[Pg145]
TOCINX
(77.)
In a letter addressed by Watt to Smeaton, dated April, 1766, Watt refers to some of these practical difficulties which he had to encounter. "I have been," says he, "tormented with exceedingly bad health, resulting from the operation of an anxious mind, the natural consequence of staking everything [Pg146] upon the cast of a die; for in that light I look upon every project which has not received the sanction of repeated success. "I have made considerable alterations in our engine lately, particularly in the condenser. That which I used at first was liable to be impaired, from incrustations from bad water; therefore we have substituted one which works by an injection. In pursuing this idea I have tried several kinds, and have at last come to one, which I am not inclined to alter. It consists of a jack-head pump, shut at bottom, with a common clack bucket, and a valve in the cover of the pump, to discharge the air and water. The eduction steam pipe, which comes from the cylinder, communicates with this pump both above and below the bucket, and has valves to prevent anything from going back from the pump to the eduction pipe. The bucket descends by its own weight, and is raised by the engine when the great piston descends, being hung to the outer end of the great lever: the injection is made both into the upper part of this pump and into the eduction pipe, and operates beyond my ideas in point of quickness and perfection."
Besides the difficulty arising from incrustation, Watt found the tubulated condensers, and indeed all other expedients for condensing by cold surfaces, subject to a fatal objection. They did not condense instantaneously, and although they were capable of ultimately effecting the condensation, yet that process was not completed until a great part of the stroke of the piston was made. Thus during more or less of the stroke the uncondensed steam resisted the piston, and robbed the moving power of a part of its effect. This objection has ever attended condensation by surface.
(78.)
Another source of difficulty arose from the necessity of constructing the piston and cylinder with greater precision than had been usual in the old engines. To fit the cover to the cylinder so as to be steam-tight; to construct the piston rod so as to move through it without allowing the escape of steam, and yet at the same time without injurious friction; to connect the piston rod with the piston, so as to drive the
[Pg147] latter through the cylinder with a perfectly straight and parallel motion; to make such connection perfectly centrical and firm, and yet to allow the piston in its ascent to come nearly into contact with the cover of the cylinder—were all difficulties peculiar to the new engine. In the atmospheric engine the shank of the piston rod was rough and square, and the rod was secured to the piston by two or four branches or stays, as represented in fig. 25. It is evident that such a construction would be inadmissible in an engine in which the piston in its ascent must be brought nearly into contact with the close cover of the cylinder. Besides this the piston rod of an atmospheric engine might throughout its whole length have any form which was most convenient, and required no other property than the strength necessary to work the beam. In the new engine, on the contrary, it was necessary that it should be accurately turned and finely polished, so as to pass through the hole in the top of the cylinder, and be maintained in it steam-tight. This was effected by a contrivance called a stuffing-box B, represented in fig. 26. A hole is made in the cover of the cylinder very little greater in magnitude than the diameter of the piston rod. Above this hole is a cup in which, around the piston, is placed a stuffing of hemp or tow, which is saturated with oil or melted tallow. This collar of hemp is pressed down by another piece, also perforated with a hole through which the piston rod plays, and which is screwed down on the said collar of hemp.
(79.)
Although the imperfect manner in which the interior of the cylinders was then formed impaired the efficiency of the [Pg148] new engines, yet such imperfections were not so injurious as in the old atmospheric engines. Any imperfection of form of the inner surface of the cylinder would necessarily cause more or less steam or air to escape between the piston and cylinder. In the improved engine this steam passing into the vacuum below the piston would rush into the condenser, and be there condensed, so that its effect in resisting the motion of the piston would necessarily be trifling. But on the other hand, any escape of air between the piston and cylinder of an atmospheric engine would introduce an elastic fluid under the piston, which would injuriously affect the action of the machine. To make the pistons move sufficiently steam-tight in these early imperfect cylinders, Watt contrived a packing formed of a collar of hemp, or tow, as represented in fig. 27. The bottom of the piston was formed of a circular plate of a diameter nearly, but not altogether equal to the interior diameter of the cylinder. The part of the piston above this was considerably less in diameter, so that the piston was surrounded by a circular groove or channel two inches wide, into which hemp or soft rope, called gasket, was run, so as to form the packing. The top of the piston was placed over this, having a rim or projecting part, which entered the circular groove and pressed upon the packing, the cover being pressed downwards by screws passing through the piston. The lower part of the groove round the piston was rounded with a curve, so that the pressure on the packing might force the latter against the inner surface of the cylinder. This packing was kept supplied with melted tallow, as already described, from the funnel, screwed into the top of the cylinder. The metallic edges of the piston were by this means prevented from coming into contact with the surface of the cylinder, which was only pressed upon by the stuffing or packing projecting beyond these.
