Conversion of Heat into Mechanical Effect

This subject may be considered under three heads.

First, an inquiry into general qualitative and quantitative relations between heat and mechanical effect.
Second, the theoretical and. practical consideration of actual engines, including those of Stirling and Ericsson.
Third, the definition of the characteristics of a perfect engine.

The first portion relates to a purely theoretical question, and would, separately considered, fall beyond the usual limits of discussion at this Institution ; but the Author is obliged to' ask for an exception in his favour, finding it would be impossible to establish the ultimate object in view, without having proved his premises, which are based upon evidence of recent discoveries.

In discussing the succeeding heads he will have to rely, to a considerable extent, on his individual judgment and experimental researches.

On the relations between Heat and Mechanical Effect

The power obtained from a steam-engine depends upon the increase of volume given to the water in its transformation into steam, by the action of the fire under the boiler. Dr. Black observed, in 1763, that the effect of the fire was, for the most part, required to effect the conversion, after the water had been raised to the temperature of the steam itself ; and, moreover, that it made no difference whether the evaporation took place in the open air, or in a closed vessel under pressure.
Upon these facts he grounded his theory, that steam was a compound of water and heat, which heat, on entering into combination with the water, lost its individual properties, or became latent.

This "material theory" of heat has been generally adopted, in preference to the "theory of undulation," according to which heat is regarded to be the undulatory motion of a supposed aetherial fluid pervading all nature.

The supporters of the material theory explain the different phenomena of sensible, radial, and latent heat, by the free, or combined state of their supposed fluids ; the "specific heat of bodies by their different degrees of affinity for that fluid." The affinity of materials for heat is supposed to be invariably increased by increase of volume, and the evolution of heat, by friction between solids, is supposed to arise from permanent compression of their particles.

The latter supposition has been disproved by Sir Humphry Davy, who showed, that heat was evolved by friction between two pieces of ice, which caused them to melt, and could not, therefore, arise from permanent compression of the solid particles. Dulong proved, moreover, that the specific heat of gases is the same before and after compression, showing that the heat lost in their expansion is not absorbed into the gas, and cannot be accounted for according to the "material theory." Joule, of Manchester, produced heat by agitating water in a closed vessel, and also by an electric current, which, in its turn, was produced by power, in turning the handle of a magneto-electric machine.

The latter experiments are not only proofs against the supposition that heat is material ; but their greater value consists in showing an intimate connection between heat and the mechanical force by which it was produced, and they are the foundation of the "dynamical theory of heat."

According to this theory, in its general form, heat, mechanical force, electricity, chemical affinity, light, and sound, are but different manifestations of one great and infinite cause: " motion." Recent discoveries and experimental researches all accord with this great principle, which seems destined to open a new era of natural sciences. Dulong and Gay-Lussac have proved, by their experiments on sound, that the greater the specific heat of a gas the more rapid are its atomic vibrations.

Elevation of temperature does not alter the rapidity, but increases the length of those vibrations, and in consequence produces "expansion" of the body. The specific heat and temperature of a body determine the vibrating velocity of the material particles, the square of which, multiplied by the weight of the particles, gives their inherent force, or "vis viva." In solids the "vis viva" is least remarkable, in fluids it is greater, and in gaseous fluids it predominates so strongly over the gravitation, that the latter force becomes practically inappreciable.

Joule explains the elastic pressure of a gas, by the rebound of its particles against the sides of the vessel containing it, and proves the correctness of his views by calculation. If one side of a vessel gradually yields to the pressure, as is the case with a working piston, then the rebound of the particles will be less than their impact, and consequently the length of their vibrations must diminish, in proportion to the outward motion produced.
It is thus shown, that vibratory motion, or heat, is converted into its equivalent of onward motion, or dynamical effect.

To express this equivalent by number, it is necessary to agree, in the first place, on an arbitrary unit of heat, which is usually the heat required to raise the temperature of 1 lb. of water through 1° Centigrade, or Fahrenheit, and also, on a unit of mechanical effect, which is usually the "foot-pound," or the power required to lift 1 lb. through 1 foot. The data for these calculations may be taken from any materials, the specific heat and density of which are well known.

The nature of the material cannot effect the result, for if one should be more favourable to the production of mechanical force by heat, than another, and the second be more favourable to the reverse process, it would follow that by a judicious selection of materials, a machine might be devised, which would reproduce more than its own cause of motion. This would be "to ascribe creative power to matter," in contradiction to the laws of nature.

