistances in the present case are so great that the motion would be to all sense uniform before the pistons have descended one-third of their stroke, even although there were no other circumstance to affect it.

But this motion is affected by a circumstance quite unconnected with any thing yet considered, depending on conditions not mechanical, and so uncertain, that we are not yet able to ascertain them with any precision; yet they are of the utmost importance to the good performance and improvement of the engine, and therefore deserve a particular consideration.

The counter weight has not only to push down the pump rods, but also to drag up the great piston. This it cannot do unless the steam be admitted into the cylinder. If the steam be no stronger than common air, it cannot enter the cylinder except in consequence of the piston's being dragged up. If common air were admitted into the cylinder, some force would be required to drag up the piston, in the same manner as it is required to draw up the piston of a common syringe; for the air would rush through the small entry of the cylinder in the same manner as through the small nozzle of the syringe. Some part of the atmospheric pressure is employed in driving in the air with sufficient velocity to fill the syringe, and it is only with the remainder that the admitted air presses on the under surface of the syringe. Therefore some of the atmospheric pressure on its upper surface is not balanced. This is felt by the hand which draws it up. The same thing must happen in the steam engine, and some part of the counter weight is expended in drawing up the steam piston. We could tell how much is thus expended if we knew the density of the steam; for this would tell us the velocity with which its elasticity would cause it to fill the cylinder. If we suppose it 12 times rarer than air, which it certainly is, and the piston rises to the top of the cylinder in two seconds, we can demonstrate that it will enter with a velocity not less than 1400 feet per second, whereas 500 feet is enough to make it maintain a density \( \frac{7}{9} \)ths of that of steam in equilibrium with the air. Hence it follows, that its elasticity will not be less than \( \frac{3}{8} \)ths of the elasticity of the air, and therefore not more than \( \frac{1}{3} \)th of counter weight will be expended in drawing up the steam-piston.

But all this is on the supposition that there is an unbounded supply of steam of undiminished elasticity. This is by no means the case. Immediately before opening the steam-cock, the steam was filling through the safety-valve and all the crevices in the top of the boiler, and (in good engines) was about \( \frac{1}{10} \)th stronger or more elastic than air. This had been gathering during something more than the descent of the piston, viz. in about three seconds. The piston rises to the top in about two seconds; therefore about twice and a half as much steam as fills the dome of the boiler is now shared between the boiler and cylinder. The dome is commonly about six times more capacious than the cylinder. If therefore no steam is condensed in the cylinder, the density of the steam, when the piston has reached the top, must be about \( \frac{1}{5} \)ths of its former density, and still more elastic than air. But as much steam is condensed by the cold cy-

linder, its elasticity must be less than this. We cannot tell how much less, both because we do not know how much is thus condensed, and because by this diminution of its pressure on the surface of the boiling water, it must be more copiously produced in the boiler; but an attentive observation of the engine will give us some information. The moment the steam-cock is opened we have a strong puff of steam through the inititing valve. At this time, therefore, it is still more elastic than air; but after this, the inititing valve remains shut during the whole rise of the piston, and no steam any longer issues through the safety-valve or crevices; nay, the whole dome of the boiler may be observed to sink.

These facts give abundant proof that the elasticity of the steam during the ascent of the piston is greatly diminished, and therefore much of the counter weight is expended in dragging up the steam piston in opposition to the unbalanced part of the atmospheric pressure. The motion of the returning stroke is therefore so much decreased by this foreign and inappreciated circumstance, that it would have been quite useless to engage in the intricate exponential investigation, and we must fit down contented with a less perfect adjustment of the counter weight and weight of water.—Any person who attends to the motion of a steam-engine will perceive that the descent of the pump-rods is so far from being accelerated, that it is nearly uniform, and frequently it is sensibly retarded towards the end. We learn by the way, that it is of the utmost importance not only to have a quick production of steam, but also a very capacious dome, or empty space above the water in the boiler. In engines where this space was but four or five times the capacity of the cylinder, we have always observed a very sensible check given to the descent of the pump-rods after having made half their stroke. This obliges us to employ a greater counter weight, which diminishes the column of water, or retards the working stroke; it also obliges us to employ a stronger steam, at the risk of bursting the boiler, and increases the expense of fuel.

It would be a most desirable thing to get an exact knowledge of the elasticity of the steam in the cylinder; and this is by no means difficult. Take a long glass tube exactly calibred, and close at the farther end. Put in the cylinder a small drop of some coloured fluid into it, so as to stand at the middle nearly.—Let it be placed in a long box filled with water to keep it of a constant temperature. Let the open end communicate with the cylinder, with a cock between. The moment the steam-cock is opened, open the cock of this instrument. The drop will be pushed towards the close end of the tube, while the steam in the cylinder is more elastic than the air, and it will be drawn the other way while it is less elastic, and, by a scale properly adapted to it, the elasticity of the steam corresponding to every position of the piston may be discovered. The same thing may be done more accurately by a barometer properly constructed, so as to prevent the oscillations of the mercury.

It is equally necessary to know the state of the cylinder during the descent of the steam-piston. We have hitherto supposed P to be the full pressure of the atmosphere on the area of the piston, supposing the vacuum below it to be complete. But the inspection of our table of elasticity shows that this can never be the case, because the cylinder is always of a temperature far above 32°. We have made many attempts to discover its tem- temperature. We have employed a thermometer in close contact with the side of the cylinder, which soon acquired a steady temperature: this was never less than 145°. We have kept a thermometer in the water which lies on the piston: this never sunk below 135°. It is probable that the cylinder within may be cooled somewhat lower; but for this opinion we cannot give any very satisfactory reason. Suppose it cooled down to 120°; this will leave an elasticity which would support three inches of mercury. We cannot think, therefore, that the unbalanced prelure of the atmosphere exceeds that of 27 inches of mercury, which is about 13 1/2d pounds on a square inch, or 10 1/2 on a circular inch. And this is the value which we should employ in the equation \( P = L + \gamma \). This question may be decided in the same way as the other, by a barometer connected with the inside of the cylinder.

And thus we shall learn the state of the moving forces in every moment of the performance, and the machine will then be as open to our examination as any water or horse mill; and till this be done, or something equivalent, we can only guess at what the machine is actually performing, and we cannot tell in what particulars we can lend it a helping hand. We are informed that Messrs Watt and Boulton have made this addition to some of their engines; and we are persuaded that, from the information which they have derived from it, they have been enabled to make the curious improvements from which they have acquired so much reputation and profit.