(80.)
Improved methods of boring soon, however, relieved [Pg149] the engine from a part of these imperfections, and Watt writes to Mr. Smeaton in the letter above quoted as follows:— "Mr. Wilkinson has improved the art of boring cylinders; so that I promise, upon a 72 inch cylinder, being not further distant from absolute truth than the thickness of a thin sixpence in the worst part. I am labouring to improve the regulators; my scheme is to make them acute conical valves, shut by a weight, and opened by the force of the steam. They bid fair for success, and will be tried in a few days."
The person here alluded to was Mr. John Wilkinson, of Bersham near Chester, who, about the year 1775, contrived a new machine for accurately boring the insides of cylinders. The cylinder being first obtained from the foundery with a surface as accurate as the process of casting would admit, had its inner surface reduced to still greater accuracy by this machine, which consists of a straight central bar extended along the axis of the cylinder, which was made to revolve slowly round it. During the operation of boring, the borer or cutter was fitted to slide along this bar, which being perfectly straight, served as a sort of ruler to guide the borer or cutter in its progress through the cylinder. In this manner the interior surface of the cylinder was rendered not only true and straight in its longitudinal direction, but also perfectly circular in its cross section.
The grease found to be most eligible for lubrication was the tallow of beef or mutton; but in the earlier cylinders this was soon consumed by reason of the imperfection of the boring, and the piston being left dry ceased to be steam-tight. To prevent this, Watt sought for some substance, which while it would thicken the tallow, and detain it around the piston, would not be subject to decomposition by heat. Black lead dust was used for this purpose, but was soon found to wear the cylinder. In the mean while, however, the improved method of boring supplied cylinders which rendered this expedient unnecessary.
When the inner surface of the cylinder is perfectly true and smooth, the packing of the piston is soon rendered solid and hard, being moulded to the cylinder by working, so as to fit it perfectly. When by wear it became loose, it was [Pg150] only necessary to tighten the screws by which the top and bottom of the piston were held together. The packing being compressed by those means, was forced outwards towards the surface of the cylinder, so as to be rendered steam-tight.
(81.)
It was not until about the year 1778, nine years after the date of the patent, and thirteen after the invention of separate condensation, that any impression was produced on the mining interests by the advantages which were presented to them by these vast improvements. This long interval, however, had not elapsed without considerable advantage; for although all the great leading principles of the contrivance were invented so early as the year 1765, yet the details of construction had been in a state of progressive and continued improvement from the time Watt joined Dr. Roebuck, in 1769, to the period now adverted to. The advantages which the engine offered in the form in which it has been just described, were numerous and important, as compared even with the most improved form of the atmospheric engine; and it should be remembered, that that machine had also gone on progressively improving, and was probably indebted for some of its ameliorations to hints derived from the labours of Watt, and to the adoption of such of his expedients as were applicable to this imperfect machine, and could be adopted without an infraction of his patent.
In the most improved forms to which the atmospheric engine had then attained, the quantity of steam wasted at each stroke of the piston was equal to the contents of the cylinder. Such engines, therefore, consumed twice the fuel which would be requisite, if all sources of waste could have been removed. In Watt's engines, the steam consumed at each stroke of the piston amounted only to 11/4 times the contents of the cylinder. The waste steam, therefore, per stroke, was only a quarter of what was usefully employed. The absolute waste, therefore, of the best atmospheric engines was four times that of the improved engine, and consequently the saving of fuel in the improved engines amounted to about three eighths of all the fuel consumed in atmospheric engines of the same power. [Pg151]
(82.)