The limits of this paper do not permit of the train of reasoning, by which the numerical equivalent of power for heat has been ascertained, in different ways, by English, French, and German natural philosophers, within the last ten years ; the Author must, therefore, content himself with merely mentioning their names and publications.

Carnot and Clapeyron produced the first general formulae, which contained, however, an uncertain function, and were still based upon the supposition that heat was material. Holtzman, of Manheim, in pursuing the views of Carnot and Clapeyron, obtained a complete mathematical solution in 1845. Joule, of Manchester, solved the problem experimentally about the same time.

The "dynamical theory" was more fully developed by Helmholtz in 1847 and Mayer. Mr. W. J. M. Rankine, C.E., and Professor Thompson, of Edinburgh, have much extended the dynamical theory of heat, and applied the same to calculate the power of steam and air engines. M. Regnault, of Paris, has, by careful experimental researches on the total heat of steam, etc., provided some important data for the development of the dynamical theory of heat.

The following are the results obtained in units of power, or foot-lbs., for one unit of heat, by different authors:

Centigrade Thermometer (in foot lbs.) Fahrenheit's Thermometer (in foot lbs.)
By Holtzman's formula 1227 682
By Joule's experiment 1386 770
By Rankine's formula 1252 695
By Thompson's formula 1390 772
For the best Cornish engine, by M. de Pambour 148 82
For a perfect low-pressure condensing engine 190.8 50.4
For an actual Boulton and Watt's engine 46 25.5

The comparatively small effect produced by the steam-engine of the present day would seem to indicate that there is still much room for improvement.

Practical Engineers will probably receive with incredulity, and certainly derive but little advantage from, the preceding numerical statement, the result of abstract calculation, unless it can be proved by simple demonstration, and in such a manner that the essential difference between the actually and the theoretically perfect engine is clearly pointed out.

The Author proposes to accomplish this by means of a diagram (Fig. 1, Plate 3), which is, in effect, the expansion curve of saturated steam indefinitely prolonged.

The vertical lines and figures at the bottom signify the pressures of saturated steam in lbs. per inch ; the horizon al lines and figures on the sides denote the volume of steam compared with the volume of water, from which it is produced ; and the horizontal lines, with figures on the curve, express the temperatures of the steam corresponding to the pressure and volume of the same.

The outer curve, a a a, is that usually employed in calculating the power of expansion engines, being the expression of Watt's law "that the total heat in steam is the same at all pressures." The inner curve, b b b, is the corrected one, in accordance with the recent discoveries of Regnault, "on the total heat of steam," and may be termed "the curve of equal heat."

The fields between the horizontal dotted lines represent the power given out by the steam, in losing equal decrements of 10° of temperature in its expansion, and it is important to observe, that the areas of these fields are nearly alike, between the limits to which the pressure and temperature of steam are experimentally known, increasing only slightly, and in a uniform ratio inversely as the temperatures. This gradual increase may be ascribed to the fact, that the curve in question is one of equal heat, whereas it has been shown, that in expanding behind a working piston, the steam must lose heat in the dynamical proportion to the power given out.

Messrs. Rankine and Clausens have first drawn attention to this circumstance, and proved that the expansion of steam, behind a piston, must be attended by partial condensation.

On the other hand, experiments made by the Author prove that steam, when expanded spontaneously, is superheated steam, being a verification of Regnault's discovery, that the total heat of steam increases with its pressure. When steam is expanded behind a working piston the excess of free heat is first absorbed, or changed into dynamical effect, and if that does not suffice, partial condensation must take place.

It appears, however, to the Author, that Messrs. Rankine and Clausens undervalue the amount of free heat, and, therefore, over estimate the amount of condensation during expansion, by taking the specific heat of steam at 0.305 (Regnault's coefficient of increasing heat), which there seems good reasons to believe is far too low, because/

1st. The specific heat of an elastic fluid must be proportionate to its rate of expansion by heat. It has been shown, however, in experiments instituted by the Author above referred to, that the rate of expansion of steam near its point of saturation, is about three times greater, than that of air at the same temperature, which would make its specific heat 3 x 0.267 = 0.801, diminishing however rapidly with the increase of temperature.

