that

vortices of heat-motion, and bases his philosophy upon hypothesis, supposing sensible heat to be employed in changing the velocity of the particles, latent heat to be the work of altering the dimensions of the orbits, and considering the effort of each vortex to enlarge its boundaries to be due to

centrifugal force. He distinguished between real and apparent specific heat, and showed that the two methods of absorption of heat, in the case of the heating of a fluid, that due to simple increase of temperature and that due to increase of volume, should be distinguished; he proposed, for the latter quantity, the term heat-potential, and for the sum of the two, the name of thermo-dynamic function.

Carnot had stated, a quarter of a century earlier, that the efficiency of a heat-engine is a function of the two limits of temperature between which the machine is worked, and

not of the nature of the working substance-an assertion which is quite true where the material does not change its physical state while working. Rankine now deduced that "general equation of thermo-dynamics" which expresses algebraically the relations between heat and mechanical energy, when energy is changing from the one state to the other, in which equation is giver, for any assumed change of the fluids, the quantity of heat transformed. He showed that steam in the engine must be partially liquefied by the process of expanding against a resistance, and proved that the total heat of a perfect gas must increase with rise of temperature at a rate proportional to its specific heat under constant pressure.

Rankine, in 1850, showed the inaccuracy of the then accepted value, 0.2669, of the specific heat of air under constant pressure, and calculated its value as 0.24. Three years later, the experiments of Regnault gave the value 0.2379, and Rankine, recalculating it, made it 0.2377. In 1851, Rankine continued his discussion of the subject, and, by his own theory, corroborated Thompson's law giving the efficiency of a perfect heat-engine as the quotient of the range of working temperature to the temperature of the upper limit, measured from the absolute zero.

During this period, Clausius, the German physicist, was working on the same subject, taking quite a different method, studying the mechanical effects of heat in gases, and deducing, almost simultaneously with Rankine (1850), the general equation which lies at the beginning of the theory of the equivalence of heat and mechanical energy. He found that the probable zero of heat-motion is at such a point that the Carnot function must be approximately the reciprocal of the "absolute" temperature, as measured with the air thermometer, or, stated exactly, that quantity as determined by a perfect gas thermometer. He confirmed Rankine's conclusion relative to the liquefaction of saturated vapors when expanding against resistance, and, in 1854,

adapted Carnot's principle to the new theory, and showed that his idea of the reversible engine and of the performance of a cycle in testing the changes produced still held good, notwithstanding Carnot's ignorance of the true nature of heat. Clausius also gave us the extremely important principle: It is impossible for a self-acting machine, unaided, to transfer heat from one body at a low temperature to another having a higher temperature.

Simultaneously with Rankine and Clausius, Prof. William Thomson was engaged in researches in thermo-dynamics (1850). He was the first to express the principle of Carnot as adapted to the modern theory by Clausius in the now generally quoted propositions: '

1. When equal mechanical effects are produced by purely thermal action, equal quantities of heat are produced or disappear by transformation of energy.

2. If, in any engine, a reversal effects complete inversion of all the physical and mechanical details of its operation, it is a perfect engine, and produces maximum effect with any given quantity of heat and with any fixed limits of range of temperature.

William Thomson and James Thompson showed, among the earliest of their deductions from these principles, the fact, afterward confirmed by experiment, that the melting-point of ice should be lowered by pressure 0.0135° Fahr. for each atmosphere, and that a body which contracts while being heated will always have its temperature decreased by sudden compression. Thomson applied the principles of energetics in extended investigations in the department of electricity, while Helmholtz carried some of the same methods into his favorite study of acoustics.

The application of now well-settled principles to the physics of gases led to many interesting and important de

1 Vide Tait's admirable "Sketch of Thermodynamics," second edition, Edinburgh, 1877; also "Manual of the Steam-Engine," chap. iii.

ductions Clausius explained the relations between the volume, density, temperature, and pressure of gases, and their modifications; Maxwell reëstablished the experimentally determined law of Dalton and Charles, known also as that of Gay-Lussac (1801), which asserts that all masses of equal pressure, volume, and temperature, contain equal numbers of molecules. On the Continent of Europe, also, Hirn, Zeuner, Grashof, Tresca, Laboulaye, and others have, during the same period and since, continued and greatly extended these theoretical researches.

During all this time, a vast amount of experimental work has also been done, resulting in the determination of important data without which all the preceding labor would have been fruitless. Of those who have engaged in such work, Cagniard de la Tour, Andrews, Regnault, Hirn, Fairbairn and Tate, Laboulaye, Tresca, and a few others have directed their researches in this most important direction with the special object of aiding in the advancement of the new-born sciences. By the middle of the present century, the time which we are now studying, this set of data was tolerably complete. Boyle had, two hundred years before, discovered and published the law, which is now known by his name and by that of Marriotte,' that the pressure of a gas varies inversely as its volume and directly as its density; Dr. Black and James Watt discovered, a hundred years later (1760), the latent heat of vapors, and Watt determined the method of expansion of steam; Dalton, in England, and Gay-Lussac, in France, showed, at the beginning of the nineteenth century, that all gaseous fluids are expanded by equal fractions of their volume by equal increments of temperature; Watt and Robison had given tables of the elastic force of steam, and Gren had shown that, at the tem

1 "New Experiments, Physico-Mechanical, etc., touching the Spring of Air," 1662.

"De la Nature de l'Air," 1676.

perature of boiling water, the pressure of steam was equal to that of the atmosphere; Dalton, Ure, and others proved (1800-1818) that the law connecting temperatures and pressures of steam was expressed by a geometrical ratio; and Biot had already given an approximate formula, when Southern introduced another, which is still in use.

The French Government established a commission in 1823 to experiment with a view to the institution of legislation regulating the working of steam-engines and boilers; and this commission, MM. de Prony, Arago, Girard, and Dulong, determined quite accurately the temperatures of steam under pressures running up to twenty-four atmospheres, giving a formula for the calculation of the one quantity, the other being known. Ten years later, the Government of the United States instituted similar experiments under the direction of the Franklin Institute.

The marked distinction between gases, like oxygen and hydrogen, and condensible vapors, like steam and carbonic acid, had been, at this time, shown by Cagniard de la Tour, who, in 1822, studied their behavior at high temperatures and under very great pressures. He found that, when a vapor was confined in a glass tube in presence of the same substance in the liquid state, as where steam and water were confined together, if the temperature was increased to a certain definite point, the whole mass suddenly became of uniform character, and the previously existing line of demarkation vanished, the whole mass of fluid becoming, as he inferred, gaseous. It was at about this time that Faraday made known his then novel experiments, in which gases which had been before supposed permanent were liquefied, simply by subjecting them to enormous pressures. He then also first stated that, above certain temperatures, liquefaction of vapors was impossible, however great the pressure.

Faraday's conclusion was justified by the researches of Dr. Andrews, who has since most successfully extended the investigation commenced by Cagniard de la Tour, and who has