But independently of this saving of steam, which would otherwise be wasted, the power of Watt's engine, as compared with the atmospheric engine, was so much augmented that the former would work against a resistance of ten pounds on the square inch under the same circumstances in which the latter would not move against more than seven pounds. The cause of this augmentation of power is easily explained. In the atmospheric engine the temperature of the condensed steam could not be reduced below 152° without incurring a greater loss than would be compensated by the advantage to be obtained from any higher degree of condensation. Now steam raised from water at 152° has a pressure of nearly four pounds per square inch. This pressure, therefore, acted below the piston resisting the atmospheric pressure above. In Watt's engine, however, the condenser was kept at a temperature of about 100°, at which temperature steam has a pressure of less than one pound per square inch. A resisting force upon the piston of three pounds per square inch was therefore saved in Watt's engine as compared with the atmospheric engine.
(83.)
Besides these direct sources of economy, there were other advantages incidental to Watt's engine. An atmospheric engine possessed very limited power of adaptation to a varying load. The moving power being the atmospheric pressure, was not under control, and, on the other hand, was subject to variations from day to day and from hour to hour, according to the changes of the barometer. In the first construction of such an engine, therefore, its power being necessarily adapted to the greatest load which it would have to move, whenever the load upon its pumps was diminished, the motion of the piston in descending would be rapidly accelerated in consequence of the moving power exceeding the resistance. By this the machinery would be subject to sudden shocks, which were productive of rapid wear, and exposed the machinery to the danger of fracture. To remedy this inconvenience, the following expedient was provided in the atmospheric engine: whenever the load on the engine was materially diminished, the quantity of water admitted through the injection valve to condense the steam was proportionally [Pg152] diminished. An imperfect condensation being therefore produced, vapour remained in the cylinder under the piston, the pressure of which resisted the atmosphere, and mitigated the force of the machine. Besides this, a cock was provided in the bottom of the cylinder, called an air cock, by which atmospheric air could be admitted to resist the piston whenever the motion was too rapid. These expedients, however, were all attended with a waste of fuel in relation to the work done by the engine; for it is evident that the consumption of steam was necessarily the same, whether the engine was working against its full load or against a reduced resistance.
On the other hand, in the improved engine of Watt, when the load, to work against which the engine exerted its full power, was diminished, a cock or valve was provided in the steam pipe leading from the boiler, which was called a throttle valve, by adjusting which the passage in that pipe could be more or less contracted. By regulating this cock the supply of steam from the boiler was checked, and the quantity transmitted to the cylinder diminished, so that its effect upon the piston might be rendered equal to the amount of the diminished resistance. By this means the quantity of steam transmitted to the cylinder was rendered exactly proportional to the work which the engine had to perform. If, under such circumstances, the boiler was worked to its full power, so as to produce steam as fast as it would when the engine was working at full power, then no saving of fuel would be effected, since the surplus steam produced in the boiler would necessarily escape at the safety valve. But in such case the fireman was directed to limit the fuel of the furnace until the discharge at the safety valve ceased.
By these expedients, the actual consumption of fuel in one of these improved engines was always in the exact proportion of the work which it performed, whether it worked at full power or at any degree under its regular power.
To remove such objections, great sacrifices were necessary on the part of Boulton and Watt; and they accordingly resolved to undertake the construction of the new engines without any profit, giving them to the parties requiring their use at first cost, on the condition of being remunerated by a small share of what they would save in fuel.
"We have no objection," writes Mr. Boulton, "to contract with the Carron Company to direct the making of an engine to return the water for their mills. **** We do not aim at profits in engine building, but shall take our profits out of the saving of fuel; so that if we save nothing, we shall take nothing. Our terms are as follows: we will make all the necessary plans, sections, and elevations for the building, and for the engine with its appurtenances, specifying all cast and forged iron work, and every other particular relative to the engine. We will give all necessary directions to your workmen, which they must implicitly obey. We will execute, for a stipulated price, the valves, and all other parts which may·require exact execution, at Soho; we will see that all the parts are put together, and set to work, properly; we will keep our own work in repair for one year, and we have no other objection to seven years than the inconvenience of the distance. We will guarantee that the engine so constructed shall raise at least 20,000 cubic feet of water twenty-four feet high with each hundred weight of coals burnt.