2nd. The actual forms of diagrams, taken from the best expansive steam engines, do not show the effect of condensation: the ordinates of the lower portion of the curve are indeed higher than those given by Watt's law, starting from the same point. This is shown by Fig. 2, Plate 3, which is a diagram taken from the Old Ford Engine, by Mr. W. Pole, in which a aa is the actual curve, b b b the curve representing Watt's law, and c c c the curve of equal heat. The rise of the actual curve toward the end, may in part be owing to the generation of steam from the heated sides of the cylinders ; but it could not be supposed, that the effect of such generation would equal that of spontaneous condensation throughout the body of the steam.

Moreover the actual curve proves to be almost the perfect dynamical curve, as is proved by the equal areas, or fields of power, obtained by drawing lines from points of the curve of equal progression of temperature. If the limits of the sheet of diagrams had admitted of a continuation of the curve horizontally, (Fig. 1, Plate 3,) it would have exhibited continually decreasing volumes, and increasing temperatures, until finally a point would have been reached, where the volume of the steam was equal only to the water producing it.

It may be assumed, that the temperature would, at that point, be 640° Centigrade (1180° Faht.), or in other words, that the entire heat of the steam would be sensible. Supposing this steam (which would have at least 2000 lbs. pressure per square inch) could be introduced below a piston, and in giving out its power be expanded, until its temperature was reduced to zero ; then the entire 640 degrees of heat, would have been converted into their equivalent of power, of which the field of the diagram would represent the integral.

The theoretical equivalent of mechanical force for heat is thus represented to the eye ; and in computing the area of the entire figure, it is found to coincide nearly with, but somewhat to exceed, the results of abstract calculation and of Mr. Joule's experiments. That portion of the diagram (Fig. 1) which is shaded darker than the rest, represents the power of a perfect low-pressure condensing engine ; it covers only about l/14th part of the entire area.

The diagram shows, that the expansive steam-engine would be theoretically a perfect engine, if the water was heated in a close boiler, to 1180° Faht., and being then introduced below the working piston, under a pressure of at least 2000 lbs., would resolve itself entirely into steam, and was allowed to expand 2000 times, before it was discharged into a vacuous space, which, in this case, would not necessarily be a condenser.

The impracticable nature of such an engine is manifest, and it becomes necessary to seek for other means of obtaining from heat its full value of power.

It may not be considered out of place to mention here, the well-known experiments on steam guns by Mr. Perkins, which went far to prove the actual possibility of charging water with sufficient heat, in close vessels, that, upon liberation, it would resolve itself entirely into steam.

Before leaving this part of the Paper, it will be necessary to show the effect produced by the expansion of air, or any other permanently elastic fluid, under a working piston.

In the diagram (Fig. 3, Plate 3), the figures on the base and vertical lines denote the pressures in lbs. per square inch, and the figures on the side denote volumes of steam, as compared with the volume of the same weight of water. The curve a a a represents Marriotte's law, and is a curve of equal heat. The curve b b b is the dynamical curve, representing the real rate of expansion of air, behind a working piston. The difference between the two curves arises from the loss of sensible heat, which is converted into effect.

The figures upon the curve show the rate of progression of temperature, in compressing air of atmospheric pressure at 60° Faht. In constructing this curve, the specific heat of air at constant volume, has been taken at -267 as determined by Delaroche and Bernard. It furnishes itself at least an approximate proof of the correctness of this number, because the curve agrees with the observed fact, that in compressing air, to double its original pressure, its temperature is raised 70° Faht. The dotted horizontal lines limit the uniform fields of power obtained for every 10° decrease of temperature.

This curve is directly applicable to air, which when reduced to atmospheric pressure, has a temperature of 60° Faht. It can, however, easily be corrected, for any degree of temperature, by adding the difference of temperature, at a corresponding pressure throughout, and by adding to each volume, the same difference of temperature, divided by 508 (the ratio of expansion of air at 60° Faht.)

The dynamical theory of heat must not be considered the creation of the last few years, but, like all abstract truths in nature, it seems to have presented itself to the minds of the greatest philosophers in all ages, to be, after them, again superseded by theories moulded, as it 'were to order, to explain some isolated phenomenon, such as the radiation of the sun, the heating flame of a fire, or the latent heat in steam ; until at length the means of observation were sufficiently perfected to cover with absolute proof, what could before be reached only by the imagination.

It may here be mentioned, as instances, a quotation by Baron Humboldt from Aristotle, " who considered the first principle in nature to be a unity in all its manifestations, and the manifestations themselves he reduced always to motion as their foundation." Again, in Lord Bacon's Aphorisms, the chapter on " The first Vintages of the Force of Heat," occurs the following remarkable passage: "From the instances taken collectively, as well as singly, the nature whose limit is heat, appears to be motion." And further on, " But that the very essence of heat, or the substantial self of heat, is motion, and nothing else limited," etc.