There is a circumstance of which we have as yet taken no notice, viz. the quantity of cold water injected. Here we confess ourselves unable to give any precise instructions. It is clear at first sight that no more than is absolutely necessary should be injected. It must generally be supplied by the engine, and this expends part of its power. An excess is much more hurtful by cooling the cylinder and piston too much, and therefore wasting steam during the next rise of the piston. But the determination of the proper quantity requires a knowledge, which we have not yet acquired, of the quantity of heat contained in the steam in a latent form. As much water must be injected as will absorb all this without rising near to the boiling temperature. But it is of much more importance to know how far we may cool the cylinder with advantage; that is, when will the loss of steam, during the next rise of the piston, compensate for the diminution of its elasticity during its present descent? Our table of elasticities shows us, that by cooling the cylinder to 120°, we will leave an elasticity equal to one-tenth of the whole power of the engine; if we cool it only to 140, we leave an elasticity of one-fifth; if we cool it to a blood-heat, we leave an elasticity of one-twentieth. It is extremely difficult to choose among these varieties. Experience, however, informs us, that the best engines are those which use the smallest quantities of injection water. We know an exceedingly good engine having a cylinder of 32 inches and a fix feet stroke, which works with something less than one-fifth of a cubic foot of water at each injection; and we imagine that the quantity should be nearly in the proportion of the capacity of the cylinder. Desaguliers observed, that a very good engine, with a cylinder of 32 inches, worked with 300 inches of water at each injection, which does not much exceed one-sixth of a cubic foot. Mr Watt's observations, by means of the barometer, must have given him much valuable information in this particular, and we hope that he will not always withhold them from the public.

We have gone thus far in the examination, in order This exa- seemingly to ascertain the motion of the engine when mination, loaded and balanced in any known manner, and in or- though not der to discover that proportion between the moving satisfac- power and the load which will produce the greatest tion to the the attention quantity of work. The result has been very unsatis- principal factory, because the computation of the returning stroke acknowledged to be beyond our abilities. But it has circumstances given us the opportunity of directing the reader's attention to the leading circumstances in this inquiry. By knowing the internal state of the cylinder in machines of very different goodnets, we learn the connection be- between the state of the steam and the performance of the machine; and it is very possible that the result of a full examination may be, that in situations where fuel is expensive, it may be proper to employ a weak steam which will expend less fuel, although less work is per- formed by it. We shall see this confirmed in the clear- est manner in some particular employments of the new engines invented by Watt and Boulton.

In the mean time, we see that the equation which we gave from the celebrated Abbé Boslut, is in every re- spect erroneous even for the purpose which he had in view. We also see that the equation which we substi- tuted in its place, and which was intended for determi- ning that proportion between the counter-weight and the moving force, and the load which would render the working stroke and returning stroke of equal duration, is also erroneous, because these two motions are extrem- ely different in kind, the one being nearly uniform, and the other nearly uniformly accelerated. This being supposed true, it should follow that the counter-weight should be reduced to one-half; and we have found this to be very nearly true in some good engines which we have examined.

We shall add but one observation more on this head. The practical engineers have almost made it a maxim, that the two motions are of equal duration. But the only reason which we have heard for the maxim, is that it is awkward to see an engine go otherwise. But we doubt exceedingly the truth of this maxim; and, without being able to give any accurate determination, we think that the engine will do more work if the working stroke be made slower than the returning stroke. Suppose the engine so constructed that they are made in equal times; an addition to the counter-weight will accelerate the returning stroke and retard the working stroke. But as the counter-weight is but small in pro- portion to the unbalanced portion of the atmospheric prelure, which is the moving force of the machine, it is evident that this addition to the counter-weight must bear a much greater proportion to the counter-weight than it does to the moving force, and must therefore accelerate the returning stroke much more than it retards the working stroke, and the time of both strokes taken together must be diminished by this addition and the performance of the machine improved; and this must be the case as long as the machine is not extravagantly loaded. The best machine which we have seen, in re- spect of performance, raises a column of water whose weight is very nearly two-thirds of the prelure of the atmosphere atmosphere on the piston, making 11 strokes of six feet each per minute, and the working stroke was almost twice as low as the other. This engine had worked pumps of 12 inches, which were changed for pumps of 14 inches, all other things remaining the same. In its former state it made from 12 and a half to 13 and a half strokes per minute, the working stroke being considerably lower than the returning stroke. The load was increased, by the change of the pumps, nearly in the proportion of three to four. This had retarded the working stroke; but the performance was evidently increased in the proportion of \(3 \times 13\) to \(4 \times 11\), or of 39 to 44. About 300 pounds were added to the counter-weight, which increased the number of strokes to more than 12 per minute. No sensible change could be observed in the time of the working stroke. The performance was therefore increased in the proportion of 39 to 48. We have therefore no hesitation in saying, that the feebly equality of the two strokes is a sacrifice to fancy. The engineer who observes the working stroke to be slow, fears that his engine may be thought feeble and unequal to its work; a similar notion has long milled him in the construction of water-mills, especially of overhot mills; and even now he is submitting with hesitation and fear to the daily correction of experience.

It is needless to engage more deeply in scientific calculations in a subject where so many of the data are so very imperfectly understood.

We venture to recommend as a maxim of construction (supposing always a large boiler and plentiful supply of pure steam unmixed with air), that the load of work be not less than 10 pounds for every square inch of the piston, and the counter-weight to proportioned that the time of the returning stroke may not exceed two-thirds of that of the working stroke. A serious objection may be made to this maxim, and it deserves mature consideration. Such a load requires the utmost care of the machine, that no admission be given to the common air; and it precludes the possibility of its working, in case the growth of water, or deepening the pit, should make a greater load absolutely necessary. These considerations must be left to the prudence of the engineer. The maxim now recommended relates only to the best actual performance of the engine.

Before quitting this machine, it will not be amiss to give some easy rules, sanctioned by successful practice, for computing its performance. These will enable any artist, who can go through simple calculations, to suit the size of his engine to the task which it is to perform.

The circumstance on which the whole computation must be founded is the quantity of water which must be drawn in a minute, and the depth of the mine; and the performance which may be expected from a good engine is at least 12 strokes per minute of six feet each, working against a column of water whose weight is equal to half of the atmospheric pressure on the steam-piston, or rather to 7.64 pounds on every square inch of its surface.

It is most convenient to estimate the quantity of water in cubic feet, or its weight in pounds, recollecting that a cubic foot of water weighs 62\( \frac{1}{2} \) pounds. The depth of the pit is usually reckoned in fathoms of six feet, and the diameter of the cylinder and pump is usually reckoned in inches.

Let Q be the quantity of water to be drawn per minute in cubical feet, and f the depth of the mine in fathoms; let c be the diameter of the cylinder, and p that of the pump; and let us suppose the arms of the beam to be of equal length.

1st. To find the diameter of the pump, the area of the piston in square feet is \(p^2 \times \frac{0.7854}{144}\). The length of the column drawn in one minute is 12 times 6 or 72 feet, and therefore its solid contents is \(p^2 \times \frac{72 \times 0.7854}{144}\) cubical feet, or \(p^2 \times 0.3927\) cubical feet. This must be equal to Q; therefore \(p^2\) must be \( \frac{Q}{0.3927} \) or nearly \( \frac{Q}{2.5} \). Hence this practical rule: Multiply the cubic feet of water which must be drawn in a minute by 2.5, and extract the square root of the product: this will be the diameter of the pump in inches.

