CHAPTER XII. GENERAL ECONOMY OF STEAM POWER.

Mechanical efficacy of steam — proportional to the quantity of water evaporated, and to the fuel consumed — Independent of the pressure. — Its mechanical efficacy by condensation alone. — By condensation and expansion combined — by direct pressure and expansion — by direct pressure and condensation — by direct pressure, condensation, and expansion. — The power of engines. — The duty of engines. — Meaning of horse power. — To compute the power of an engine. — Of the power of boilers. — The structure of the grate-bars. — Quantity of water and steam room. — Fire surface and flue surface. — Dimensions of steam pipes. — Velocity of piston. — Economy of fuel. — Cornish duty reports.

(130.) Having explained in the preceding chapters the most important circumstances connected with the principal varieties of steam engines, it remains now to explain some matters of detail connected with the power, efficiency, and economy of these machines, which, though perhaps less striking and attractive than the subjects which have hitherto engaged us, are still not undeserving of attention.

It has been shown in the first chapter, that water exposed to the ordinary atmospheric pressure (the amount of which may be expressed by a column of 30 inches of mercury) will pass from the liquid into the vaporous state when it arrives at the temperature of 212°; and the vapour thus produced from it will have an elastic force equal to that of the atmosphere. If the water, however, to which heat is applied, be submitted to a greater or less pressure than that of the atmosphere, it will boil at a greater or less temperature, and will always produce steam of an elastic force equal to the pressure under which it boils. Now it is a fact as remarkable as it is important, that to convert a given weight of water into vapour will require the same quantity of heat, under whatever pressure, and at whatever temperature the water may boil. Let us suppose a tube, the base of which is equal to a square foot, in which a piston fits air-tight and steam-tight. Immediately under the piston, let a cubic inch of water be placed, which will be spread in a thin layer over the bottom of the tube. Let the piston be counterbalanced by a weight (acting over a pulley) which will be equivalent to the weight of the piston, so that it shall be free to ascend by the application of any pressure below it. Now let the flame of a lamp be applied at the bottom of the tube: the water under the piston being affected by no pressure from above, except that of the atmosphere acting upon the piston, will boil at the temperature of 212°, and by the continued application of the lamp it will at length be converted into steam. The steam into which the cubic inch of water is converted will expand into the magnitude of a cubic foot, exerting an elastic force equal to the atmospheric pressure; consequently the piston will be raised one foot above its first position in the tube, and the cubic foot beneath it will be completely filled with steam. Let us suppose, that to produce this effect required the lamp to be applied to the tube for the space of fifteen minutes.

The water being again supposed at its original temperature, and the piston in its first position, let a weight be placed upon the piston equal to the pressure of the atmosphere, so that the water beneath the piston will be pressed down by double the atmospheric pressure. If the lamp be once more applied, the water will, as before, be converted into vapour; but the piston will now be raised to the height of only six inches[48] from the bottom, the steam expanding into only half its former bulk. The temperature at which the water would commence to be converted into vapour, instead of being 212°, would be 250°; but the time elapsed between the moment of the first application of the lamp, and the complete conversion of the water into steam, will still be fifteen minutes.

Again, if the piston be loaded with a weight equal to double the atmospheric pressure, the water will be pressed down by the force of three atmospheres. If the lamp be applied as before, the water would be converted into steam in the same time; but the piston will now be raised only four inches above its first position, and the steam will consequently be three times as dense as when the piston was pressed down only by the atmosphere.

From these and similar experiments we infer:—

First, That the elastic pressure of steam is equal to the mechanical pressure under which the water producing the steam has been boiled.

Secondly, That the bulk which steam fills is diminished in the same proportion as the pressure of the steam is increased; or, in other words, that the density of steam is always in the same proportion as its pressure.

Thirdly, That the same quantity of heat is sufficient to convert the same weight of water into steam, whatever be the pressure under which the water is boiled, or whatever be the density and pressure of the steam produced.

Fourthly, That the same quantity of water being converted into steam, produces the same mechanical effect, whatever be the pressure or the density of the steam. Thus, in the first case, the weight of one atmosphere was raised a foot high; in the second case, the weight of two atmospheres was raised through half a foot; and, in the third case, the weight of three atmospheres was raised through the third of a foot; the weight raised being in every case increased in the same proportion as the height through which it is elevated is diminished. Every increase of the weight is, therefore, compensated by a proportionate diminution of the height through which it is raised, and the mechanical effect is consequently the same.

Fifthly, That the same quantity of heat or fuel is necessary and sufficient to produce the same mechanical effect, whatever be the pressure of the steam which it produces.

If steam be used to raise a piston against the atmospheric pressure only, although a definite physical force will be exerted by it, and a mechanical effect produced, yet under such circumstances it will exert no directly useful efficiency; but after the piston has been raised, and the tube beneath it filled with steam balancing the atmosphere above it, a useful effect to the same amount may be obtained by cooling the tube, and thereby reconverting the steam into water. The piston will thus be urged downwards by the unresisted force of the atmosphere, and any chain or rod attached to it will be drawn downwards with a corresponding force. If the area of the piston be, as already supposed, equal to the magnitude of one square foot, the atmospheric pressure upon it, being 15 pounds for each square inch, will amount to 144 times 15 pounds, or 2160 pounds. By drawing down a chain or rope acting over a pulley, the piston would in its descent (omitting the consideration of friction, &c.) raise a weight of 2160 pounds a foot high. Since 2160 pounds are nearly equal to one ton, it may, for the sake of round numbers be stated thus:—

"A cubic inch of water, being converted into steam, will, by the condensation of that steam, raise a ton weight a foot high." Such is the way in which the force of steam is rendered practically available in the atmospheric engine.