"When all this is done, a fair and candid comparison shall be made between it, and your own engine, or any other engine in Scotland, from which comparison the amount of savings in fuel shall be estimated, and that amount being [Pg154] divided into three parts, we shall be entitled to one of those parts, in recompense for our patent licence, our drawings, &c. &c. Our own share of savings shall be estimated in money, according to the value of your coals delivered under the boiler, and you shall annually pay us that sum, during twenty-five years from the day you begin to work; provided you continue the use of the engine so long. And in case you sell the engine, or remove it to any other place, you must previously give us notice, for we shall then be entitled to our third of the savings of fuel, according to the value of coals at such new place. This is a necessary condition, otherwise the engine which we make for you at an expense of two thousand pounds may be sold in Cornwall for ten thousand pounds.
"Such parts of the engine as we execute at Soho we will be paid for at a fair price; I conclude, from all the observations I have had an opportunity of making, that our engines are four times better than the common engines. In boilers, which are a very expensive article, the savings will be in proportion to the savings of coal. If you compare our engine with the common engine (not in size, but in power), you will find the original expense of erecting one to be nearly the same.
"Mr. Wilkinson has bored us several cylinders, almost without error; that of fifty inches diameter, which we put up at Tipton, does not err the thickness of an old shilling in any part; so that you must either improve your method of boring, or we must furnish the cylinder to you."
The reluctance of mining companies to relinquish the old engines, even on these terms, led them to propose to Mr. Watt to grant them a licence for the use of his condenser, to be applied to the atmospheric engine, without the introduction of other improvements. Such a proposition was made to him by Mr. Smeaton, in the year 1778, to which he returned the following answer:—
"I have several times considered the propriety of the application of my condensers to common engines, and have made experiments with that view upon our engine at Soho, but have never found such results as would induce me to try [Pg155] it any where else; and, in consequence, we refused to make that application to Wheal Virgin engines in Cornwall, and to some others; our reasons were, that though it might have enabled them to have gone deeper with their present engines, yet, the savings of fuel would not have been great, in comparison to the complete machine. By adding condensers to engines that were not in good order, our engine would have been introduced into that country (which we look upon as our richest mine) in an unfavourable point of view, and without such profits as would have been satisfactory either to us or to the adventurers; and if we had granted the use of condensers to one, we must have done so to all, and thereby have curtailed our profits, and perhaps injured our reputation. Besides, where a new engine is to be erected, and to be equally well executed in point of workmanship and materials, an engine of the same power cannot be constructed materially cheaper on the old plan than on ours; for our boiler and cylinder are much smaller, and the building, the lever, the chains, together with all the pump and pit work, are only the same. * * **
"We charge our profits in proportion to the saving made in fuel by our engine, when compared with a common one which burns the same kind of coals; we ask one third of these savings to be paid us annually, or half yearly; the payment being redeemable in the option of our employer, at ten years' purchase; and when the coals are low priced, we should also make some charge as engineers. In all these comparisons our own interest has made us except your (Mr. Smeaton) improved engines, unless we were allowed a greater proportion of the savings."
Their exertions to improve the manufacture of engines at Soho is shown by the following letter from Mr. Boulton, in the same correspondence to Mr. Smeaton:—
"We are systematising the business of engine making, as we have done before in the button manufactory; we are training up workmen, and making tools and machines to form the different parts of Mr. Watt's engines with more accuracy, and at a cheaper rate than can possibly be done by the ordinary methods of working. Our workshop and apparatus will be of [Pg156] sufficient extent to execute all the engines which are likely to be soon wanted in this country; and it will not be worth the expense for any other engineers to erect similar works, for that would be like building a mill to grind a bushel of corn.
"I can assure you from experience, that our small engine at Soho is capable of raising 500,000 cubic feet of water 1 foot high with every 112 lbs. of coals, and we are in hopes of doing much more. Mr. Watt's engine has a very great advantage in mines, which are continually working deeper: suppose, for instance, that a mine is 50 fathoms deep, you may have an engine which will be equal to draining the water when the mine is worked, to 100 fathoms deep, and yet you can constantly adapt the engine to its load, whether it be 50 or 100 fathoms, or any intermediate depth; and the consumption of coals will be less in proportion when working at the lesser than at the greater depths; supposing it works, as our engines generally do, at 11 lbs. per square inch, when the mine becomes 100 fathoms deep."