Thus suppose that 58 cubic feet must be drawn every minute; 58 multiplied by 2.5 gives 145, of which the square root is 12, which is the required diameter of the pump.

2. To find the proper diameter of the cylinder.

The piston is to be loaded with 7.64 pounds on every square inch. This is equivalent to fix pounds on a circular inch very nearly. The weight of a cylinder of water an inch in diameter and a fathom in height is \(2 \frac{1}{3}\) pounds, or nearly two pounds. Hence it follows that \(6c^2\) must be made equal to \(2f p^2\), and that \(c^2\) is equal to \( \frac{2f p^2}{6} \), or to \( \frac{f p^2}{3} \).

Hence the following rule: Multiply the square of the diameter of the pump piston (found as above) by the fathoms of lift, and divide the product by 3; the square root of the quotient is the diameter of the cylinder.

Suppose the pit to which the foregoing pump is to be applied is 24 fathoms deep; then \( \frac{24 \times 144}{3} \) gives 1152, of which the square root is 34 inches very nearly.

This engine, constructed with care, will certainly do the work.

Whatever is the load of water proposed for the engine, let 10 be the pounds on every circular inch of the steam piston, and make \(c^2 = p^2 \times \frac{2f}{m}\), and the square root will be the diameter of the steam piston in inches.

To free the practical engineer as much as possible from all trouble of calculation, we subjoin the following Table of the Dimensions and Power of the Steam Engine, drawn up by Mr Beighton in 1717, and fully verified by practice since that time. The measure is in English ale gallons of 282 cubic inches. Mr Beighton's table of the dimensions and power of the steam-engine.

<table> <tr> <th rowspan="2">Diam. of pump.</th> <th colspan="3">Holds by a fixt stroke.</th> <th colspan="2">Weighs in one yard.</th> <th colspan="2">At 16 strokes per min.</th> <th colspan="2">Ditto in hogheads.</th> <th colspan="2">Ditto per hour.</th> </tr> <tr> <th>Inch.</th> <th>Gall.</th> <th>Gall.</th> <th>Lb. avor.</th> <th>Gall.</th> <th>Hd. Gal.</th> <th>Gall.</th> <th>Hd. Gal.</th> </tr> <tr><td>12</td><td>14.4</td><td>28.8</td><td>146</td><td>462</td><td>7.21</td><td>440.</td></tr> <tr><td>11</td><td>12.13</td><td>24.26</td><td>123.5</td><td>338</td><td>6.20</td><td>369.33</td></tr> <tr><td>10</td><td>10.02</td><td>20.04</td><td>102</td><td>320</td><td>5.5</td><td>304.48</td></tr> <tr><td>9</td><td>8.12</td><td>16.24</td><td>82.7</td><td>259.8</td><td>4.7</td><td>247.7</td></tr> <tr><td>8½</td><td>7.26</td><td>14.52</td><td>73.9</td><td>232.3</td><td>3.43</td><td>221.15</td></tr> <tr><td>8</td><td>6.41</td><td>12.82</td><td>65.3</td><td>205.2</td><td>3.16</td><td>195.22</td></tr> <tr><td>7½</td><td>6.01</td><td>12.02</td><td>61.2</td><td>192.3</td><td>3.2</td><td>182.13</td></tr> <tr><td>7¾</td><td>5.66</td><td>11.32</td><td>57.6</td><td>181.1</td><td>2.55</td><td>172.30</td></tr> <tr><td>7</td><td>4.91</td><td>9.82</td><td>50.0</td><td>157.7</td><td>2.31</td><td>149.40</td></tr> <tr><td>6½</td><td>4.23</td><td>8.46</td><td>43.0</td><td>135.3</td><td>2.9</td><td>128.54</td></tr> <tr><td>6</td><td>3.61</td><td>7.2</td><td>36.7</td><td>115.5</td><td>1.52</td><td>110.1</td></tr> <tr><td>5½</td><td>3.13</td><td>6.2</td><td>31.8</td><td>99.2</td><td>1.36</td><td>94.30</td></tr> <tr><td>5</td><td>2.51</td><td>5.0</td><td>25.5</td><td>85.3</td><td>1.7</td><td>66.61</td></tr> <tr><td>4½</td><td>2.02</td><td>4.04</td><td>20.5</td><td>64.6</td><td>1.1</td><td>66.60</td></tr> <tr><td>4</td><td>1.6</td><td>3.2</td><td>16.2</td><td>51.2</td><td>0.51</td><td>48.51</td></tr> </table>

The depth to be drawn in yards.

<table> <tr> <th>Diameter of cylinder in inches.</th> <th>15</th> <th>20</th> <th>25</th> <th>30</th> <th>35</th> <th>40</th> <th>45</th> <th>50</th> <th>60</th> <th>70</th> <th>80</th> <th>90</th> </tr> <tr><td>18½</td><td>21½</td><td>24</td><td>26½</td><td>28</td><td>30</td><td>32</td><td>34</td><td>37</td><td>40</td><td>43½</td><td></td><td></td></tr> <tr><td>17</td><td>19½</td><td>22</td><td>25</td><td>26½</td><td>28</td><td>29½</td><td>31</td><td>34</td><td>37</td><td>39½</td><td></td><td></td></tr> <tr><td>15½</td><td>18</td><td>20</td><td>22</td><td>23</td><td>25</td><td>27</td><td>28</td><td>31</td><td>34</td><td>36</td><td>38</td><td></td></tr> <tr><td>14</td><td>16½</td><td>18</td><td>20</td><td>21</td><td>23</td><td>24</td><td>25</td><td>28</td><td>30</td><td>33</td><td>35</td><td></td></tr> <tr><td>13½</td><td>15</td><td>17</td><td>19</td><td>20</td><td>21</td><td>23</td><td>24</td><td>26</td><td>28</td><td>31</td><td>32</td><td></td></tr> <tr><td>12½</td><td>14</td><td>16</td><td>18</td><td>19</td><td>20</td><td>21</td><td>23</td><td>25</td><td>27</td><td>29</td><td>30</td><td></td></tr> <tr><td>12</td><td>14</td><td>15½</td><td>17½</td><td>18½</td><td>19</td><td>21</td><td>22</td><td>24</td><td>26</td><td>28</td><td>29½</td><td></td></tr> <tr><td>11</td><td>13</td><td>15</td><td>16½</td><td>18</td><td>19</td><td>20</td><td>21</td><td>23</td><td>25</td><td>27</td><td>28</td><td></td></tr> <tr><td>10½</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>18</td><td>19</td><td>20</td><td>22</td><td>24</td><td>25</td><td>27</td><td></td></tr> <tr><td>10</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>18</td><td>19</td><td>20</td><td>22</td><td>23</td><td>24</td><td></td></tr> <tr><td>9½</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>17</td><td>19</td><td>20</td><td>22</td><td>23</td><td></td></tr> <tr><td>9</td><td>10</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>17</td><td>19</td><td>20</td><td>21</td><td></td></tr> <tr><td>8½</td><td>10</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>17</td><td>19</td><td>20</td><td>21</td><td></td></tr> <tr><td>8</td><td>10</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>17</td><td>19</td><td>20</td><td>21</td><td></td></tr> <tr><td>7½</td><td>9</td><td>10</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>17</td><td>19</td><td>20</td><td></td></tr> <tr><td>7</td><td>9</td><td>10</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16½</td><td>17</td><td>19</td><td>20</td><td></td></tr> </table>

The first part of the table gives the size of the pump suited to the growth of water. The second gives the size of the cylinder suited to the load of water. If the depth is greater than any in this table, take its fourth part, and double the diameter of the cylinder. Thus if 150 hogheads are to be drawn in an hour from the depth of 100 fathoms, the last column of part first gives for 149.40 a pump of seven inches bore. In a line with this, under the depth of 50 yards, which is one-fourth of 100 fathoms, we find 20½, the double of which is 41 inches for the diameter of the cylinder.