Bacon fails, however, in his attempts to prove his philosophy, in confounding the visible motion of heating water, or of fire, with the intrinsic motion of the particles that manifests itself as heat.

On the performance of actual engines, including the air-engines of Stirling and Ericsson

In accordance with the principles put forth, the power of an engine is expressed by a simple formula :

Indicated HP = (ac / 33,000) x (rp - p' + (rA x (t - t') / v ))

in which c is the velocity of the piston in feet per minute ; a the area of the same in square inches ; t the temperature of the steam, or air, on entering the cylinder ; t' its temperature on leaving the same ; v expresses the volumes of the steam, or air, on entering the cylinder, as compared to one volume of water ; r the ratio of expansion, or fraction of stroke at which the supply is shut off ; A a constant, denoting the mechanical equivalent, per unit of heat, being (as shown by the diagrams) for steam = 400, and for air = 0.267 X 400 = 106 ; p the pressure of the fluid on entering the cylinder (pressure in boiler) in lbs. per square inch ; and p' the pressure against the working piston (back pressure) in lbs. per square inch.

The power required to work air, or feed pumps, has to be deducted from the result of this formula.

Take, for example, an expansive and condensing steam-engine of 16 inches diameter and 200 feet velocity of piston ; the total pressure of steam in the boiler 60 lbs., cut off at one fourth part of the stroke ; the vacuum in the cylinder averaging 11 lbs. (having 4 lbs. resisting pressure) ; the initial temperature of the steam = 295° ; and the final temperature t' = 207° Faht. ; the volume at 60 lbs. pressure would be = 460° (see diagram, or any table on the pressure, temperature, and volume of steam).

The indicated HP of this engine will be

(201 x 200) / 33,000 x (0.25 x 60 - 4 + (0.25 x 400 x (295 - 207) / 460)) = 36.75

The evaporation in the boiler is 2 x (rac/ 2 x 4 v) = 9.l cubic feet of water per hour.

The result agrees with that obtained by the usual method of computing the contents of the expansion curve, and is certainly more accurate and more expeditiously arrived at.

For non-expansive engines, the factor (rA x (t - t') / v ) has no value, because t = t', and r = 1.

In applying this formula, to ascertain the power of an air engine, the value of the constant A is = 106, as shown by the diagram, Fig. 3, Plate 3. If the object is to ascertain merely the relative economy of an engine, as compared with a perfect engine, it suffices to determine: 1st. the total units of heat which are imparted to the working fluid, and, 2nd, the units of heat which disappear in producing useful effect ; and inasmuch as the former exceed the latter, so the engine falls short of producing a full equivalent of mechanical effect for the heat expanded.

Take the example of an air-engine consisting of a working cylinder A, an air-pump B, and a reservoir D between them (Fig. 4, Plate 3). To obtain the greatest effect, the admission of air into the working cylinder should, under all circumstances, be so regulated, that it may expand down to atmospheric pressure before it is discharged.

Supposing that nothing was known of the proportion between the cylinders, of the working pressure, nor of the rate of expansion, but that the temperature of the air was known to be:

  • 60° Faht. On entering the pump at m.
  • 130° On entering the vessel D, which would be the case if compressed to half its original volume.
  • 710° On entering the working cylinder, which would be the heat required to double its volume at constant pressure, and
  • 570° On being discharged, having lost 140° in its expansion down to the atmospheric pressure.

Then the heat supplied by the fire would be = 710 — 130 = 580° Faht. and the difference of temperature of the air, on entering and on leaving the engine, would be = 570 — 60 = 510° Faht. It follows, that 580 - 510 = 70° of heat have been converted into their equivalent of mechanical effect, and the duty performed by the engine, for every one unit (Faht.) of heat employed, is 70/580 x 770 = 91.2 lbs. lifted 1 foot high.

The expansive air-engine is, therefore, theoretically superior to Boulton and Watt's condensing engine, but inferior to a good expansive engine. Practically considered it is certainly inferior to both, because one-half of the gross power of the working piston is absorbed by the pump, and the losses by friction and leakage are trebled in consequence.

Moreover, it has been found by its earliest promoter, Mr. Stirling, of Dundee, that the working of a tight piston, in a highly-heated cylinder, is attended with almost insurmountable difficulty.