(85.)
The great improvement which has been introduced within the last half century, in the details of Watt's steam engine, will be rendered manifest by comparing the effects of a given weight of fuel here supplied by Mr. Boulton with the effects which the same weight of fuel is now known to produce in the best pumping engines worked in Cornwall. One of these engines, in good working order, has been known to raise 125,000,000 lbs. 1 foot high, by the combustion of a bushel of coals. But the average performance of even the best engines is below this amount. If we take it at 90,000,000, this will be equivalent to the weight of about 11/2 million cubic feet of water, a bushel of coals being 3/4 cwt. It will therefore follow that, with the present engines, one hundred weight of coals is capable of raising about two million cubic feet of water one foot high, being a duty four times that assigned to the early engines by Mr. Boulton.
(86.)
At the time that Watt, in conjunction with Dr. Roebuck, obtained the patent for his improved engine, the idea occurred to him, that the steam which had impelled the piston in its descent rushed from the cylinder with a mechanical force much more than sufficient to overcome any resistance [Pg157] which it had to encounter in its passage to the condenser; and that such force might be rendered available as a moving power, in addition to that already obtained from the steam during the stroke of the piston. This notion involved the whole principle of the expansive action of steam, which subsequently proved to be of such importance in the performance of steam engines. Watt was, however, so much engrossed at that time, and subsequently, by the difficulties he had to encounter in the construction of his engines, that he did not attempt to bring this principle into operation. It was not until after he had organised that part of the establishment at Soho which was appropriated to the manufacture of steam engines, that he proceeded to apply the expansive principle. Since the date of the patent which he took out for this (1782), was subsequent to the application of the same principle by another engineer, named Hornblower, it is right to state, that the claim of Mr. Watt to this important step in the improvement of the steam engine, is established by a letter addressed by him to Dr. Small, of Birmingham, dated Glasgow, May, 1769:— "I mentioned to you a method of still doubling the effect of the steam, and that tolerably easy, by using the power of steam rushing into a vacuum, at present lost. This would do little more than double the effect, but it would too much enlarge the vessels to use it all: it is peculiarly applicable to wheel engines, and may supply the want of a condenser, where the force of steam only is used; for open one of the steam valves, and admit steam until one fourth of the distance between it and the next valve is filled with steam, then shut the valve, and the steam will continue to expand, and to press round the wheel, with a diminishing power, ending in one fourth of its first exertion. The sum of the series you will find greater than one half, though only one fourth of steam was used. The power will indeed be unequal, but this can be remedied by a fly, or by several other means."
In 1776 the engine, which had been then recently erected at Soho, was adapted to act upon the principle of expansion. When the piston had been pressed down in the cylinder for a certain portion of the stroke, the further supply of steam [Pg158] from the boiler was cut off, by closing the upper steam valve, and the remainder of the stroke was accomplished by the expansive power of the steam which had already been introduced into the cylinder.
(87.)
To make this method of applying the force of steam intelligible, some previous explanation of mechanical principles will be necessary. If a body which offers a certain resistance be urged by a certain moving force, the motion which it will receive will depend on the relation between the energy of the moving force and the amount of the resistance opposed to it. If the moving force be precisely equal to the resistance, the motion which the body will receive will be perfectly uniform.
If the energy of the moving force be greater than the resistance, then its surplus or excess above the amount of resistance will be expended in imparting momentum to the mass of the body moved, and the latter will, consequently, continually acquire augmented speed. The motion of the body will, therefore, be in this case accelerated.
If the energy of the moving force be less in amount than the resistance, then all that portion of the resistance which exceeds the amount of the moving force will be expended in depriving the mass of the body of momentum, and the body will therefore be moved with continually diminished speed until it be brought to rest.
(88.)