It is almost impossible to give a general rule for strokes of different lengths, &c. but any one who professes the ability to erect an engine, should surely know as much arithmetic as will accommodate the rule now given to any length of stroke.

We venture to say, that no ordinary engineer can tell à priori the number per minute which an engine will give. We took 12 strokes of fixt feet each for a standard, which a careful engineer may easily accomplish, and which an employer has a right to expect, the engine being loaded with water to half the pressure of the atmosphere: if the load be less, there is some fault—an improper counter weight, or too little boiler, or leaks, &c. &c.

Such is the state in which Newcomen's steam-engine had continued in use for 60 years, neglected by the philosopher, although it is the most curious object which human ingenuity has yet offered to his contemplation, and abandoned to the efforts of the unlettered artif. Its use has been entirely confined to the raising of water. Mr Keane Fitzgerald indeed published in the Philosophical Transactions a method of converting its reciprocating motion into a continued rotary motion by employing the great beam to work a crank or a train of wheel-work. As the real action of the machine is confined to its working stroke, to accomplish this, it became necessary to connect with the crank or wheeled work a very large and heavy fly, which should accumulate in itself the whole prelude of the machine during its time of action, and therefore continue in motion, and urge forward the working machinery, while the steam-engine was going through its inactive returning stroke. This will be the case, provided that the resistance exerted by the working machine during the whole period of the working and returning stroke of the steam-engine, together with the friction of both, does not exceed the whole pressure exerted by the steam-engine during its working stroke; and provided that the momentum of the fly, arising from its great weight and velocity, be very great, so that the resistance of the work during one returning stroke of the steam-engine do not make any very sensible diminution of the velocity of the fly. This is evidently possible and easy. The fly may be made of any magnitude; and being exactly balanced round its axis, it will soon acquire any velocity consistent with the motion of the steam-engine. During the working stroke of the engine it is uniformly accelerated, and by its acquired momentum it produces in the beam the movement of the returning stroke; but in doing this, its momentum is shared with the inert matter of the steam-engine, and consequently its velocity diminished, but not entirely taken away. The next working stroke therefore, by pressing on it afresh, increases its remaining velocity by a quantity nearly equal to the whole that it acquired during the first stroke. We say nearly, but not quite equal, because the time of the second working stroke must be shorter than that of the first, on account of the velocity already in the machine. In this manner the fly will be more and more accelerated every succeeding stroke, because the prelude of the engine during the working stroke does more than restore to the fly the momentum which it lost in producing the returning movement of the steam-engine. Now suppose the working part of the machine to be added. The acceleration of the fly during each working stroke of the steam-engine will be less than it was before, because the impelling pressure is now partly employed in driving the working machine, and because the fly will lose more of its momentum during the returning stroke of the steam-engine, part of it being expended in driving the working machine. It is evident, therefore, that a time will come come when the successive augmentation of the fly's velocity will cease; for, on the one hand, the continual acceleration diminishes the time of the next working stroke, and therefore the time of action of the accelerating power. The acceleration must diminish in the same proportion; and on the other hand, the resistance of the working machine generally, though not always, increases with its velocity. The acceleration ceases whenever the addition made to the momentum of the fly during a working stroke of the steam-engine is just equal to what it looses by driving the machine, and by producing the returning movement of the steam engine.

This must be acknowledged to be a very important addition to the engine, and though sufficiently obvious, it is ingenious, and requires considerable skill and address to make it effective (b).

The movement of the working machine, or mill of whatever kind, must be in some degree hobbiling or unequal. But this may be made quite insensible, by making the fly exceedingly large, and disposing the greatest part of its weight in the rim. By these means its momentum may be made so great, that the whole force required for driving the mill and producing the returning movement of the engine may bear a very small proportion to it. The diminution of its velocity will then be very trifling.

No counter weight is necessary here, because the returning movement is produced by the inertia of the fly. A counter weight may, however, be employed, and should be employed, viz. as much as will produce the returning movement of the steam-engine. It will do this better than the same force accumulated in the fly; for this force must be accumulated in the fly by the intervention of rubbing parts, by which some of it is lost; and it must be afterwards returned to the engine with a similar loss. But, for the same reason, it would be improper to make the counter weight able to drive the mill during the returning stroke.

By this contrivance Mr Fitzgerald hoped to render the steam-engine of most extensive use; and he, or others associated with him, obtained a patent excluding all others from employing the steam-engine for turning a crank. They also published proposals for erecting mills of all kinds driven by steam-engines, and stated very fairly their powers and their advantages. But their proposals do not seem to have acquired the confidence of the public; for we do not know of any mill ever having been erected under this patent.

The great obstacle to this extensive use of the steam-engine is the prodigious expense of fuel. An engine having a cylinder of four feet diameter, working night and day, consumes about 3400 chaldron (London) of good coals in a year.

This circumstance limits the use of steam-engines exceedingly. To draw water from coal-pits, where they can be stocked with unsaleable small coal, they are of universal employment; also for valuable mines, for supplying a great and wealthy city with water, and a few other purposes where a great expense can be borne, they are very proper engines; but in a thousand cases, where their unlimited powers might be vastly serviceable, the enormous expense of fuel completely excludes them. We cannot doubt but that the attention of engineers was much directed to every thing that could promise a diminution of this expense. Every one had his particular notion for the construction of his furnace, and some were undoubtedly more successful than others. But science was not yet sufficiently advanced: It was not till Dr Black had made his beautiful discovery of latent heat, that we could know the intimate relation between the heat expended in boiling off a quantity of water and the quantity of steam that is produced.

Much about the time of this discovery, viz. 1763, Mr James Watt, established in Glasgow in the commercial line, was amusing himself with repairing a working model of the steam-engine which belonged to the philosophical apparatus of the university. Mr Watt was a person of a truly philosophical mind, eminently conversant in all branches of natural knowledge, and the pupil and intimate friend of Dr Black. In the course of the above-mentioned amusement many curious facts in the production and condensation of steam occurred to him; and among others, that remarkable fact which is always appealed to by Dr Black as the proof of the immense quantity of heat which is contained in a very minute quantity of water in the form of elastic steam. When a quantity of water is heated several degrees above the boiling point in a close digester, if a hole be opened, the steam rushes out with prodigious violence, and the heat of the remaining water is reduced, in the course of three or four seconds, to the boiling temperature. The water of the steam which has escaped amounts only to a very few drops; and yet these have carried off with them the whole excess of heat from the water in the digester.