The most essential difference between the steam-engine and the air-engine is, that in the former, the unproductive heat is expended in the boiler, where it becomes latent, in effecting increase of volume without displacement of the piston, whereas in the latter, it presents itself as free heat at the exhaust port.

Mr. Stirling, and after him Captain Ericsson, in taking advantage of this circumstance in favour of the air-engine, employed the free lost heat to warm the fresh air on entering the reservoir from the pump.

Ericsson constructed an engine on this plan, in 1833, which, according to received accounts, worked with considerable economy of fuel, but failed, in consequence of a defective heating apparatus, and the continual derangement of the working piston in a heated cylinder.

The apparatus he employed for recovering the lost heat resembled a locomotive boiler, through the tubes of which the cold air passed, while the heated and expanded air circulated in the opposite direction, through the intervening spaces. He termed this apparatus, the "regenerator," because he supposed, that by its means the same heat might be used perpetually over and over again, to produce motive power.

Formula for calculating the power of a Stirling engine

Stirling, of Dundee, patented an air-engine in 1816, and improvements in 1827 and in 1840. He constructed one of these machines, an account of which he brought before the Institution in 1845. In it he had combined several important advantages over former attempts, namely:

  • 1st. The hot working piston was dispensed with.
  • 2nd. The working pressure was increased, by using the same body of highly-compressed air over and over again.
  • 3rd. The reabsorption of the waste heat was carried out to greater perfection, by means of a series of thin iron plates, presenting a very large aggregate surface, which were held a small distance apart by fillets, to allow of the passage of air between them.

The lower extremities of these plates were heated by the fire to about 650° Faht., while the upper extremities were maintained at the lowest possible temperature, by coils of cold water pipes. The air was made to pass to and fro between the same surfaces, for every stroke of the engine, by means of a large displacing plunger, which was not required to work tight in its cylinder. In descending, the air absorbed heat, in the gradual proportion of the increasing temperature of the plates, and in consequence its elastic pressure was increased during the ascending stroke. By the reverse process, a fall to the former temperature and a decrease of pressure, inversely proportionate to the temperature and the space occupied, was effected, which space was, in the meantime, increased by the amount of the capacity of the working cylinder.

The opposite ends of the working cylinder communicated with two distinct heating apparatuses, the displacing plungers of which were attached to the opposite ends of a beam and made stroke, while the working piston was on its dead centres.

The excessive pressure of the heated air, beneath the one, over the cold air above the other displacing plunger, constituted the working pressure ; and the capacities of the displacing cylinders had to be so proportioned to the working cylinder, that the working pressure was not exceeded by the resisting pressures at the end of each stroke ; or supposing the volume of the air was doubled by the heat, it follows, that the net capacity of each displacing cylinder had to be equal to at least twice the capacity of the working cylinder.

Fig. 5, Plate 3, is a theoretical diagram of Stirling's engine ; the curve a a a represents the entire expansion of the air, from the time when it is all confined in the heated space, below the displacing plunger, to the moment when it occupies the cold extended space, above the displacing plunger, and the working cylinder.

The power due to this expansion is measured by the field a a a x y z, and is equivalent to 123 units of heat, as shown by (Fig. 3, Plate 3) ; whereas the power actually imparted to the working piston is represented by the portion of the diagram marked b b b, the corners of which are rounded off, in the ratio produced by the two cranks working over right angles, and is equivalent to 27.5 units, being about 2/9th parts of the entire area.
The field b b b y z, immediately below the sectioned portion, represents the back pressure on the working piston, or the power required to force the air from the working cylinders back into the displacing vessels.

The theoretical effect produced by a Stirling's engine, is to that of a perfect engine, as the units of heat expended in the entire expansion to the units producing useful effect, or as 123 to 27.5.

There remains to be considered the necessary mechanical loss of heat, owing to the difference of temperature between the air on entering the cool ends of the metallic plates, (the regenerators) and on returning from the same, which loss has been proved, by experiments hereafter to be explained, to amount to about 25° Faht., or to 3/4 x 25 = 19° Faht., if distributed upon the entire quantity of air employed, because only three-quarters of the same are actually heated each time.

The real effect of a Stirling's engine, as compared with a perfect engine, is therefore as (123 + 19) / 27.5 = 5.16, or it yields the power of 770 / 5.16 = 130 lbs. lifted 1 foot high, for every water unit of heat expended.