Whenever, therefore, a uniform motion is produced in a body, it may be taken as an indication of the equality of the moving force to the resistance; and, on the other hand, according as the speed of the body is augmented or diminished, it may be inferred that the energy of the moving force has been greater or less than the resistance. It is an error to suppose that rest is the only condition possible for a body to assume when under the operation of two or more mechanical forces which are in equilibrium. By the laws of motion the state of a body which is not under the operation of any external force must be either in a state of rest or of uniform motion. Whichever be its state, it will suffer no change if the body be brought under the operation of two or more forces which are in equilibrium; for to suppose [Pg159] such forces to produce any change in the state of the body, whether from rest to motion, or vice versÂ, or in the velocity of the motion which the body may have previously had, would be equivalent to a supposition that the forces applied to the body being in equilibrium were capable of producing a dynamical effect, which would be a contradiction in terms. This, though not always clearly understood by mere practical men, or by persons superficially informed, is, in fact, among the fundamental principles of mechanical science.
(89.)
When the piston is at the top of the cylinder, and about to commence its motion downwards, the steam acting upon it will have not only to overcome the resistance arising from the friction of the various parts of the engine, but will also have to put in motion the whole mass of matter of the piston pump rods, pump pistons, and the column of water in the pump barrels. Besides imparting to this mass the momentum corresponding to the velocity with which it will be moved, it will also have to encounter the resistance due to the preponderance of the weight of the water and pump rods over that of the steam piston. The pressure of steam, therefore, upon the piston at the commencement of the stroke must, in accordance with the mechanical principles just explained, have a greater force than is equal to all the resistances which it would have to overcome, supposing the mass to be moving at a uniform velocity. The moving force, therefore, being greater than the resistance, the mass, when put in motion, will necessarily move with a gradually augmented speed, and the piston of the engine which has been described in the last chapter would necessarily move from the top to the bottom of the cylinder with an accelerated motion, having at the moment of its arrival at the bottom a greater velocity than at any other part of the stroke. As the piston and all the matter which it has put in motion must at this point come to rest, the momentum of the moving mass must necessarily expend itself on some part of the machinery, and would be so much mechanical force lost. It is evident, therefore, independently of any consideration of the expansive principle, to which we shall presently refer, that the action of the [Pg160] moving power in the descent of the piston ought to be suspended before the arrival of the piston at the bottom of the cylinder, in order to allow the momentum of the mass which is in motion to expend itself, and to allow the piston to come gradually to rest at the termination of the stroke. Thus, if we were to suppose that after the piston had descended through three fourths of the whole length of the cylinder, and had acquired a certain velocity, the steam above it were suddenly condensed, so as to leave a vacuum both above and below it, the piston, being then subject to no impelling force, would still move downwards, in virtue of the momentum it had acquired, until the resistance would deprive it of that momentum, and bring it to rest; and if the remaining fourth part of the cylinder were necessary for the accomplishment of this, then it is evident that that part of the stroke would be accomplished without further expenditure of the moving power.
In fact, this part of the stroke would be made by the expenditure of that excess of moving power, which, at the commencement of the stroke, had been employed in putting the machinery and its load in motion, and in subsequently accelerating that motion.
Although under such circumstances the resistance, during the operation of the moving power, shall not have been at any time equal to the moving power, since while the motion was accelerated it was less, and while retarded greater than that power, yet as the whole moving power has been expended upon the resistance, the mechanical effect which the moving power has produced under such circumstances will be equal to the actual amount of that power. If in an engine of this kind the steam was not cut off till the conclusion of the stroke, a part of the moving power would be lost upon those fixed points in the machinery which would sustain the shock produced by the instantaneous cessation of motion at the end of the stroke.
Independently, therefore, of any consideration of the expansive principle, it appears that, in an engine of this kind, the steam ought to be cut off before the completion of the stroke. [Pg161]
(90.)