Since then a certain quantity of steam contains so great a quantity of heat, it must expend a great quantity of fuel; and no construction of furnace can prevent this. Mr Watt therefore set his invention to work to discover methods of husbanding this heat. The cylinder of his little model was heated almost in an instant, so that it could not be touched by the hand. It could not be otherwise, because it condensed the vapour by abstracting its heat. But all the heat thus communicated to the cylinder, and wafted by it on surrounding bodies, contributed nothing to the performance of the engine,

(b) We do not recollect at present the date of this proposal of Mr Fitzgerald; but in 1781 the Abbé Arnal, canon of Alais in Languedoc, entertained a thought of the same kind, and proposed it for working lighters in the inland navigations; a scheme which has been successfully practised (we are told) in America. His brother, a major of engineers in the Austrian service, has carried the thing much farther, and applied it to manufactures; and the Aulic Chamber of Mines at Vienna has patronized the project: (See Journal Encyclopedique, 1781). But these schemes are long posterior to Mr Fitzgerald's patent, and are even later than the erection of several machines driven by steam-engines which have been erected by Messrs Watt and Boulton. We think it our duty to state these particulars, because it is very usual for our neighbours on the continent to assume the credit of British inventions. engine, and must be taken away at every injection, and again communicated and wafted. Mr Watt quickly understood the whole process which was going on within the cylinder, and which we have considered so minutely, and saw that a very considerable portion of the steam must be wafted in warming the cylinder. His first attempts were made to ascertain how much was thus wafted, and he found that it was not less than three or four times as much as would fill the cylinder and work the engine. He attempted to diminish this waste by using wooden cylinders. But though this produced a sensible diminution of the waste, other reasons forced him to give them up. He then casted his metal cylinders in a wooden case with light wood ashes between. By this, and using no more injection than was absolutely necessary for the condensation, he reduced the waste almost one half. But by using too small a quantity of cold water, the inside of the cylinder was hardly brought below the boiling temperature; and there consequently remained in it a steam of very considerable elasticity, which robbed the engine of a proportional part of the atmospheric pressure. He saw that this was unavoidable as long as the condensation was performed in the cylinder. The thought struck him to attempt the condensation in another place. His first experiment was made in the simplest manner. A globular vessel communicated by means of a long pipe of one inch diameter with the bottom of his little cylinder of four inches diameter and 30 inches long. This pipe had a stop-cock, and the globe was immersed in a vessel of cold water. When the piston was at the top, and the cylinder filled with strong steam, he turned the cock. It was scarcely turned, nay he did not think it completely turned, when the sides of his cylinder (only strong tin-plate) were crushed together like an empty bladder. This surprised and delighted him. A new cylinder was immediately made of brass sufficiently thick, and nicely bored. When the experiment was repeated with this cylinder, the condensation was so rapid, that he could not say that any time was expended in it. But the most valuable discovery was, that the vacuum in the cylinder was, as he hoped, almost perfect. Mr Watt found, that when he used water in the boiler purged of air by long boiling, nothing that was very sensibly inferior to the pressure of the atmosphere on the piston could hinder it from coming quite down to the bottom of the cylinder. This alone was gaining a great deal, for in most engines the remaining elasticity of the steam was not less than one-eighth of the atmospheric pressure, and therefore took away one-eighth of the power of the engine.

Having gained this capital point, Mr Watt found many difficulties to struggle with before he could get the machine to continue its motion. The water produced from the condensed steam, and the air which was extricated from it, or which penetrated through unavoidable leaks, behaved to accumulate in the condensing vessel, and could not be voided in any way similar to that adopted in Newcomen's engine. He took another method: He applied pumps to extract both, which were worked by the great beam. The contrivance is easy to any good mechanic; only we must observe, that the piston of the water-pump must be under the surface of the water in the condenser, that the water may enter the pump by its own weight, because there is no atmospherical pressure there to force it in. We must also observe, that a considerable force is necessarily expended here, because, as there is but one stroke for rarefying the air, and this rarefaction must be nearly complete, the air-pump must be of large dimensions, and its piston must act against the whole pressure of the atmosphere. Mr Watt, however, found that this force could be easily spared from his machine, already so much improved in respect of power.

Thus has the steam-engine received a very considerable improvement. The cylinder may be allowed to remain very hot; nay, boiling hot, and yet the condensation be completely performed. The only elastic steam that now remains is the small quantity in the pipe of communication. Even this small quantity Mr Watt at last got rid of, by admitting a small jet of cold water up this pipe to meet the steam in its passage to the condenser. This both cooled this part of the apparatus in a situation where it was not necessary to warm it again, and it quickened the condensation. He found at last that the small pipe of communication was of itself sufficiently large for the condensation, and that no separate vessel, under the name of condenser, was necessary. This circumstance shows the prodigious rapidity of the condensation. We may add, that unless this had been the case, his improvement would have been vastly diminished; for a large condenser would have required a much larger air-pump, which would have expended much of the power of the engine. By these means the vacuum below the piston is greatly improved: for it will appear clear to any person who understands the subject, that as long as any part of the condenser is kept of a low temperature, it will abstract and condense the vapour from the warmer parts, till the whole acquires the elasticity corresponding to the coldest part. By the same means much of the waste is prevented, because the cylinder is never cooled much below the boiling temperature. Many engines have been erected by Mr Watt in this form, and their performance gave universal satisfaction.

We have contented ourselves with giving a very slight description without a figure of this improved engine, because we imagine it to be of very easy comprehension, and because it is only a preparation for still greater improvements, which, when understood, will at the same time leave no part of this more simple form unexplained.

During the progress of these improvements Mr Watt made many experiments on the quantity and density of the steam of boiling water. These fully convinced him that although he had greatly diminished the waste of the steam, a great deal yet remained, and that the steam of steam expended during the rise of the piston was at least three times more than what would fill the cylinder. The cause of this was very apparent. In the subsequent descent of the piston, covered with water much below the boiling temperature, the whole cylinder was necessarily cooled and exposed to the air. Mr Watt's fertile genius immediately suggested to him the expedient of employing the elasticity of the steam from the boiler to impel the piston down the cylinder, in place of the pressure of the atmosphere; and thus he restored the engine to its first principles, making it an engine really moved by steam. As this is a new epoch in its history, we shall be more particular in the description; at the fame fame time still restricting ourselves to the essential circumstances, and avoiding every peculiarity which is to be found in the prodigious varieties which Mr Watt has introduced into the machines which he has erected, every individual of which has been adapted to local circumstances, or diversified by the progress of Mr Watt's improvements.

