Finally, all unutilized heat rejected from the steam-cylinder is carried away from the machine, either by the water of condensation, or, in the non-condensing engine, by the atmosphere into which it is discharged.

Having traced the method of operation of the steam-engine, it is easy to discover what principles are comprehended in its philosophy, to learn what are known facts bearing upon its operation, and to determine what are the directions in which improvement must take place, what are the limits beyond which improvement cannot possibly be carried, and, in some directions, to determine what is the proper course to pursue in effecting improvements. The general direction of change in the past, as well as at present, is easily seen, and it may usually be assumed that there will be no immediate change of direction in a course which has long been preserved, and which is well defined. We may, therefore, form an idea of the probable direction in which to look for improvement in the near future.

Reviewing the operations which go on in this machine during the process of transformation of energy which has been outlined, and studying it more in detail, we may deduce the principles which govern its design and construction, guide us in its management, and determine its efficiency.

In the furnace of the boiler, the quantity of heat developed in available form is proportional to the amount of fuel burned. It is available in proportion to the temperature attained by the products of combustion; were this temperature no higher than that of the boiler, the heat would all pass off unutilized. But the temperature produced by a given quantity of heat, measured in heat-units, is greater as the volume of gas heated is less. It follows that, at this point, therefore, the fuel should be perfectly consumed with the least possible air-supply, and the least possible abstraction of heat before combustion is complete. High temperature of furnace, also, favors complete combustion. We hence conclude that, in the steam-boiler furnace, fuel should be burned completely in a chamber having non-conducting walls, and with the smallest air-supply compatible with thorough combustion; and, further, that the air should be free from moisture, that greatest of all absorbents of heat, and that the products of combustion should be removed from the furnace before beginning to drain their heat into the boiler. A fire-brick furnace, a large combustion-chamber with thorough intermixture of gases within it, good fuel, and a restricted and carefully-distributed supply of air, seem to be the conditions which meet these requisites best.

The heat generated by combustion traverses the walls which separate the gases of the furnace from the steam and water confined within the boiler, and is then taken up by those fluids, raising their temperature from that of the entering “feed-water” to that due the steam-pressure, and expanding the liquid into steam occupying a greatly-increased volume, thus doing a certain amount of work, besides increasing temperature. The extent to which heat may thus be usefully withdrawn from the furnace-gases depends upon the conductivity of the metallic wall, the rate at which the water will take heat from the metal, and the difference of temperature on the two sides of the metal. Extended “heating-surface,” therefore, a metal of high conducting power, and a maximum difference of temperature on the two sides of the separating wall of metal, are the essential conditions of economy here. The heating-surface is sometimes made of so great an area that the temperature of the escaping gases is too low to give good chimney-draught, and a “mechanical draught” is resorted to, revolving “fan-blowers” being ordinarily used for its production. It is most economical to adopt this method. The steam-boiler is generally constructed of iron—sometimes, but rarely, of cast-iron, although “steel,” where not hard enough to harden or temper, is better in consequence of its greater strength and homogeneousness of structure, and its better conductivity. The maximum conductivity of flow of heat for any given material is secured by so designing the boiler as to secure rapid, steady, and complete circulation of the water within it. The maximum rapidity of transfer throughout the whole area of heating-surface is secured, usually, by taking the feed-water into the boiler as nearly as possible at the point where the gases are discharged into the chimney-flue, withdrawing the steam nearer the point of maximum temperature of flues, and securing opposite directions of flow for the gases on the one side and the water on the other. Losses of heat from the boiler, by conduction and radiation to surrounding bodies, are checked as far as possible by non-conducting coverings.

The mechanical equivalent of the heat generated in the boiler is easily calculated when the conditions of working are known. A pound of pure carbon has been found to be capable of liberating by its perfect combustion, resulting in the formation of carbonic acid, 14,500 British thermal units, equivalent to 14,500 × 772 = 11,194,000 foot-pounds of work, and, if burned in one hour, to 11194000∕1980000 = 5.6 horse-power. In other words, with perfect utilization, but 10∕56 = 0.177, or about one-sixth, of a pound of carbon would be needed per hour for each horse-power of work done. But even good coal is not nearly all carbon, and has but about nine-tenths this heat-producing power, and it is usually rated as yielding about 10,000,000 foot-pounds of work per pound. The evaporative power of pure carbon being rated at 15 pounds of water, that of good coal may be stated at 131∕2. In metric measures, one gramme of good coal should evaporate about 131∕2 grammes of water from the boiling-point, producing the equivalent of about 3,000,000 kilogrammetres of work from the 7,272 calories of heat thus generated. A gramme of pure carbon generates in its combustion 8,080 calories of heat. Per hour and per horse-power, 0.08, or less than one-twelfth, of a kilogram of carbon burned per hour evolves heat-energy equal to one horse-power.

Of the coal burned in a steam-boiler, it rarely happens that more than three-fourths is utilized in making steam; 7,500,000 foot-pounds (1,036,898 kilogrammetres) is, therefore, as much energy as is usually sent to the engine per pound of good coal burned in the steam-boiler. The “efficiency” of a good steam-boiler is therefore usually not far from 0.75 as a maximum. Rankine estimates this quantity for ordinary boilers of good design and with chimney-draught at

E = 0.92 ;
1 + 0.5
F
S

in which F∕S is the ratio of weight of fuel burned per square foot of grate to the ratio of heating to grate surface; this is a formula of fairly close approximation for general practice.

The steam in the engine first drives the piston some distance before the induction or steam valve is closed, and it then expands, doing work, and condensing in proportion to work done as the expansion proceeds, until it is finally released by the opening of the exhaust or eduction valve. Saturated steam is modified in its action by a process which has already been described, condensing at the beginning and reëvaporating at the end of the stroke, thus carrying into the condenser considerable quantities of heat which should have been utilized in the development of power. Whether this operation takes place in one cylinder or in several is only of importance in so far as it modifies the losses due to conduction and radiation of heat, to condensation and reëvaporation of steam, and to the friction of the machine. It has already been seen how these losses are modified by the substitution of the compound for the single-cylinder engine.