To render the expansive action of steam intelligible, let
A B (
fig. 28.) represent a cylinder whose area we will suppose, for the sake of illustration, to be a square foot, and whose length,
A B, shall also be a foot. If steam of a pressure equal to the atmosphere be supplied to this cylinder, it will exert a pressure of about one ton on the piston; and if such steam be uniformly supplied from the boiler, the piston will be moved from
A to
B with the force of one ton, and that motion will be uniform if the piston be opposed throughout the same space by a resistance equal to a ton. When the piston has arrived at
B, let us suppose that the further supply of steam from the boiler is stopped by closing the upper steam valve, and let us also suppose the cylinder to be continued downwards so that
B C shall be equal to
A B, and suppose that
B C has been previously in communication with the condenser, and is therefore a vacuum. The piston at
B will then be urged with a force of one ton downwards, and as it descends the steam above it will be diffused through an increased volume, and will consequently acquire a diminished pressure. We shall, for the present, assume that this diminution of pressure follows the law of elastic fluids in general; that it will be decreased in the same proportion as the volume of the steam is augmented. While the piston, therefore, moves from
B downwards it will be urged by a continually decreasing force. Let us suppose, that by some expedient, it is also subject to a continually decreasing resistance, and that this resistance decreases in the same proportion as the force which urges the piston. In that case the motion of the piston would continue uniform. When the piston would arrive at
P', the middle of the second cylinder, then the space occupied by the steam being increased in the proportion of 2 to 3, the pressure on the piston would be diminished in the proportion of 3 to 2, and the pressure at B being one ton, it would be two-thirds of a ton at
P'. In like manner when the piston would arrive at
C, the space occupied by the steam being double that which
[Pg162] it occupied when the piston was at B, the pressure of the steam would be half its pressure at B, and therefore at the termination of the stroke, the pressure on the piston would be half a ton. If the space from B to C, through which the steam is here supposed to act expansively, be divided into ten equal parts, the pressure on the piston at the moment of passing each of those divisions would be calculated upon the same principle as in the cases now mentioned. After moving through the first division, the volume of the steam would be increased in the proportion of 10 to 11, and therefore its pressure would be diminished in the proportion of 11 to 10. The pressure, therefore, driving the piston at the end of the first of these ten divisions would be 10/11ths of a ton. In like manner, its pressure at the second of the divisions would be 10/12ths of a ton, and the third 10/13ths of a ton; and so on, as indicated in the figure.
Now if the pressure of the steam through each of these divisions were to continue uniform, and, instead of gradually diminishing, to suffer a sudden change in passing from one division to another, then the mechanical effect produced from B to C would be obtained by taking a mean or average of the several pressures throughout each of the ten divisions. In the present case it has been supposed that the force on the piston at B was 2240 pounds. To obtain the pressure in pounds corresponding to each of the successive divisions, it will therefore only be necessary to multiply 2240 by 10, and to divide it successively by 11, 12, 13, &c. The pressures, therefore, in pounds, at each of the ten divisions, will be as follows:—
| 1st | 2036·3 |
| 2d | 1866·6 |
| 3d | 1723·1 |
| 4th | 1600·0 |
| 5th | 1493·3 |
| 6th | 1400·0 |
| 7th | 1317·6 |
| 8th | 1244·4 |
| 9th | 1179·0 |
| 10th | 1120·0 |
If the mean of these be taken by adding them together [Pg163] and dividing by 10, it will be found to be 1498 pounds. It appears, therefore, that the pressures through each of the ten divisions being supposed to be uniform (which however, strictly, they are not,) the mechanical effect of the steam from B to C would be the same as if it acted uniformly throughout that space upon the piston with a force of about 1500 pounds, being rather less than three-fourths of its whole effect from A to B.
But it is evident that this principle will be equally applicable if the second cylinder had any other proportion to the first. Thus it might be twice the length of the first; and in that case, a further mechanical effect would be obtained from the expansion of the steam.
The more accurate method of calculating the effect of the expansion from B to C, would involve more advanced mathematical principles than could properly be introduced here; but the result of such a computation would be that the actual average effect of the steam from B to C would be equal to a uniform pressure through that space, amounting to one thousand five hundred and forty-five pounds, being greater than the result of the above computation, the difference being due to the expansive action through each of the ten divisions, which was omitted in the above computation.
(91.)