(131.) The method by which steam is used in the single-acting steam engine of Watt is, in all respects, similar, except that the piston, instead of being urged downwards by the force of the atmosphere, is pressed by steam of a force equal to the atmospheric pressure. It is evident, however, that this does not alter the mechanical result.

We have stated that a considerable increase of power, from a given quantity of steam, was produced by cutting off the steam after the piston had made a part of its descent, and allowing the remainder of the descent to be produced by the expansive force of the steam already admitted. We shall now more fully explain the principle on which this increase of power depends.

Let A B ( fig. 69 .,) as before, represent a tube, the bottom of which is equal to a square foot, and let P be a piston in it, resting upon a cubic inch of water spread over the bottom; and let w be an empty vessel, the weight of which exactly counterpoises the piston. By the application of the lamp, the water will be converted into steam of the atmospheric pressure, and the piston will be raised from P to P´, through the height of one foot, the space in the tube beneath it being filled with steam, and the vessel w will have descended through one foot. Let half a ton of water be now poured into the vessel W; its weight will draw the piston P´ upwards, so that the steam below it will expand into a larger space. When the piston P´ was only balanced by the empty vessel W, it was pressed downwards by the whole weight of the atmosphere above, which amounts to about one ton: now, however, half of this pressure is balanced by the half ton of water poured into the vessel W; consequently the effective downward pressure on the piston P´ will be only half a ton, or half its former amount. The piston will therefore rise, until the pressure of the steam below it is diminished to the same extent. By what has been already explained, this will take place when the steam is allowed to expand into double its former bulk; consequently, when the piston has risen to P´´, one foot higher, or two feet from the bottom of the tube, the steam will then exactly balance the downward pressure on the piston, and the latter will remain stationary; the vessel W, with the half ton of water it contains, will have descended one foot lower, or two feet below its first position. Let the steam now be cooled and reconverted into water, and at the same time let another half ton of water be supplied to the vessel W; the pressure below the piston being entirely removed, the atmospheric pressure will act above it with undiminished force; and this force, amounting to one ton, will draw up the vessel W, with its contents. When the piston descends, as it will do, to the bottom of the tube, the ton of water contained in the vessel W will be raised through two perpendicular feet.[49]

Now, in this process it will be observed that the quantity of steam consumed is not more than in the former case, viz. the vapour produced by boiling one cubic inch of water. Let us consider, however, the mechanical effect which has resulted from it; half a ton of water has been allowed to descend through one foot, while a ton has been raised through two feet: deducting the force lost by the descent of half a ton through one foot from the force obtained by the ascent of one ton through the two feet, we obtain for the whole mechanical effect one ton and a half raised through one foot; for it is evident that half a ton has been raised from the lowest point to which the vessel W descended one foot above that point, and one ton has been raised through the other foot, which is equivalent to one ton and a half through one foot.

Comparing this with the effect produced in the first case, where the steam was condensed without causing its expansion, it will be evident that there is an increase of 50 per cent. upon the whole mechanical effect produced.

But this is not the limit of the increase of power by expansion. Instead of condensing the steam when the piston had arrived at P´´, let a further quantity of water amounting to one sixth of a ton be poured into the vessel W, in addition to the half ton which it previously contained; the effective pressure on the piston P´´, being only half a ton, will be overbalanced by the preponderating weight in the vessel w, and the piston will consequently ascend. It will become stationary when the steam by expansion loses a quantity of force equal to the additional weight which the vessel W has received: now, that vessel, having successively received a half and a sixth of a ton will contain two thirds of a ton; consequently the effective downward pressure on the piston will be only a third of a ton, and the steam to balance this must expand into three times the space it occupied when equal, to the atmospheric pressure. It must therefore ascend to P´´´, three feet above the bottom of the tube. If the steam in the tube be now condensed, and at the same time one third of a ton of water be supplied to the vessel W, so as to make its total contents amount to one ton, the piston will descend, being urged downwards by the unresisted atmospheric pressure, and the ton of water contained in the vessel W will be raised through three perpendicular feet.

In this case, as in the former, the total quantity of steam consumed is that of one cubic inch of water; but the mechanical effect it produces is still further increased. To calculate its amount, we must consider that half a ton of water has fallen through two feet, which is equivalent to a ton falling through one foot, besides which the sixth part of a ton has fallen through one foot. The total loss, therefore, by the fall of water has been one ton and one sixth through one foot, while the force gained by the ascent of water has been one ton raised through three feet, which is equivalent to three tons through one foot. If, then, from three tons we deduct one and one sixth, the remainder will be one ton and five sixths raised through one foot; this effect being above 80 per cent. more than that which is produced in the first case, where the steam was not allowed to expand.

To carry the inquiry one step further: Let us suppose that, upon the arrival of the piston at P´´´, a further addition of water to the amount of one twelfth of a ton be added to it: this, with the water it already contained, would make the total contents three fourths of a ton; consequently, the effective pressure upon the piston would now be reduced to one fourth of the atmospheric pressure. The atmospheric steam would balance this when expanded into four times its original volume: consequently, the piston would come to a state of rest at P´´´´, four feet above the bottom of the tube, and the vessel W would consequently have descended through four perpendicular feet. If the steam in the tube be now condensed as in the former cases, and at the same time a quarter of a ton of water be added to the vessel W, the piston will descend to the bottom of the tube, and the ton of water in the vessel W will be raised through four perpendicular feet. To estimate the mechanical effect thus produced, we have, as before, to deduct the total force lost by the fall of water from the force gained by its elevation: the water has fallen in three distinct portions: first, half a ton has fallen through three perpendicular feet, which is equivalent to one ton and a half through one foot; secondly, one sixth of a ton has fallen through two perpendicular feet, which is equivalent to one third of a ton through one foot; and thirdly, one twelfth of a ton has fallen through one foot: these added together will be equivalent to one ton and eleven twelfths through one foot. One ton has been raised through four feet, which is equivalent to four tons through one foot: deducting from this the force lost by the descent, the surplus gained will be two tons and one twelfth through one foot, being about 108 per cent. more than the force resulting from the condensation of steam without expansion.