As a matter of a fact, 770 / 5.16 = 149 lbs.

It follows from the above, that the Stirling's engine converts into dynamical effect about one-fifth of the heat supplied, which is about equal to the performance of the best Cornish engines.

For calculating the actual power of a Stirling's engine of given proportions, the formula assumes the following more simple form:

Indicated HP = (ac / 33,000) x (A (t - t') / 5.16v)

in which A = 106 and t - t' the decrease of temperature, by the expansion of the air from the greatest to the lowest pressure.

The causes of the failure of Mr. Stirling's engine

The cause of the failure of Mr. Stirling's engine in practice, may apparently be traced, chiefly to insufficiency of heating surface, occasioned apparently from misapprehension of the principle involved, it having been thought, that the same heat would serve over and over again to produce power, and that the necessary expenditure of heat consisted only in the mechanical loss by imperfect action of the respirative plates, which were approached to each other to the utmost limits, consistent with an unobstructed passage of the air.

By the aid of the dynamical theory of heat it has been shown, that there is another and far more important expenditure of heat, which should have been provided for.

Another great practical defect in Stirling's engine, arises from the necessity of providing a reservoir of highly-compressed air to start with, and from the difficulty of preventing the escape of that stock of air, through the stuffing-boxes, etc.

The Ericsson Caloric Engine

Ericsson patented in 1851 another form of engine, which has lately been executed on a gigantic scale and continues to excite public attention.
This engine, of which (Fig. 6, Plate 3), represents the theoretical diagram, differs from the expansive air-engine (Fig. 4, Plate 3), only in the application to it of Stirling's respirator, or regenerator, and in the proportion between the capacities of the working and pumping cylinder, which in his engine are as three to two.

A is the working cylinder, the bottom of which is made of wrought iron, and exposed to the fire ; B is the pumping cylinder, which draws in atmospheric air through the valve u and delivers it into the air reservoir C through the valve v ; D is a slide valve, regulating the admission of air to and from the working cylinders; E is the respirator, or regenerator (a box filled with wire gauze), which is heated at the bottom by the fire, but is maintained cool towards the upper end, by the alternate rush of cold air downwards.

The top of the working cylinder and the bottom of the pumping cylinder are left open to the atmosphere, and the two pistons are attached to the same rod by which motion is imparted to the crank. The pressure in the air reservoir C is said to be maintained at 10 lbs. per superficial inch ( = 25 lbs. total pressure).

In the diagram, the figure a b c d e represents the entire pressure below the working piston amounting to 28 lbs. pressure per inch, up to the point c, where the admission is supposed to be cut off, in order to expand the air down to atmospheric pressure, before it is discharged, whereby the maximum effect will be obtained. From this gross effect has to be deducted, first the resisting pressure of the atmosphere against the working piston, which is represented by the field a b f e, and secondly the power absorbed by the pumping cylinder B, as represented by the field b g h f.

By laying this field of resistance upon the field of power b c df of the working cylinder, there remains the field b c d h g representing the entire effective pressure upon the working piston. This pressure amounts, on the average, to nearly 3 lbs. per square inch on the working piston.

In order to estimate the comparative economy of Ericsson's engine, it is necessary to consider the total quantity of heat absorbed for one revolution, the proportion of it which is transferred into useful effect, and the difference between the two, which, of necessity, escapes in the form of sensible heat.

If the atmospheric air enters the pumping cylinder at a temperature of 60° Faht., it will be raised, by compression, to 10 lbs. additional pressure and to a temperature of 111° Faht., as is shown in the dynamical diagram (Fig. 3, Plate 3).

This air has to be heated on its passage to the working cylinder, so that its volume is increased in the proportion of two to three, in order that the air delivered by the pumping cylinder may each time suffice to fill the working cylinder. To effect this it must be heated to 391° Faht.

The expansion that takes place in the working cylinder, will reduce that temperature to 314°, which is the temperature at which the pumping cylinder full of air at 60° will fill the working cylinder of one-half greater capacity (for 508 / 2 + 60
= 314).

The temperature lost, during expansion in the working cylinder, is 391 — 314 = 77°, which must be supplied to it again by the fire, before it reaches the respirator, in order not to cool down its lower extremity, and 25° in addition, to make up for the loss, on account of the imperfect action of the same. The air issues into the atmosphere at a temperature 25° above that of the upper extremity of the respirator, or at 111 + 25 = 136° Faht., being 136 - 60 = 76° hotter than when it entered.


