first to use the fire-tubular boiler for locomotive engines, published in 1839 a work, "Sur l'Influence des Chemins de Fer," in which he gave the requisite data for a rough determination of the value of the mechanical equivalent of heat, although he does not himself deduce that value.

Dr. Julius R. Mayer, three years later (1842), published the results of a very ingenious and quite closely approximate calculation of the heat-equivalent, basing his estimate upon the work necessary to compress air, and on the specific heats of the gas, the idea being that the work of compression is the equivalent of the heat generated. Seguin had taken the converse operation, taking the loss of heat of expanding steam as the equivalent of the work done by the steam while expanding. The latter also was the first to point out the fact, afterward experimentally proved by Hirn, that the fluid exhausted from an engine should heat the water of condensation less than would the same fluid when originally taken into the engine.

A Danish engineer, Colding, at about the same time (1843), published the results of experiments made to determine the same quantity; but the best and most extended work, and that which is now almost universally accepted as standard, was done by a British investigator.

James Prescott Joule commenced the experimental investigations which have made him famous at some time previous to 1843, at which date he published, in the Philosophical Magazine, his earliest method. His first determination gave 770 foot-pounds. During the succeeding five or six years Joule repeated his work, adopting a considerable variety of methods, and obtaining very variable results. One method was to determine the heat produced by forcing air through tubes; another, and his usual plan, was to turn a paddle-wheel by a definite power in a known weight of water. He finally, in 1849, concluded these

researches.

The method of calculating the mechanical equivalent of

heat which was adopted by Dr. Mayer, of Heilbronn, is as beautiful as it is ingenious: Conceive two equal portions of atmospheric air to be inclosed, at the same temperature-as at the freezing-point-in vessels each capable of containing one cubic foot; communicate heat to both, retaining the

one portion at the original volume, and permitting the other to expand under a constant pressure equal to that of the atmosphere. In each vessel there will be inclosed 0.08073 pound, or 1.29 ounce, of air. When, at the same temperature, the one has doubled its pressure and the other has doubled its volume, each will be at a temperature of 525.2° Fahr., or 274° C., and each will have double the original temperature, as measured on the absolute scale from the

zero of heat-motion. But the one will have absorbed but 63 British thermal units, while the other will have absorbed 9. In the first case, all of this heat will have been employed in simply increasing the temperature of the air; in the second case, the temperature of the air will have been equally increased, and, besides, a certain amount of work— 2,116.3 foot-pounds-must have been done in overcoming the resistance of the air; it is to this latter action that we must debit the additional heat which has disappeared. Now, 2,116.3 = 770 foot-pounds per heat-unit-almost precisely 23 the value derived from Joule's experiments. Had Mayer's measurement been absolutely accurate, the result of his calculation would have been an exact determination of the heat-equivalent, provided no heat is, in this case, lost by internal work.

Joule's most probably accurate measure was obtained by the use of a paddle-wheel revolving in water or other fluid. A copper vessel contained a carefully weighed portion of the fluid, and at the bottom was a step, on which stood a vertical spindle carrying the paddle-wheel. This wheel was turned by cords passing over nicely-balanced grooved wheels, the axles of which were carried on frictionrollers. Weights hung at the ends of these cords were the moving forces. Falling to the ground, they exerted an easily and accurately determinable amount of work, W× H, which turned the paddle-wheel a definite number of revolutions, warming the water by the production of an amount of heat exactly equivalent to the amount of work done. After the weight had been raised and this operation repeated a sufficient number of times, the quantity of heat communicated to the water was carefully determined and compared with the amount of work expended in its development. Joule also used a pair of disks of iron rubbing against each other in a vessel of mercury, and measured the heat thus developed by friction, comparing it with the

work done. The average of forty experiments with water gave the equivalent 772.692 foot-pounds; fifty with mercury gave 774.083; twenty with cast-iron gave 774.987the temperature of the apparatus being from 55° to 60° Fahr.

Joule also determined, by experiment, the fact that the expansion of air or other gas without doing work produces no change of temperature, which fact is predicable from the now known principles of thermo-dynamics. He stated the results of his researches relating to the mechanical equivalent of heat as follows:

1. The heat produced by the friction of bodies, whether solid or liquid, is always proportional to the quantity of work expended.

2. The quantity required to increase the temperature of a pound of water (weighed in vacuo at 55° to 60° Fahr.) by one degree requires for its production the expenditure of a force measured by the fall of 778 pounds from a height of one foot. This quantity is now generally called "Joule's equivalent."

During this series of experiments, Joule also deduced the position of the "absolute zero," the point at which heatmotion ceases, and stated it to be about 480° Fahr. below the freezing-point of water, which is not very far from the probably true value, −493.2° Fahr. (−273° C.), as deduced afterward from more precise data.

The result of these, and of the later experiments of Hirn and others, has been the admission of the following principle:

Heat-energy and mechanical energy are mutually convertible and have a definite equivalence, the British thermal unit being equivalent to 778 foot-pounds of work, and the metric calorie to 426.8, or, as usually taken, 427 kilogrammetres. The exact measure is not fully determined, how

ever.

It has now become generally admitted that all forms of

energy due to physical forces are mutually convertible with a definite quantivalence; and it is not yet determined that even vital and mental energy do not fall within the same great generalization. This quantivalence is the sole basis of the science of Energetics.

The study of this science has been, up to the present time, principally confined to that portion which comprehends the relations of heat and mechanical energy. In the study of this department of the science, thermo-dynamics, Rankine, Clausius, Thompson, Hirn, and others have acquired great distinction. In the investigations which have been made by these authorities, the methods of transfer of heat and of modification of physical state in gases and vapors, when a change occurs in the form of the energy considered, have been the subjects of especial study.

According to the law of Boyle and Marriotte, the expansion of such fluids follows a law expressed graphically by the hyperbola, and algebraically by the expression PV' = A, in which, with unchanging temperature, x is equal to 1. One of the first and most evident deductions from the principles of the equivalence of the several forms of energy is that the value of x must increase as the energy expended in expansion increases. This change is very marked with a vapor like steam-which, expanded without doing work, has an exponent less than unity, and which, when doing work by expanding behind a piston, partially condenses, the value of x increases to, in the case of steam, 1.111 according to Rankine, or, probably more correctly, to 1.135 or more, according to Zeuner and Grashof. This fact has an important bearing upon the theory of the steam-engine, and we are indebted to Rankine for the first complete treatise on that theory as thus modified.

Prof. Rankine began his investigations as early as 1849, at which time he proposed his theory of the molecular constitution of matter, now well known as the theory of molecular vortices. He supposes a system of whirling rings or