To the increase of mechanical effect to be produced in this way, there is no theoretical limit. According to the manner in which we have here explained it, to produce the greatest possible effect by a given extent of expansion, it would be necessary to supply the water or other counterpoise to the vessel W, not in separate masses, as we have here supposed, but continuously, so as to produce a regular motion of the piston upwards.

Such is the principle on which the advantages of the expansive engine of Watt and Hornblower depend, explained so far as it can be without the aid of the language and reasoning of analysis.[50]

(132.) We have here, however, only considered the mechanical effect produced by the condensation of steam. Let us now examine its direct action.

Let the piston P be supposed to be connected by a rod with a load or resistance which it is intended to raise, and let the load placed upon it be supposed to amount to one ton, the total pressure on the piston will then be two tons; one due to the atmospheric pressure, and the other to the amount of the load. Upon applying heat to the water, steam will be produced; and when the water has been completely evaporated, the piston will rise to the height of six inches from the bottom of the tube. The total mechanical effect thus produced will be one ton weight raised through six perpendicular inches, which is equivalent to half a ton raised through one foot.

Again, let the load upon the piston be two tons; this will produce a total pressure upon the water below it amounting to three tons, including the atmospheric pressure. The water, when converted into vapour under this pressure, will raise the piston and its load through four perpendicular inches: the useful mechanical effect will then be two tons raised through the third of a foot, which is equivalent to two thirds of a ton raised one foot. In the same manner, if the piston were loaded with three tons, the mechanical effect would be equivalent to three fourths of a ton raised through one foot, and so on.

It appears therefore from this reasoning, that when the direct force of steam of greater pressure than the atmosphere is used without condensation, the total mechanical effect is always less than that produced by the condensation of atmospheric steam without expansion; but that the greater the pressure under which the steam is produced, the less will be the difference between these effects. In general, the proportion of the mechanical effect of high-pressure steam to the effect produced by the condensation of atmospheric steam, will be as the number of atmospheres expressing the pressure of the steam to the same number increased by one. Thus, if steam be produced under the pressure of six atmospheres, the proportion of its effect to that of the condensation of atmospheric steam will be as six to seven.

(133.) Another method of applying the power of steam mechanically is, to combine its direct action with condensation but without expansion.

The piston being, as before, loaded with one ton, the evaporation of the water will raise it through six perpendicular inches, and the result so far will be equivalent to a ton raised half a foot; but if the piston-rod be supposed also to act by a chain or cord over a wheel, so as to pull a weight up, the steam which has just raised the ton weight through six inches, may be condensed, and the piston will descend with a force of one ton into the vacuum thus produced, and another ton may be thus raised through half a foot. The total mechanical power thus yielded by the steam, adding to its direct action its effect by condensation, will then be one ton raised through one foot, being an effect exactly equal to that obtained by the condensation of atmospheric steam.

If the piston be loaded with two tons, its direct action will, as we have shown, raise these two tons through four inches, which is equivalent to two thirds of a ton raised a foot. By condensing this steam a ton weight may be raised in the same manner, by the descent of the piston through a third of a foot, which is equivalent to the third of a ton raised through one foot.

By pursuing like reasoning, it will appear that, if the direct force of high-pressure steam be combined with the indirect force produced by its condensation, the total mechanical effect will be precisely equal to the mechanical effect by the mere condensation of atmospheric steam.

(134.) In applying the principle of expansion to the direct action of high-pressure steam, advantages are gained analogous to those already explained with reference to the method of condensation.

Let the piston be supposed to be loaded with three tons: the evaporation of the water beneath it will raise this weight, including the atmospheric pressure, through three perpendicular inches. Let one ton be now removed, and the remaining two tons will be raised, by the expansion of the steam, through another perpendicular inch. Let the second ton be now removed, and the piston loaded with the remaining ton will rise, by the expansion of the steam, to the height of six inches from the bottom. These consequences follow immediately from the principle that steam will expand in proportion as the pressure upon it is diminished, observing that in this case the atmospheric pressure, amounting to one ton, must always be added to the load. In this process three separate effects are produced: one ton is raised through three inches, which is equivalent to a quarter of a ton raised through one foot; another ton is raised through four inches, which is equivalent to a third of a ton through a foot, and the third ton is raised through six inches, which is equivalent to half a ton raised through a foot. The total of these effects amounts to one and one-twelfth of a ton raised through one foot, while the same load, raised by the high-pressure steam without expansion, would be equivalent to only half a ton raised through one foot.

Again, let the load placed upon the piston be five tons: the evaporation of the water will raise this through the sixth part of a foot; if one ton be now removed, the other four tons will be raised to a height above the bottom of the tube equal to a fifth part of a foot; another ton being removed, the remaining three will be raised to a height from the bottom equal to a fourth of a foot; and so on, the last ton being raised through half a foot. To estimate the total mechanical effect thus produced, we are to consider that the several tons raised from their first position are raised through the sixth, fifth, fourth, third, and half of a perpendicular foot, giving a total effect equal to the sixth, fifth, fourth, third, and half of a ton severally raised through one foot; these, therefore, added together, will give a total of nineteen twentieths of a ton raised through one foot.

In general, the expansive force applied to the direct action of high-pressure steam, therefore, will increase its effect according to the same law, and subject to the same principles as were shown with respect to the method of condensation accompanied with expansion.