Let A (fig. 9.) represent the boiler. This has received great improvements from his complete acquaintance with the procedure of nature in the production of steam. In some of his engines the fuel has been placed in the midst of the water, surrounded by an iron or copper vessel, while the exterior boiler was made of wood, which transmits, and therefore wastes the heat very slowly. In others, the flame not only plays round the whole outside, as in common boilers, but also runs along several flues which are conducted through the midst of the water. By such contrivances the fire is applied to the water in a most extensive surface, and for a long time, so as to impart to it the greatest part of its heat. So skilfully was it applied in the Albion mills, that although it was perhaps the largest engine in the kingdom, its unconsumed smoke was inferior to that of a very small brew-house. In this second engine of Mr Watt, the top of the cylinder is shut up by a strong metal plate g h, in the middle of which is a collar or box of leathers k l, formed in the usual manner of a jack-head pump, through which the piston rod PD, nicely turned and polished, can move up and down, without allowing any air to pass by its sides. From the dome of the boiler proceeds a large pipe BCIOQ, which, after reaching the cylinder with its horizontal part BC, descends parallel to its side, sending off two branches, viz. IM to the top of the cylinder, and ON to its bottom. At I is a puppet valve opening from below upwards. At L, immediately below this branch, there is a similar valve, also opening from below upwards. The pipe descends to Q, near the bottom of a large cistern c d e f, filled with cold water constantly renewed. The pipe is then continued horizontally along the bottom of this cistern (but not in contact), and terminates at R in a large pump ST. The piston S has clack valves opening upwards, and its rod S s, passing through a collar of leathers at T, is suspended by a chain to a small arch head on the outer arm of the beam. There is a valve R in the bottom of this pump, as usual, which opens when pressed in the direction QR, and shuts against a contrary pressure. This pump delivers its contents into another pump XY, by means of the small pipe X, which proceeds from its top. This second pump has a valve at X, and a clack in its piston Z as usual, and the piston rod Z z is suspended from another arch head on the outer arm of the beam. The two valves I and L are opened and shut by means of spanners and handles, which are put in motion by a plug frame, in the same manner as in Newcomen's engine.

Lastly, there may be observed a crooked pipe a b o, which enters the upright pipe laterally a little above Q. This has a small jet hole at o; and the other end a, which is considerably under the surface of the water of the condensing cistern, is covered with a puppet valve v, whose long stalk v u rises above the water, and may be raised or lowered by hand or by the plug beam. The valves R and X, and the clacks in the pistons S and Z, are opened or shut by the pressure to which they are immediately exposed.

This figure is not an exact copy of any of Mr Watt's engines, but has its parts so disposed that all may come distinctly into view, and exactly perform their various functions. It is drawn in its quietest position, the outer end of the beam preponderating by the counter weight, and the piston P at the top of the cylinder, and the pistons S and Z in their lowest situations.

In this situation let us suppose that a vacuum is (by any means) produced in all the space below the piston, the valve I being shut. It is evident that the valve R will also be shut, as also the valve v. Now let the valve I be opened. The steam from the boiler, as elastic as common air, will rush into the space above the piston, and will exert on it a pressure as great as that of the atmosphere. It will therefore press it down, raise the outer end of the beam, and cause it to perform the same work as an ordinary engine.

When the piston P has reached the bottom of the cylinder, the plug frame shuts the valve I, and opens L. By so doing the communication is open between the top and bottom of the cylinder, and nothing hinders the steam which is above the piston from going along the passage MLON. The piston is now equally affected on both sides by the steam, even though a part of it is continually condensed by a cylinder, and in the pipe IOQ. Nothing therefore hinders the piston from being dragged up by the counter weight, which acts with its whole force, undiminished by any remaining unbalanced elasticity of steam. Here therefore this form of the engine has an advantage (and by no means a small one) over the common engines, in which a great part of the counter weight is expended in overcoming unbalanced atmospheric pressure.

Whenever the piston P arrives at the top of the cylinder, the valve L is shut by the plug frame, and the valves I and v are opened. All the space below the piston is at this time occupied by the steam which came from the upper part of the cylinder. This being a little wafted by condensation, is not quite a balance for the pressure of the atmosphere. Therefore, during the ascent of the piston, the valve R was shut, and it remains so. When, therefore, the valve v is opened, the cold water of the cistern must spout up through the hole o, and condense the steam. To this must be added the coldness of the whole pipe OQS. As fast as it is condensed, its place is supplied by steam from the lower part of the cylinder. We have already remarked, that this successive condensation is accomplished with astonishing rapidity. In the mean time steam from the boiler passes on the upper surface of the piston. It must therefore descend as before, and the engine must perform a second working stroke.

But in the mean time the injection water lies in the bottom of the pipe OQR, heated to a considerable degree by the condensation of the steam; also a quantity of air has been disengaged from it and from the water in the boiler. How is this to be discharged?—This is the office of the pumps ST and XY. The capacity of ST is very great in proportion to the space in which the air and water are lodged. When, therefore, the piston S has got to the top of its course, there must be a vacuum in the barrel of this pump, and the water and air must open the valve R and come into it. When the piston S comes down again in the next returning stroke, this water and air gets through the valve of the piston; and in the next working stroke they are discharged by the piston into the pump XY, and raised by its piston. The air escapes at Y, and as much of the water as is necessary is delivered into the boiler by a small pipe Yg to supply its waste. It is a matter of indifference whether the pistons S and Z rise with the outer or inner end of the beam, but it is rather better that they rise with the inner end. They are otherwise drawn here, in order to detach them from the rest and show them more distinctly.

Such is Mr Watt's second engine. Let us examine its principles, that we may see the causes of its avowed and great superiority over the common engines.

We have already seen one ground of superiority, the full operation of the counter weight. We are authorised by careful examination to say, that in the common engines at least one-half of the counter weight is expended in counteracting an unbalanced prelure of the air on the piston during its ascent. In many engines, which are not the worst, this extends to \( \frac{1}{3} \)th of the whole pressure. This is evident from the examination of the engine at Montrelaix by Boffut. This makes a very great counter weight necessary, which exhausts a proportional part of the moving force,

But the great advantage of Mr Watt's form is the almost total annihilation of the waste of steam by condensation in the cylinder. The cylinder is always boiling hot, and therefore perfectly dry. This must be evident to any person who understands the subject. By the time that Mr Watt had completed his improvements, his experiments on the production of steam had given him a pretty accurate knowledge of its density; and he found himself authorised to say, that the quantity of steam employed did not exceed twice as much as would fill the cylinder, so that not above one-half was unavoidably wasted. But before he could bring the engine to this degree of perfection, he had many difficulties to overcome: He inclosed the cylinder in an outer wooden case at a small distance from it. This diminished the expense of heat by communication to surrounding bodies. Sometimes he allowed the steam from the boiler to occupy this interval. This undoubtedly prevented all dissipation from the inner cylinder; but in its turn it diffused much heat by the outer case, and a very sensible condensation was observed between them. This has occasioned him to omit this circumstance in some of his best engines. We believe it was omitted in the Albion mills.