Formula for calculating the power of the Ericsson Caloric engine

The total heat supplied to the air = 77 + 25 = 102° Faht.
The sensible heat carried off = 136 — 60 = 76 Faht.

There remains the heat absorbed by being converted into effect 26° Faht.

Or the Ericsson engine produces the effect of 26 / 102 x 770 = 196 lbs. lifted 1 foot high, for every (water) unit of heat expended.

This proves, that the Ericsson engine realises, theoretically, nearly one-third the effect of a perfect engine, and would possess a considerable advantage over any of those before considered, but for the following serious imperfections:

1st. Its gross working pressure has been demonstrated to be 3 lbs. per square inch, but the engine being single-acting, the true average pressure is only 1.5 lb. per inch, and supposing the engine will move with 0.5 lb. pressure per inch upon the working piston, its mere friction will absorb one-third of the whole power.

2nd. The working piston has to move air-tight in a heated cylinder, which by former attempts has been proved to be attended with great practical difficulties. These are no doubt reduced, by the air being heated in a smaller degree than had been attempted before ; but the temperature still remains sufficient to carbonise the lubricating material, and by affecting the shape of the cylinder, to cause leakage.

3rd. The available heating surface of the engine is confined to the bottom surface of the working cylinder, and to the passage leading to the regenerator.
Taking into account the intermittent action and slow heat absorbing power of the air, the heating surface of an air-engine should, in the opinion of the Author, not be less than 6 superficial feet for 1 lb. of coal consumed per hour, or about seven times larger than in the engines of the "Ericsson."

4th The weight, bulk, and first cost of Ericsson's engine are inversely proportionate to its low working pressure and slow speed.

5th Incidental losses of heat, by radiation from the large exposed surface of the heated cylinder, necessitate a very considerable addition to the expenditure of fuel.

The engines of the "Ericsson" are said to consist of 4 working cylinders of 14 feet diameter and 6-feet stroke, making upwards of 14 strokes per minute.

Their collective indicated HP is (4 x 21168 x 84 x 3) / 33000 = 676 

from which must be deducted 33 per cent for friction of pistons alone, and say 27 per cent for friction of general machinery and of the air in rushing through the regenerator ; in all 60 per cent., leaving 271 actual HP.

The combined steam and ether engine

There still remains one distinct class of engine for consideration, namely, the combined Steam and Ether engine.
This consists of an ordinary steam-engine with a tubular condenser.

Instead of the cold water, which is usually admitted into the chamber surrounding the tubes, ether, or chloroform, is substituted, which, it is well known, boil at a temperature far below the boiling-point of water, and therefore will generate their own vapours, under a considerable pressure, by the heat given off by the steam in the act of condensation. The vapours of ether, or chloroform, are made to give motion to a second engine, and are in their turn condensed by very cold water.

It would seem, at first sight, that by this ingenious arrangement the power obtained for a given quantity of fuel was doubled, if compared with the performance of the steam-engine alone ; but the preceding investigations will have proved, that the heat imparted to the ether must fall short of that given out under the steam-boiler, in proportion as the heat is changed into the dynamic effect obtained from the steam-engine.

The additional effect of the ether-engine might indeed be obtained at once from the steam, if the expansive action of the steam was sufficiently extended ; considering, however that an engine, in which the steam is expanded at one-third part of the stroke, absorbs only about one-eighth portion of the entire heat of the steam, and considering also that it is very inconvenient to extend the rate of expansion much further, in rotary engines, there remains, at present a considerable advantage in favour of the combined steam and ether engine, if the practical difficulties involved, such as the tightness of the joints, are not taken into account.

Supposing the dynamic equivalent per unit of heat obtained by the engine, to be 90 foot-lbs., that of the ether engine may be taken at two-thirds, or 60 foot-lbs., making a total of 150 foot-lbs.,—which nearly equals the performance of the best Cornish engines.

The following table is intended to convey a more distinct idea of the comparative merits of the different steam and air engines referred to.

Description of engines Theoretical Performance in Foot-lbs Actual Performance in Foot-lbs. Actual Performance (consumption) in lbs. of Coal per Hour
A Boulton and Watt condensing engine, low pressure 51.8 29 8.00
The best Cornish engine 158.8 82 2.38
Combined steam and expansive ether engine 150.0 75 3.09
Stirling's engine 130.0 65 3.57
Ericsson's engine 196.0 65 6.63
A perfect engine 770.0 385 0.60

The statements of the actual performance of air-engines must be considered as only rough approximations, as it is not possible to calculate losses of heat, with any degree of precision. The actual performance of the "Ericsson" engine may be deemed too low, considering its theoretical superiority ; but the Author considers the disproportion to be fully accounted for, by the extraordinary losses of useful effect, arising from the exposure of the heated cylinder, and the low working pressure.