The expansive action of high-pressure steam may be accompanied with condensation, so as considerably to increase the mechanical effect produced; for, after the weights with which the piston is loaded have been successively raised to the extent permitted by the elastic force of the steam, and are removed from the piston, the steam will expand until it balances the atmospheric pressure. It may afterwards be made further to expand, by adding weights to the counterpoise W in the manner already explained; and, the steam being subsequently condensed, all the effects will be produced upon the descent of the piston which we have before noticed. It is evident that by this means the mechanical effect admits of very considerable increase.

(135.) We have hitherto considered the piston to be resisted by the atmospheric pressure above it; but, as is shown in the preceding chapters, in the modern steam engines, the atmosphere is expelled from the interior of the machine by allowing the steam to pass freely through all its cavities in the first instance, and to escape at some convenient aperture, which, opening outwards, will effectually prevent the subsequent re-admission of air. The piston-rod and other parts which pass from the external atmosphere to the interior of the machine, are likewise so constructed and so supplied with oil or other lubricating matter that neither the escape of steam nor the entrance of air is permitted. We are therefore now to consider the effect of the action of steam against the piston P, when subjected to a resistance which may be less in amount, to any extent, than the atmospheric pressure.

In such machines the steam always acts both directly by its power, and indirectly by its condensation. In calculating its effects, excluding friction, &c., we have therefore only to estimate its total force upon the piston, and to deduct the force of the uncondensed vapour which will resist the motion of the piston.

Supposing, then, the total force exerted upon the piston, after deducting the resistance from the uncondensed vapour, to be one ton, and the length of the cylinder to be one foot, each motion of the piston from end to end of the cylinder will produce a mechanical force equivalent to a ton weight raised one foot high. If in this case the magnitude of the piston be equivalent to one square foot, the pressure of the steam will be equal to that of the atmosphere, and the quantity of water in the form of steam which the cylinder will contain will be a cubic inch, while the quantity of steam in it will be a cubic foot. In proportion as the area of the piston is enlarged the pressure of the steam will be diminished, if the moving force is required to remain the same; but with every diminution of pressure the density of the steam will be diminished in the same proportion, and the cylinder will still contain the same quantity of water in the form of vapour. In this way steam may be used, as a mechanical agent, with a pressure to almost any extent less than that of the atmosphere, and at temperatures considerably lower than 212°. To obtain the same mechanical force, it is only necessary to enlarge the piston in the same proportion as the pressure of the steam is diminished.

By a due attention to this circumstance, the expansive power of steam, both in its direct action and by condensation, may be used with very much increased advantage; and such is the principle on which the benefits derived from Woolf's contrivances depend. If steam of a high-pressure, say of three or four atmospheres, be admitted to the piston, and allowed to impel it through a very small portion of the descent, it may then be cut off and its expansion may be allowed to act upon the piston until the pressure of the steam is diminished considerably below the atmospheric pressure; the steam may then be condensed and a vacuum produced, and the process repeated.

In the double-acting engines, commonly used in manufactures and in navigation, and still more in the high-pressure engines used for locomotion, the advantageous application of the principle of expansion appears to have been hitherto attended with difficulties; for, notwithstanding the benefits which unquestionably attend it in the economy of fuel, it has not been generally resorted to. To derive from this principle full advantage, it would be necessary that the varying power of the expanding steam should encounter a corresponding, or a nearly corresponding, variation in the resistance: this requisite may be attained, in engines applied to the purpose of raising water, by many obvious expedients; but when they have, as in manufactures, to encounter a nearly uniform resistance, or, in navigation and locomotion, a very irregular resistance, the due application of expansion is difficult, if indeed it be practicable.

We have seen that the mechanical effect produced by steam when the principle of expansion is not used, is always proportional to the quantity of water contained in the steam, and is likewise in the same proportion so long as a given degree of expansion is used. It is apparent, therefore, that the mechanical power which is or ought to be exerted by an engine is in the direct proportion of the quantity of water evaporated. It has also been shown that the quantity of water evaporated, whatever be the pressure of the steam, will be in the direct proportion of the quantity of heat received from the fuel, and therefore in the direct proportion of the quantity of fuel itself, so long as the same proportion of its heat is imparted to the water.

(136.) The POWER of an engine is a term which has been used to express the rate at which it is able to raise a given load, or overcome a given resistance. The DUTY of an engine is another term, which has been adopted to express the load which may be raised a given perpendicular height, by the combustion of a given quantity of fuel.

When steam engines were first introduced, they were commonly applied to work pumps or mills which had been previously wrought by horses. It was, therefore, convenient, and indeed necessary, in the first instance, to be able to express the performance of these machines by reference to the effects of animal power, to which manufacturers, miners, and others, had been long accustomed. When an engine, therefore, was capable of performing the same work in a given time, as any given number of horses of average strength usually performed, it was said to be an engine of so many horses' power. This term was long used with much vagueness and uncertainty: at length, as the use of steam engines became more extended, it was apparent that confusion and inconvenience would ensue, if some fixed and definite meaning were not assigned to it, so that the engineers and others should clearly understand each other in expressing the powers of these machines. The term horse-power had so long been in use, that it was obviously convenient to retain it. It was only necessary to agree upon some standard by which it might be defined. The performance of a horse of average strength, working for eight hours a day, was, therefore, selected as a standard or unit of steam-engine power. Smeaton estimated the amount of mechanical effect which the animal could produce at 22,916 pounds, raised one foot per minute; Desaguiliers makes it 27,500 pounds, raised through the same height. Messrs. Bolton and Watt caused experiments to be made with the strong horses used in the breweries in London; and from the result of these they assigned 33,000 pounds raised one foot per minute, as the value of a horse's power: this is, accordingly, the estimate now generally adopted; and, when an engine is said to be of so many horses' power, it is meant that, when in good working order and properly managed, it is capable of overcoming a resistance equivalent to so many times 33,000 pounds raised one foot per minute. Thus, an engine of ten-horse-power would be capable of raising 330,000 pounds one foot per minute.