The greatest difficulty was to make the great piston tight. The old and effectual method, by water lying on it, was inadmissible. He was therefore obliged to have his cylinders most nicely bored, perfectly cylindrical, and finely polished; and he made numberless trials of different soft substances for packing his piston, which should be tight without enormous friction, and which should long remain so, in a situation perfectly dry, and hot almost to burning.

After all that Mr Watt has done in this respect, he thinks that the greatest part of the waste of steam which he still perceives in his engines arises from the unavoidable escape by the sides of the piston during its descent.

But the fact is, that an engine of this construction, of the same dimensions with a common engine, making the same number of strokes of the same extent, does not consume above one-fourth part of the fuel that is consumed by the best engines of the common form. It is also a very fortunate circumstance, that the performance of the engine is not immediately destroyed, nor indeed sensibly diminished, by a small want of tightness in the piston. In the common engine, if air get in, in this way, it immediately puts a stop to the work; but although even a considerable quantity of steam get past the piston during its descent, the rapidity of condensation is such, that hardly any diminution of pressure can be observed.

Mr Watt's penetration soon discovered another most valuable property of this engine. When an engine of the common form is erected, the engineer must make an accurate estimate of the work to be performed, and must proportion his engine accordingly. He must be careful that it be fully able to execute its task; but its power must not exceed its load in any extravagant degree. This would produce a motion which is too rapid, and which, being alternately in opposite directions, would occasion jolts which no building or machinery could withstand. Many engines have been shattered by the pumps drawing air, or a pump-rod breaking; by which accidents the steam-piston descends with such rapidity that every thing gives way. But in most operations of mining, the task of the engine increases, and it must be so constructed at first as to be able to bear this addition. It is very difficult to manage an engine that is much superior to its task; and the easiest way is, to have it almost full loaded, and to work it only during a few hours each day, and allow the pit water to accumulate during its repose. This increases the first cost, and wastes fuel during the inaction of the engine.

But this new engine can at all times be exactly fitted (at least during the working stroke) to the load of work can away that then happens to be on it. We have only to add, that the engine may be equal to twice its task, if the which has admitted above the cylinder be equal to that of pens to be common boiling water; but when once the ebullition on it is fairly commenced, and the whole air expelled from all parts of the apparatus, it is evident, that by damping the fire, steam of half this elasticity may be continually supplied, and the water will continue boiling although its temperature does not exceed 185° of Fahrenheit's thermometer. This appears by inspecting our table of vaporous elasticity, and affords another argument for rendering that table more accurate by new experiments. We hope that Mr Watt will not withhold from the public the knowledge which he has acquired on this subject. It may very possibly result from an accurate investigation, that it would be advisable to work our steam-engines with weak steams, and that the diminution of work may be more than compensated by the diminution of fuel. It is more probable indeed, and it is Mr Watt's opinion, that the contrary is the case, and that it is much more economical to employ great heats. At any rate, the decision of this question is of great importance for improving the engine; and we fee, in the mean time, that the engine can at all times be fitted so as to perform its task with a moderate and manageable motion, and that as the task increases we can increase the power of the engine. But the method now proposed has a great inconvenience. While the steam is weaker than the atmosphere, there is an external force tending to squeeze in the fides and bottom of the boiler. This could not be rectified when the difference is considerable, and common air would rush in through every crevice of the boiler and soon choke the engine: it must therefore be given up.

But the same effect will be produced by diminishing the passage for the steam into the cylinder. For this purpose, the puppet valve by which the steam enters the cylinder was made in the form of a long taper spigot, and it was lodged in a cone of the same shape; consequently the passage could be enlarged or contracted at pleasure by the distance to which the inner cone was drawn up.

In this way several engines were constructed, and the general purpose of suiting the power of the engine to its task was completely answered: but (as the mathematical reader will readily perceive) it was extremely difficult to make this adjustment precise and constant. In a great machine like this going by jerks, it was hardly possible that every successive motion of the valve should be precisely the same. This occasioned very sensible irregularities in the motion of the engine, which increased and became hazardous when the joints worked loose by long use.

Mr Watt's genius, always fertile in resources, found out a complete remedy for all these inconveniences. Making the valve of the ordinary form of a puppet clack, he adjusted the button of its stalk or tail so that it should always open full to the same height. He then regulated the pins of the plug-frame, in such a manner that the valve should shut the moment that the piston had descended a certain proportion (suppose one-fourth, one-third, one-half, &c.) of the cylinder. So far the cylinder was occupied by steam as elastic as common air. In pressing the piston farther down, it behoved the steam to expand, and its elasticity to diminish. It is plain that this could be done in any degree we please, and that the adjustment can be varied in a minute, according to the exigency of the case, by moving the plug pins.

In the mean time, it must be observed, that the pressure on the piston is continually changing, and consequently the accelerating force. The motion therefore will no longer be uniformly accelerated: it will approach much faster to uniformity; nay, it may be retarded, because although the pressure on the piston at the beginning of the stroke may exceed the resistance of the load, yet when the piston is near the bottom the resistance may exceed the pressure. Whatever may be the law by which the pressure on the piston varies, an ingenious mechanic may contrive the connecting machinery in such a way that the chains or rods at the outer end of the beam shall continually exert the same pressure, or shall vary their pressure according to any law he finds most convenient. It is in this manner that the watchmaker, by the form of the fusee, produces an equal pressure on the wheel-work by means of a very unequal action of the main-spring. In like manner, by making the outer arch heads portions of a proper spiral instead of a circle, we can regulate the force of the beam at pleasure.

Thus we see how much more manageable an engine is in this form than Newcomen's was, and also more easily investigated in respect of its power in its various positions. The knowledge of this last circumstance was of mighty consequence, and without it no notion could be formed of what it could perform. This suggested to Mr Watt the use of the barometer communicating with the cylinder; and by the knowledge acquired by these means has the machine been so much improved by its ingenious inventor.

We must not omit in this place one deduction made by Mr Watt from his observations, which may be called a discovery of great importance in the theory of the engine.

Let ABCD (fig. 10.) represent a section of the cylinder of a steam-engine, and EF the surface of its piston. Let us suppose that the steam was admitted of great while EF was in contact with AB, and that as soon as it had pressed it down to the situation EF the steam cock is shut. The steam will continue to press it down, and as the steam expands its pressure diminishes. We Fig. 10. may express its pressure (exerted all the while the piston moves from the situation AB to the situation EF) by the line EF. If we suppose the elasticity of the steam proportional to its density, as is nearly the case with air, we may express the pressure on the piston in any other position, such as KL or DC, by K' and Dc, the ordinates of a rectangular hyperbola F/c, of which AE, AB are the asymptotes, and A the centre. The accumulated pressure during the motion of the piston from EF to DC will be expressed by the area EFcDE, and the pressure during the whole motion by the area ABFcDA.