It is evident that the expansive principle, as here explained, involves the condition of a variation in the intensity of the moving power. Thus, if the steam act with a uniform energy on the piston so long as its supply from the boiler continues, the moment that supply is stopped, by closing the steam valve, the steam contained in the cylinder will fill a gradually increasing volume by the motion of the piston, and therefore will act above the piston with a gradually decreasing energy. If the resistance to the moving power produced by the load, friction, &c. be not subject to a variation corresponding precisely to such variation in the moving power, then the consequence must be that the motion imparted to the load will cease to be uniform. If the energy of the moving power at any part of the stroke be greater than the resistance, the motion produced will be accelerated; if it be less, the motion will be retarded; and if it be at one time greater, and another [Pg164] time less, as will probably happen, then the motion will be alternately accelerated and retarded. This variation in the speed of the body moved will not, however, affect the mechanical effect produced by the power, provided that the momentum imparted to the moving mass be allowed to expend itself at the end of the stroke, so that the piston may be brought to rest as nearly as possible by the resistance of the load, and not by any shock on any fixed points in the machine. This is an object which, consequently, should be aimed at with a view to the economy of power, independently of other considerations connected with the wear and tear of the machinery. So long as the engine is only applied to the operation of pumping water, great regularity of motion is not essential, and, therefore, the variation of speed which appears to be an almost inevitable consequence of any extensive application of the expansive principle, is of little importance. In the patent which Watt took out for the application of the expansive principle, he specified several methods of producing a uniform effect upon a uniform resistance, notwithstanding the variation of the energy of the power which necessarily attended the expansion of the steam. This he proposed to accomplish by various mechanical means, some of which had been previously applied to the equalisation of a varying power. One consisted in causing the piston to act on a lever, which should have an arm of variable length, the length increasing in the same proportion as the energy of the moving power diminished. This was an expedient which had been already applied in mechanics for the purpose of equalising a varying power. A well-known example of it is presented in the main-spring and fuzee of a watch. According as the watch goes down, the main-spring becomes relaxed, and its force is diminished; but, at the same time, the chain by which it drives the fuzee acts upon a wheel or circle, having a diameter increased in the same proportion as the energy of the spring is diminished. Another expedient consisted in causing the moving power, when acting with greatest energy, to lift a weight which should be allowed to descend again, assisting the piston when the energy of the moving force was diminished. [Pg165]
Another method consisted in causing the moving force, when acting with greatest energy, to impart momentum to a mass of inert matter, which should be made to restore the same force when the moving power was more enfeebled. We shall not more than allude here to these contrivances proposed by Watt, since their application has never been found advantageous in cases where the expansive principle is used.
(92.)
The application of the expansive principle in the engines constructed by Boulton and Watt, was always very limited, by reason of their confining themselves to the use of steam having a pressure not much exceeding that of the atmosphere. If the principle of expansion, as above explained, be attentively considered, it will be evident that the extent of its application will mainly depend on the density and pressure of the steam admitted from the boiler. If the density and pressure be not considerable when the steam is cut off, the extent of its subsequent expansion will be proportionally limited. It was in consequence of this, that this principle from which considerable economy of power has been derived, was applied with much less advantage by Mr. Watt than it has since been by others, who have adopted the use of steam of much higher pressure. In the engines of Boulton and Watt, where the expansive principle was applied, the steam was cut off after the piston had performed from one half to two thirds of the stroke, according to the circumstances under which the engine was worked. The decreasing pressure produced by expansion was, in this case, especially with the larger class of engines, little more than would be necessary to allow the momentum of the mass moved to spend itself, before the arrival of the piston at the end of the stroke. Subsequently, however, boilers producing steam of much higher pressure were applied, and the steam was cut off when the piston had performed a much smaller part of the whole stroke. The great theatre of these experiments and improvements has been the mining districts in Cornwall, where, instead of working with steam of a pressure not much exceeding that of the atmosphere, it has been found advantageous to use steam whose pressure is at least four times as great as [Pg166] that of the atmosphere; and instead of limiting its expansion to the last half or fourth of the stroke, it is cut off after the piston has performed one fourth part of the stroke or less, all the remainder of the stroke being accomplished by the expansive power of the steam, and by momentum.
BRIDGE OVER THE CLYDE AT HAMILTON,
DESIGNED BY WATT.
DOUBLE-ACTING ENGINE,
ZINC WORKS, CITY ROAD, LONDON.