As the same quantity of water converted into steam will always produce the same mechanical effect, whatever be the density of the steam produced from it, and at whatever rate the evaporation may proceed, it is evident that the power of a steam engine will depend on two circumstances: first, the rate at which the boiler with its appendages is capable of evaporating water; and, secondly, the rate at which the engine is capable of consuming the steam by its work. We shall consider these two circumstances separately.

The rate at which the boiler produces steam will depend upon the rate at which heat can be transmitted from the fire to the water which it contains. Now this heat is transmitted in two ways: either by the direct action of the fire radiating heat against the surface of the boiler; or by the flame, and heated air which escapes from the fire, passing through the flues, as already explained. The surface of the boiler exposed to the direct radiation of the fire is technically called fire surface; and that which takes heat from the flame and air, on its way to the chimney, is called flue surface. Of these the most efficient in the generation of steam is the former. In stationary boilers, used for condensing engines, where magnitude and weight are matters of little importance, it has been found that the greatest effect has been produced in general by allowing four and a half square feet of fire surface, and four and a half square feet of flue surface, for every horse-power. By means of this quantity of fire and flue surface, a cubic foot of water per hour may be evaporated.

It has been already shown that the total power exerted by a cubic inch of water, converted into steam, will be equivalent to 2160 pounds raised one foot. A cubic foot of water consists of 1728 cubic inches, and the power produced by its evaporation will therefore be found by multiplying 2160 by 1728; the product, 3,732,480, expresses the number of pounds' weight which the evaporation of a cubic foot of water would raise one foot high, supposing that its entire mechanical force were rendered available: but to suppose this in practice, would be to suppose the machine, through the medium of which it is worked, moved without any power being expended upon its own parts. It would be, in fact, supposing all its moving parts to be free from friction and other causes of resistance. To form a practical estimate, then, of the real quantity of available mechanical power obtained from the evaporation of a given quantity of water, it will be necessary to inquire what quantity of this power is intercepted by the engine through which it is transmitted. In different forms of steam engine—indeed, we may say in every individual steam engine—the amount thus lost is different; nevertheless, an approximate estimate may be obtained, sufficiently exact to form the basis of a general conclusion.

Let us consider, then, severally, the means by which mechanical power is intercepted by the engine.

First, The steam must flow from the boiler into the cylinder to work the piston; it passes necessarily through pipes more or less contracted, and is, therefore, subject to friction as well as cooling in its passage.

Second, Force is lost by the radiation of heat from the cylinder and its appendages.

Third, The friction of the piston in the cylinder must be overcome.

Fourth, Loss of steam takes place by leakage.

Fifth, Force is expended in expelling the steam after having worked the piston.

Sixth, Force is required to open and close the several valves, to pump up the water for condensation, and to overcome the friction of the various axes.

Seventh, Force is expended upon working the air-pump.

In engines which do not condense the steam, and which, therefore, work with steam of high-pressure, some of these sources of waste are absent, but others are of increased amount. If we suppose the total effective force of the water evaporated per hour in the boiler to be expressed by 1000, it is calculated that the waste in a high-pressure engine will be expressed by the number 392; or, in other words, taking the whole undiminished force obtained by evaporation as expressed by 10, very nearly 4 of these parts will be consumed in moving the engine, and the other 6 only will be available.

In a single-acting engine which condenses the steam, taking, as before, 1000 to express the total mechanical power of the water evaporated in the boiler, 402 will express the part of this consumed in moving the engine, and 598, therefore, will express the portion of the power practically available; or, taking round numbers, we shall have the same result as in the non-condensing engine, viz. the whole force of the water evaporated being expressed by 10, 4 will express the waste, and 6 the available part.

In a double-acting engine the available part of the power bears a somewhat greater proportion to the whole. Taking, as before, 1000 to express the whole force of the water evaporated, 368 will express the proportion of that force expended on the engine, and 632 the proportion which is available for work.

In general, then, taking round numbers, we may consider that the mechanical force of four tenths of the water evaporated in the boiler is intercepted by the engine, and the other six tenths are available as a moving force. In this calculation, however, the resistance produced in the condensing engine by the uncondensed steam is not taken into account: the amount of this force will depend upon the temperature at which the water is maintained in the condenser. If this water be kept at the temperature of 120°, the vapour arising from it will have a pressure expressed by three inches seven tenths of mercury; if we suppose the pressure of steam in the boiler to be measured by 37 inches of mercury, then the resistance from the uncondensed steam will amount to one tenth of the whole power of the boiler; this, added to the four tenths already accounted for, would show a waste amounting to half the whole power of the boiler, and consequently only half the water evaporated would be available as a moving power.

If the temperature of the condenser be kept down to 100°, then the pressure of uncondensed steam will be expressed by two inches of mercury, and the loss of power consequent upon it would amount to a proportionally less fraction of the whole power.

The following example will illustrate the method of estimating the effective power of an engine.

In a double-acting engine, in good working condition, the total power of steam in the boiler being expressed by 1000, the proportion intercepted by the engine, exclusive of the resistance of the uncondensed steam, will be 368, and the effective part 632. Now, suppose the pressure of steam in the boiler to be measured by a column of 35 inches of mercury; the thousandth part of this will be seven two hundredths of an inch of mercury, and 632 of these parts will express the effective portion of the power. By multiplying seven two hundredths by 632, we obtain 22 nearly. Now, suppose the temperature in the condenser is 1200, the pressure of steam corresponding to that temperature will be measured by 3-7/10 inches of mercury. Subtracting this from 22, there will remain 18-3/10 inches of mercury, as the effective moving force upon the piston; this will be equivalent to about 7 lbs. on each circular inch.

