in which E represents the ratio of heat utilized to the whole calorific value of the fuel, T is the furnace-temperature, T′ the temperature of the chimney, and t that of the external air. The higher the furnace-temperature and the lower that of the chimney, the greater the proportion of heat available. It is further evident that, however perfect the combustion, no heat can be utilized if either the temperature of the chimney approximates to that of the furnace, or if the temperature of the furnace is reduced by dilution approximately to that of the boiler. Concentration of heat in the furnace is secured, in some cases, by special expedients, as by heating the entering air, or as in the Siemens gas-furnace, heating both the combustible gases and the supporter of combustion. Detached fire-brick furnaces have an advantage over the “fire-boxes” of steam-boilers in their higher temperature; surrounding the fire with non-conducting and highly heated surfaces is an effective method of securing high furnace-temperature.

In arranging heating-surface, the effort should be to impede the draught as little as possible, and so to place them that the circulation of water within the boiler should be free and rapid at every part reached by the hot gases. The directions of circulation of water on the one side and of gas on the other side of the sheet should, whenever possible, be opposite. The cold water should enter where the cooled gases leave, and the steam should be taken off farthest from that point. The temperature of chimney-gases has thus been reduced in practice to less than 300° Fahr., and an efficiency equal to 0.75 to 0.80 the theoretical has been attained.

The extent of heating-surface simply, in all of the best forms of boiler, determines the efficiency, and in them the disposition of that surface seldom affects it to any great extent. The area of heating-surface may also be varied within very wide limits without very greatly modifying efficiency. A ratio of 25 to 1 in flue and 30 to 1 in tubular boilers represents the relative area of heating and grate surfaces as chosen in the practice of the best-known builders.

The material of the boiler should be tough and ductile iron, or, better, a soft steel containing only sufficient carbon to insure melting in the crucible or on the hearth of the melting-furnace, and so little that no danger may exist of hardening and cracking under the action of sudden and great changes of temperature.

Where iron is used, it is necessary to select a somewhat hard, but homogeneous and tough, quality for the fire-box sheets or any part exposed to flames.

The factor of safety is invariably too low in this country, and is never too high in Europe. Foreign builders are more careful in this matter than our makers in the United States. The boiler should be built strong enough to bear a pressure at least six times the proposed working-pressure; as the boiler grows weak with age, it should be occasionally tested to a pressure far above the working-pressure, which latter should be reduced gradually to keep within the bounds of safety. In the United States, the factor of safety is seldom more than four in the new boilers, frequently much less, and even this is reduced practically to one and a third by the operation of our inspection-laws.

The principles just enunciated are those generally, perhaps universally, accepted principles which are stated in all text-books of science and of steam-engineering, and are accepted by both engineers and men of science.

These principles are correct, and the deductions which have been here formulated are rigidly exact, as applied to all types of heat-engine in use; and they lead us to the determination, in all cases, of the “modulus” of efficiency of the engine, i. e., to the calculation of the ratio of its actual efficiency to that efficiency which it would have, were it absolutely free from loss of heat by conduction or radiation, or other method of loss of heat or waste of power, by friction of parts or by shock.

The best modern marine compound engines sometimes, as we have seen, consume as little as two pounds of coal per horse-power and per hour; but this is but about one-tenth the power derivable from the fuel, were all its heat thoroughly utilized. This loss may be divided thus: 70 per cent. rejected in exhausted steam; 20 per cent. lost by conduction and radiation and by faults of mechanism and design; and only the 10 per cent. remaining is utilized. Thirty per cent. of the heat generated in the furnace is usually lost in the chimney, and of the remainder, which enters the engine, 20 per cent. at most is all which we can hope to save any portion of by improvements effected in our best existing type of steam-engine. It has already been shown how the engineer can best proceed in attempting this economy.

The direction in which further improvement must take place in the standard type of engine is plainly that which shall most efficiently check losses by internal condensation and reëvaporation by the transfer of heat to and from the metal of the steam-cylinder. The condensation of steam doing work is evidently not a disadvantage, but, on the contrary, a decided advantage.