In Stirling's engine, the heated cylinder is closed and surrounded by flues and brickwork, in consequence of which, its economical effect is thought to be equal to that of Ericsson's engine, although it is in theory inferior.

On the necessary characteristics of a perfect engine

In the first part of this Paper it has been shown, that an engine would be theoretically perfect, if all the heat applied to the elastic medium was consumed in its extension behind a working piston, (or its substitutes, such as a disc, a flexible bag, etc.) leaving no portion of it to be thrown into a condenser, or into the atmosphere.

In the second part, several actual engines have been examined, with a view to test their degree of theoretical and practical perfection. Such an inquiry should have for its end, the attainment of some more perfect result than could hitherto be obtained. The Author will therefore attempt to state his views of the characteristics of a perfect engine.

1st. All the elastic material employed should actually enter the working cylinder, (or its substitute,) and produce its full value of effective displacement of piston, without deduction for the resisting pressure, or the working of pumps.

2nd. The production of the elastic material, previous to its entering the working cylinder, should not require a continuous expenditure of heat, or in the case of the steam-engine, the latent heat expended in the boiler should be recovered.

3rd. That working material is the best which is capable of receiving the largest possible quantity of heat in a given space. Its temperature and pressure should be raised to the highest point which the vessel containing it will admit of, but on leaving the working cylinder, the temperature should be reduced to a minimum. This may be accomplished, either by infinite expansion, or practically by the application of a regenerator.

4th. Losses of heat by radiation and leakage, should be reduced to the smallest possible amount, by working at high pressure and velocity, and by covering all heated surfaces with non-conducting materials. These losses being, proportionally, more to be apprehended in a perfect, than in an imperfect engine.

5th. Large and compact heating surface and considerable body of material are essential, to attain a high temperature, without rapid destruction of the vessels.

6th. No working part of the engine should be brought into contact with highly-heated material.

The respirator, or regenerator, is undoubtedly a useful agent, for recovering the free, or otherwise unproductive heat of a caloric engine, and the following experimental investigations on its action, by the Author, may not be thought devoid of interest.

The annular space between two concentric cylinders was fitted with 750 brass strips, each 5 feet 9 inches long, and held 1/16th of an inch apart from each other, by projecting ribs upon every alternate strip. The internal cylinder contained a piston, with an enlarged hollow piston rod, passing through a stuffing box, and was worked to and fro by an engine. The lower extremity of the external cylinder was heated by a fire to 650° Faht., as indicated by the pyrometer, and was maintained at that temperature.

A second, or charging cylinder was provided, which by the motion of its working piston, alternately withdrew and returned the same air to the first cylinder. The capacity of the charging cylinder was 24 cubic feet, and its piston made 18 strokes per minute : about two-thirds of its contents, or 16 cubic feet of air of atmospheric pressure, passed with each stroke, to and fro through the respirator, and all the heat carried away was absorbed by the sides of the cylinder.

After 2.5 hours' working, the temperature of the charging cylinder was raised from 60° to 110° Faht. (50°). Its capacity for heat had been previously ascertained, by suddenly admitting steam, and weighing the condensed water obtained (in heating it from 60° to 210° Faht.) (150°), which amounted to about 54 lbs.

The quantity of air which passed from the respirator into the cylinder was 43,200 cubic feet, and its weight 3360 lbs.: this, if multiplied by its specific heat 0.267, is equal to 897 lbs. of water-power of absorbing heat.

The heat given off was 50 / 150 x 1000 = 18000 units, and consequently the air left the respirator, each time, at a temperature of 18000 / 897 = 20.01° higher than that at which it entered.

Adding to this, for loss of heat by radiation during the experiment, which according to established rules may be taken at 5°, the entire loss of heat by the respirator amounts to 25° Faht. when air is employed. In using steam it does not exceed 10° Faht., owing to the greater conducting power of that fluid.

The regenerator condenser, which was designed and executed some years ago by the Author, is an illustration that water may be also subjected to respirative action.

The Paper is illustrated by a series of diagrams from whence Plate 3 is compiled.