If the diameter of the piston then be 24 inches, its surface will consist of a number of circular inches expressed by the square of 24, or 24 × 24 = 576; and, as upon each of these circular inches there is an effective pressure of 7 lbs., we shall find the total pressure in pounds by multiplying 576 by 7, which gives 4032 lbs.

We shall find the space through which this force works per minute, by knowing the length of the cylinder and the number of strokes per minute. Suppose the length of the cylinder to be 5 feet, and the number of strokes per minute 21-1/2. In each stroke[51] the piston will, therefore, move through 10 feet, and in one minute it will move through 215 feet. The moving force, therefore, is 4032 lbs. moved through 215 feet per minute, which is equivalent to 215 times 4032 lbs., or 866,880 lbs., raised one foot per minute.

For every 33,000 lbs. contained in this, the engine has a horse-power. To find the horse-power, then, of the engine, we have only to divide 866,880 by 33,000; the quotient is 26 nearly, and, therefore, the engine is one of 26 horse power.

Let it be required to determine the quantity of water which a boiler must evaporate per hour, for each horse-power of the engine which it works.

It has been already explained that one horse-power expresses 33,000 lbs. raised one foot high per minute, or, 1,980,000 lbs. raised one foot high per hour. The quantity of water necessary to produce this mechanical effect by evaporation, will be found by considering that a cubic inch of water, being evaporated, will produce a mechanical force equivalent to 2160 lbs. raised a foot high. If we divide 1,980,000, therefore, by 2160, we shall find the number of cubic inches of water which must be evaporated per hour, in order to produce the mechanical effect expressed by one horse-power; the result of this division will be 916,6, which is therefore the number of cubic inches of water per hour, whose evaporation is equivalent to one horse-power. But it has been shown that, for every 6 cubic inches of water evaporated in the boiler which are available as a moving power, there will be 4 cubic inches intercepted by the engine. To find, then, the quantity of waste corresponding to 916 cubic inches of water, it will be necessary to divide that number by 6, and to multiply the result by 4: this process will give 610 as the number of cubic inches of water wasted. The total quantity of water, therefore, which must be evaporated per hour, to produce the effect of one horse-power, will be found by adding 610 to 916, which gives 1526.

This result, however, being calculated upon a supposition of a degree of efficiency in the engines which is, perhaps, somewhat above their average state, it has been customary with engineers to allow a cubic foot of water per hour for each horse-power, a cubic foot being 1728 cubic inches, or above 11 per cent. more than the above estimate.

(137.) It has been stated, that to evaporate a cubic foot of water per hour requires 9 square feet of surface exposed to the action of the fire and heated air. This, therefore, is the quantity of surface necessary for each horse-power, and we shall find the total quantity of fire and flue surface necessary for a boiler of a given power, by multiplying the number of horses in the power by 9; the product will express, in square feet, the quantity of boiler surface which must be exposed to the fire, one half of this being fire surface and the other half flue surface.

Since the supply of heat to the boiler must be proportionate to the quantity of fuel maintained in combustion, and the quantity of that fuel must depend on the extent of grate surface, it is clear that a determinate proportion must exist between the power of the boiler, and the extent of grating in the fire place. The quantity of oxygen which combines with the fuel varies with the quality of that fuel; for different kinds of coal it varies from two to three pounds for each pound of coal.

We shall take it an average of 2-1/2 pounds. Now 2-1/2 pounds of oxygen will measure 30 cubic feet; also 5 cubic feet of atmospheric air contain 1 cubic foot of oxygen; and consequently 150 cubic feet of atmospheric air will be necessary for the combustion of 1 pound of average coals. At least one third of the air, which passes through a fire, escapes uncombined into the chimney. We must, therefore, allow 220 cubic feet of atmospheric air to pass through the grate-bars for every pound of fuel which is consumed. Now since land boilers will consume 15 pounds, and marine boilers 10 pounds, per hour per horse-power, it follows that the spaces between the grate-bars, and the extent of grate surface, must be sufficient to allow 3000 cubic feet of air per hour in land boilers, and 2000 cubic feet in marine boilers, to pass through them for each horse-power, or, what is the same, for each foot of water converted into steam per hour. The quantity of grate surface necessary for this does not seem to be ascertained with precision; but, perhaps, we may take as an approximate estimate for land boilers one square foot of grate surface per horse-power, and for marine boilers two thirds of a square foot, the spaces between the grate-bars being equal to their breadth.

It is evident that the capacity of a boiler for water and steam must have a determinate relation to the power of the engine it is intended to supply. For each horse-power of the engine, it has been shown that a cubic foot of water must pass from the boiler in the form of steam per hour. Now, it is evident that the steam could not be supplied of a uniform force, if the quantity of steam contained at any moment in the boiler were not considerably greater than the contents of the cylinder. For example, if the volume of steam in the boiler were precisely equal to the capacity of the cylinder, then one measure of the cylinder would for the moment cause the steam to expand into double its bulk and to lose half its force, supposing it to pass freely from the boiler to the cylinder. In the same manner, if the volume of steam contained in the boiler were twice the contents of the cylinder, the steam would for a moment lose a third of its force, and so on. It is clear, therefore, that the space allotted to steam in the boiler must be so many times greater than the magnitude of the cylinder, that the abstraction of a cylinder full of steam from it shall cause a very trifling diminution of its force.

In the same manner, we may perceive the necessity of maintaining a large proportion between the total quantity of water in the boiler, and the quantity supplied in the form of steam to the cylinder. If, for example (taking as before an extreme case,) the quantity of water in the boiler were only equal to the quantity supplied in the form of steam to the cylinder in a minute, it would be necessary that the contents of the boiler should be replaced by cold water once in each minute: and, under such circumstances, it is evident that the action of the heat upon the water would be quite unmanageable. But, independent of this, the quantity of water must be sufficient to fill the boiler above the point at which the flue surface terminates, otherwise the heat of the fuel would act upon the part of the boiler containing steam and not water; and, steam receiving heat sluggishly, the metal of the boiler would be gradually destroyed by undue temperature.