Now it is well known that the area EFcDE is equal to ABFc multiplied by the hyperbolic logarithm of \( \frac{AD}{AE} = L \cdot \frac{AD}{AE} \), and the whole area ABFcDA is

\[ ABFc \times \left( 1 + L \cdot \frac{AD}{AE} \right). \]

Thus let the diameter of the piston be 24 inches, and the pressure of the atmosphere on a square inch be 14 pounds; the pressure on the piston is 6333 pounds. Let the whole stroke be 6 feet, and let the steam be stopped when the piston has descended 18 inches, or 1.5 feet. The hyperbolic logarithm of \( \frac{6}{1.5} \) is 1.3862943. Therefore the accumulated pressure ABFcDA is \( 6333 \times 2.3862943 = 15114 \) pounds.

As few professional engineers are possessed of a table of hyperbolic logarithms, while tables of common logarithms are or should be in the hands of every person who is much engaged in mechanical calculations, let the following method be practised. Take the common logarithm of \( \frac{AD}{AE} \), and multiply it by 2.3026; the product is the hyperbolic logarithm of \( \frac{AD}{AE} \).

The accumulated pressure while the piston moves from AB to EF is 6333 × 1, or simply 6333 pounds. Therefore the steam while it expands into the whole cylinder adds a pressure of 8781 pounds.

Suppose that the steam had got free admission during the whole descent of the piston, the accumulated pressure would have been 6333 × 4, or 25332 pounds.

Here Mr Watt observed a remarkable result. The steam expended in this case would have been four times greater greater than when it was flopped at one-fourth, and yet the accumulated pressure is not twice as great, being nearly five-thirds. One-fourth of the steam performs nearly three-fifths of the work, and an equal quantity performs more than twice as much work when thus admitted during one-fourth of the motion.

This is a curious and an important information, and the advantage of this method of working a steam-engine increases in proportion as the steam is sooner flopped; but the increase is not great after the steam is rarefied four times. The curve approaches near to the axis, and small additions are made to the area. The expense of such great cylinders is considerable, and may sometimes compensate this advantage.

<table> <tr> <th>Let the steam be stopped at</th> <th>Its performance is mult.</th> </tr> <tr> <td>\( \frac{1}{2} \)</td> <td>-</td> <td>1.7</td> </tr> <tr> <td>\( \frac{1}{3} \)</td> <td>-</td> <td>2.1</td> </tr> <tr> <td>\( \frac{1}{4} \)</td> <td>-</td> <td>2.4</td> </tr> <tr> <td>\( \frac{1}{5} \)</td> <td>-</td> <td>2.6</td> </tr> <tr> <td>\( \frac{1}{6} \)</td> <td>-</td> <td>2.8</td> </tr> <tr> <td>\( \frac{1}{7} \)</td> <td>-</td> <td>3.</td> </tr> <tr> <td>\( \frac{1}{8} \)</td> <td>-</td> <td>3.2</td> </tr> <tr> <td>&amp;c.</td> <td>&amp;c.</td> <td>&amp;c.</td> </tr> </table>

It is very pleasing to observe so many unlooked-for advantages resulting from an improvement made with the sole view of lessening the waste of steam by condensation. While this purpose is gained, we learn how to husband the steam which is not thus wasted. The engine becomes more manageable, and is more easily adapted to every variation in its task, and all its powers are more easily computed.

The active mind of its ingenious inventor did not stop here: It had always been matter of regret that one-half of the motion was unaccompanied by any work. It was a very obvious thing to Mr Watt, that as the steam admitted above the piston preflled it down, so steam admitted below the piston preflled it up with the same force, provided that a vacuum were made on its upper side. This was easily done, by connecting the lower end of the cylinder with the boiler and the upper end with the condenser.

Fig. 11. is a representation of this construction exactly copied from Mr Watt's figure accompanying his specification. Here BB is a section of the cylinder, surrounded at a small distance by the cafe IIII. The section of the piston A, and the collar of leathers which embraces the piston rod, gives a distinct notion of its construction, of the manner in which it is connected with the piston-rod, and how the packing of the piston and collar contributes to make all tight.

From the top of the cylinder proceeds the horizontal pipe. Above the letter D is observed the seat of the steam valve, communicating with the box above it. In the middle of this may be observed a dark shaded circle. This is the mouth of the upper branch of the steam pipe coming from the boiler. Beyond D, below the letter N, is the seat of the upper condensing valve. The bottom of the cylinder is made spherical, fitting the piston, so that they may come into entire contact. Another horizontal pipe proceeds from this bottom. Above the letter E is the seat of the lower steam valve, opening into the valve box. This box is at the extremity of another steam pipe marked C, which branches off from the upper horizontal part, and descends obliquely, coming forward to the eye. The lower part is represented as cut open, to show its interior conformation. Beyond this steam valve, and below the letter F, may be observed the seat of the lower condensing valve. A pipe descends from hence, and at a small distance below unites with another pipe GG, which comes down from the upper condensing valve N. These two eduction-pipes thus united go downwards, and open at L into a rectangular box, of which the end is seen at L. This box goes backward from the eye, and at its farther extremity communicates with the air-pump K, whose piston is here represented in section with its butterfly valves. The piston delivers the water and air laterally into another rectangular box M, darkly shaded, which box communicates with the pump I. The piston-rods of this and of the air-pump are suspended by chains from a small arch head on the inner arm of the great beam. The lower part of the eduction-pipe, the horizontal box L, the air-pump K, with the communicating box M between it and the pump I, are all immersed in the cold water of the condensing cistern. The box L is made flat, broad, and shallow, in order to increase its surface and accelerate the condensation. But that this may be performed with the greatest expedition, a small pipe H, open below (but occasionally flopped by a plug valve), is inserted laterally into the eduction-pipe G, and then divides into two branches; one of which reaches within a foot or two of the upper valve N, and the other approaches as near to the valve F.

As it is intended by this construction to give the piston a strong impulse in both directions, it will not be proper to suspend its rod by a chain from the great beam; for it must not only pull down that end of the beam, but also push it upwards. It may indeed be suspended by double chains like the pistons of the engines for extinguishing fires; and Mr Watt has accordingly done so in some of his engines. But in his drawing from which this figure is copied, he has communicated the force of the piston to the beam by means of a toothed rack OO, which engages or works in the toothed sector QQ on the end of the beam. The reader will understand, without any farther explanation, how the impulse given to the piston in either direction is thus transmitted to the beam without diminution. The fly XX, with its pinion Y, which also works in the toothed arch QQ, may be supposed to be removed for the present, and will be considered afterwards.

We shall take the present opportunity of describing Mr Watt's method of communicating the force of the steam-engine to any machine of the rotary kind. VV represents the rim and arms of a very large and heavy metalline fly. On its axis is the concentric toothed wheel U. There is attached to the end of the great beam a strong and stiff rod TT, to the lower end of which a toothed wheel W is firmly fixed by two bolts, so that it cannot turn round. This wheel is of the same size and in the same vertical plane with the wheel U; and an iron link or strap (which cannot be seen here, because it is on the other side of the two wheels) connects the centres of the two wheels, so that the one cannot quit the other. The engine being in the position represented in the figure, suppose the fly to be turned once round by any external force in the direction of the darts. It is plain, that since the toothed wheels cannot quit each other, being kept together by