The total quantity of space for water and steam in boilers is subject to considerable variation in proportion to their power. Small boilers require a greater proportion of steam and water-room, or a greater capacity of boiler, in proportion, than large ones; and the same applies to their fire surface and flue surface.

The general experience of engineers has led to the conclusion, that a low-pressure boiler of the common kind requires ten cubic feet of water-room, and ten cubic feet of steam-room in the boiler, for every cubic foot which the engine consumes per hour, or, what is the same, for each horse-power of the engine. Thus, an engine of ten-horse-power, according to this rule, would require a boiler having the capacity of 200 cubic feet which should be constantly kept half filled with water. There are, however, different estimates of this. Some engineers hold that a boiler should have twenty-five cubic feet of capacity for each horse-power of the engine, while others reduce the steam so low as eight cubic feet.

In a table of the capacities of boilers of different powers, and the feed of water necessary to be maintained in them, Mr. Tredgold assigns to a boiler of five-horse-power fourteen cubic feet of water per horse-power; for one of ten-horse power, twelve and a half cubic feet; and, for one of forty-horse, eleven cubic feet.

For engines of greater power it is generally found advantageous to have two or more boilers of small power, instead of one of large power. This method is almost invariably adopted on board steam boats, and has the advantage of securing the continuance of the working of the engine, in case of one of the boilers being deranged. It is also found convenient to keep an excess of power in the boilers, above the wants of the engine. Thus, an engine of sixty-horse-power may be advantageously supplied with two forty-horse boilers, and an engine of eighty-horse-power with two fifty-horse boilers, and so on.

(138.) The pressure of steam in the cylinder of an engine is always less than the pressure of steam in the boiler, owing to the obstructions which it encounters in its passage through the steam pipes and valves. The difference between these pressures will depend upon the form and magnitude of the passages: the straighter and wider they are, the less the difference will be; if they are contracted and subject to bends, especially to angular inflexions, the steam will be considerably diminished in its pressure before it reaches the cylinder. The throttle valve placed in the steam pipe may also be so managed as to diminish the pressure of steam in the cylinder to any extent: this effect, which is well understood by practical engineers, is called wire-drawing the steam. By such means it is evidently possible for the steam in the boiler to have any degree of high-pressure while the engine is worked at any degree of low pressure. Since, however, the pressure of the steam in the cylinder is a material element in the performance of the engine, the magnitude, position, and shape of the steam pipe and of the valves are a matter of considerable practical importance. But theory furnishes us with little more than very general principles to guide us. One practical rule which has been adopted is, to make the diameter of the steam pipe about one fifth of that of the cylinder: by this means the area of the transverse action of the pipe will be one twenty-fifth part of the superficial magnitude of the piston; and, since the same quantity of steam per minute must flow through this pipe as through the cylinder, it follows that the velocity of the steam, in passing through the steam pipe, will be twenty-five times the velocity of the piston.

(139.) Another rule which has been adopted is, to allow a square inch of magnitude, in the section of the steam pipe, for each horse-power of the engine.

The result of this and all similar rules is, that the steam should always pass through the steam pipe with the same velocity, whatever be the power of the engine.

In engines of the same power, the piston will have very different velocities in the cylinder, according to the effective pressure of the steam, and the proportions and capacity of the cylinder. It is clear from what has been already explained, that, when the power is the same, the same actual quantity of water, in the form of steam, must pass through the cylinder per minute: but, if the steam be used with a considerable pressure, being in a condensed state, the same weight of it will occupy a less space; and consequently the cylinders of high-pressure engines are smaller than those of the same power in low-pressure engines: the magnitude of the cylinder and the piston therefore, as well as the velocity of the latter, will depend first upon the pressure of the steam.

But with steam of a given pressure, the velocity of the piston will be different: with a given capacity of cylinder, and a given pressure of steam, the power of the engine will determine the number of strokes per minute. But the actual velocity of the piston will depend, in that case, on the proportion which the diameter of the cylinder bears to its length; the greater the diameter of the piston is with respect to its length, the less will be its velocity. In case of stationary engines used on land, that proportion of the diameter of the cylinder to its length is selected, which is thought to contribute to the most efficient performance of the machine. According to some engineers, the length of the cylinder should be twice its diameter;[52] others make the length equal to two diameters and a half; but there are circumstances in which considerations of practical convenience render it necessary to depart from these proportions. In marine engines, where great length of cylinder would be inadmissible, and where, on the other hand, considerable power is required, cylinders of short stroke and great diameter are used. In these engines the length of the stroke is often not greater than the diameter of the piston, and sometimes even less.

The actual velocity which has been found to have the best practical effect, for the piston in low-pressure engines, is about 200 feet per minute. This, however, is subject to some variation.

(140.) A given weight or measure of fuel burnt under the boiler of an engine is capable of producing a mechanical effect through the means of that engine, which, when expressed in an equivalent number of pounds' weight lifted a foot high, is called the duty of the engine. If all the heat developed in the combustion of the fuel could be imparted to the water in the boiler, and could be rendered instrumental in producing its evaporation; and if, besides, the steam thus produced could be all rendered mechanically available at the working point; then the duty of the engine would be the entire undiminished effect of the heat of combustion; but it is evident that this can never practically be the case. In the first place, the heat developed by the combustion can never be wholly imparted to the water in the boiler: some part of it will necessarily escape without reaching the boiler at all; another portion will be consumed in heating the metal of the boiler, and in supplying the loss by radiation from its surface; another portion will be abstracted by the various sources of the waste and leakage of steam; another portion will be abstracted by the reaction of the condensed steam; and another portion of the power will be consumed in overcoming the friction and resistance of the engine itself. It is apparent that all these sources of waste will vary according to the circumstances and conditions of the machine, and according to the form and construction of the furnace, flues, boilers, &c. The duty, therefore, of different engines will be different; and when such machines are compared, with a view to ascertain their economy of fuel, it has been found necessary carefully to register and to compare the fuel consumed with the weight or resistance overcome. In engines applied to manufactures generally or navigation, it is not easy to measure the amount of resistance which the engine encounters, but when the engine is applied to the pumping of water, its performance is more easily determined.

In the year 1811, several of the proprietors of the mines in Cornwall, suspecting that some of their engines might not be doing a duty adequate to their consumption of fuel, came to a determination to establish a uniform method of testing the performance of their engines. For this purpose a counter was attached to each engine, to register the number of strokes of the piston. All the engines were put under the superintendence of Messrs. Thomas and John Lean, engineers; and the different proprietors of the mines, as well as their directing engineers, respectively pledged themselves to give every facility and assistance in their power for the attainment of so desirable an end. Messrs. Lean were directed to publish a monthly report of the performance of each engine, specifying the name of the mine, the size of the cylinder, the load upon the engine, the length of the stroke, the number of pump lifts, the depth of the lift, the diameter of the pumps, the time worked, the consumption of coals, the load on the pump, and, finally, the duty of the engine, or the number of pounds lifted one foot high by a bushel of coals. The publication of these monthly reports commenced in August, 1811, and have been regularly continued to the present time.

The favourable effect which these reports have produced upon the vigilance of the several engineers, and the emulation they have excited, both among engine-makers and those to whom the working of the machines are intrusted, are rendered conspicuous in the improvement which has gradually taken place in the performance of the engines, up to the present time. In a report published in December, 1826, the highest duty was that of an engine at Wheal Hope mine in Cornwall. By the consumption of one bushel of coals, this engine raised 46,838,246 pounds a foot high, or, in round numbers, forty-seven millions of pounds.

In a report published in the course of the present year (1835) it was announced that a steam engine, erected at a copper mine near St. Anstell, in Cornwall, had raised by its average work 95 millions of pounds 1 foot high, with a bushel of coals. This enormous mechanical effect having given rise to some doubts as to the correctness of the experiments on which the report was founded, it was agreed that another trial should be made in the presence of a number of competent and disinterested witnesses. This trial accordingly took place a short time since, and was witnessed by a number of the most experienced mining engineers and agents: the result was, that for every bushel of coal consumed under the boiler the engine raised 125-1/2 millions of pounds weight one foot high.

(141.) It may not be uninteresting to illustrate the amount of mechanical virtue, which is thus proved to reside in coals, in a more familiar manner.

Since a bushel of coal weighs 84 lbs. and can lift 56,027 tons a foot high, it follows that a pound of coal would raise 667 tons the same height; and that an ounce of coal would raise 42 tons one foot high, or it would raise 18 lbs. a mile high.

Since a force of 18 lbs. is capable of drawing 2 tons upon a railway, it follows that an ounce of coal possesses mechanical virtue sufficient to draw 2 tons a mile, or 1 ton 2 miles, upon a level railway.[53]

The circumference of the earth measures 25,000 miles. If it were begirt by an iron railway, a load of one ton would be drawn round it in six weeks by the amount of mechanical power which resides in the third part of a ton of coals.

The great pyramid of Egypt stands upon a base measuring 700 feet each way, and is 500 feet high; its weight being 12,760,000,000 lbs. To construct it, cost the labour of 100,000 men for 20 years. Its materials would be raised from the ground to their present position by the combustion of 479 tons of coals.

The weight of metal in the Menai bridge is 4,000,000 lbs., and its height above the level of the water is 120 feet: its mass might be lifted from the level of the water to its present position by the combustion of 4 bushels of coals.[54]

The enormous consumption of coals in the arts and manufactures, and in steam navigation, has of late years excited the fears of some persons as to the possibility of the exhaustion of our mines. These apprehensions, however, may be allayed by the assurance received from the highest mining and geological authorities, that, estimating the present demand from our coal mines at 16 millions of tons annually, the coal fields of Northumberland and Durham alone are sufficient to supply it for 1700 years, and after the expiration of that time the great coal basin of South Wales will be sufficient to supply the same demand for 2000 years longer.

But, in speculations like these, the probable, if not certain, progress of improvement and discovery ought not to be overlooked; and we may safely pronounce that, long before a minute fraction of such a period of time shall have rolled over, other and more powerful mechanical agents will altogether supersede the use of coal. Philosophy already directs her finger at sources of inexhaustible power in the phenomena of electricity and magnetism. The alternate decomposition and recomposition of water, by magnetism and electricity, has too close an analogy to the alternate processes of vaporisation and condensation, not to occur at once to every mind: the development of the gases from solid matter by the operation of the chemical affinities, and their subsequent condensation into the liquid form, has already been essayed as a source of power. In a word, the general state of physical science, at the present moment, the vigour, activity, and sagacity with which researches in it are prosecuted in every civilized country, the increasing consideration in which scientific men are held, and the personal honours and rewards which begin to be conferred upon them, all justify the expectation that we are on the eve of mechanical discoveries still greater than any which have yet appeared; and that the steam engine itself, with the gigantic powers conferred upon it by the immortal Watt, will dwindle into insignificance in comparison with the hidden powers of nature still to be revealed; and that the day will come when that machine, which is now extending the blessings of civilisation to the most remote skirts of the globe, will cease to have existence except in the page of history.