PHYSICS
66
PHYSICS
which this point was verified, and Jean-Baptiste Biot
(1774-1862), whose experimental researches were
numerous and skilful, and who had furnished recent
optics with very valuable matter, remained strongly
attached to the system of emission by which he
endeavoured to explain all the phenomena that Frcs-
nel had discovered and ex-plained by the undulatory
system. Moreover, Biot would not acknowledge
himself defeated, or regard the system of emission as
condemned until Foucault (1819-68) proved that Hght
is propagated much more quickly in air than in water.
XXIX. Theories of Heat. — The idea of the quantity of heat and the invention of the calorimeter intended for measuring the amount of heat emitted or absorbed by a bodv under given circumstances are du_e to Joseph Black (1728-99) and Adair Crawford (1749-95), who, by joining calorimetrj' with ther- mometry, veritably created the science of heat, which science remained unborn as long as the only thing done was the comparison of temperatures. Like Descartes, Newton lield that heat consisted in a very hvely agitation of the smallest parts of which bodies are composed. By showing that a certain quantity of heat is furnished to ice which melts, without how- ever raising the temperature of the ice, that this heat remains in a "latent state" in the water resulting from the mehing and that it again becomes manifest when the water returns to ice, the experiments of Black and Crawford led ph3'sicists to change their opinion concerning the nature of heat. In it they beheld a certain fiuid which combines ■nith other matter when heat passes into the latent state, and separates from it when heat is liberated again, and, in the new nomenclature that perpetuated the rev- olution brought about by Antoine-Laurent Lavoisier (1743-94), this imponderable fluid was assigned a place among simple bodies and named caloric.
Air becomes heated when it is compressed, and cools again when rarefied under the receiver of the pneumatic machine. JohannHcinrich Lambert (1728- 77), Horace de Saussure (1740-79), and John Dalton (1766-1844) recognized the importance of this already old experiment, but it is to Laplace that we are indebted for a complete explanation of this phenome- non. The experiment proved to Laplace that, at a given temperature, a mass of air contains a quantity of caloric proportional to its volume. If we admit the accuracy of the law of compressibility enunciated by Boyle and Mariotte, this quantity of heat combined with a given mass of air, also of given temperature, is proportional to the volume of this air. In 1803 Laplace formulated these propositions in a short note inserted in Berthollet's "Statique chimique". In order to verify the consequences which Laplace deduced therefrom concerning the expansion of gases, Louis-Joseph Gay-Lussac (1778-1850) began re- searches on this subject, and in 1807 on the variations of temperature produced when a gas contained in a receiver enters another receiver previously empty.
Laplace's \-iews entail an evident corollary; to raise to a certain number of degrees the temperature of a gas of a fixed volume, the communication of less heat is required than if this gas were ex-panded under an invariable pressure. Hence a gas admits of two distinct kinds of specific heat which depend on whether it is heated at constant volume or under constant pressure; the specific heat being greater in the latter case than in the former. Through these remarks the study of the specific heat of gases was signalized as one of the most important in which ex-perimenters could engage. The Institute made this study the subject of a competition which called forth two notable memoirs, one by Delaroche and Berard on the measurement of the specific heats of various gases under constant pressure; and the other by Desormes and Clement, published in 1812, on the de- termination of the increase of heat due to a given com-
pression in a given mass of air. The experiments
of Desormes and Clement enabled Laplace to deduce,
in the case of air, the ratio of specific heat under con-
stant pressure to specific heat under constant volume,
and hence to test the ideas he had formed on the
propagation of sound.
In applying to air the law of compressibility dis- covered by Boyle, Ne^i,on had attempted to calculate the velocitj- of the propagation of sound in this fluid, and the formula which he had established gave values very inferior to those furnished by experimental determination. Lagrange had already shown that, by modifying Boyle's law of compressibility, this dis- agreement could be overcome; however, the modifi- cation was to be justified not by what Lagrange said but by what Laplace discovered. ^Yhen sound is propagated in air by alternate condensations and rarefactions, the temperature at each point instead of remaining unchanged, as Boyle's law supposed, is alternately raised and lowered about a mean value. Hence velocity of sound was no longer expressed by the formula Newton had proposed; this ex-pression had to be multiplied by the square root of the ratio of specific heat under constant pressure to specific heat under constant volume. Laplace had this thought in mind in 1803 (BerthoUet, "Statique chimique"); its consequences being developed in 1807 by Poisson, his disciple. In 1816 Laplace published his new formula ; fresh experiments by Desormes and Clement, and analogous experiments by Gay-Lussac and Welter gave him tolerably exact values of the re- lation of the specific heats of gases. Henceforth the great geometrician could compare the result given by his formula with that furnished by the direct deter- mination of the velocity of sound, the latter, in metres per second, being represented by the number 340-889, and the former by the number 337-715. This agree- ment seemed a very strong confirmation of the hypoth- esis of caloric and the theory of molecular action, to both of which it was attributable. It would appear that Laplace had a right to say: "The phenomena of the expansion of heat and ^•ibration of gases lead back to the attractive and repellent forces sensible only at imperceptible distances. In my theory on capillary action, I have traced to similar forces the effects of capillarity. All terrestrial phenomena depend upon this species of force, just as celestial phenomena depend upon universal gra^-itation, and the study of these forces now seems to me the principal object of mathematical philosophy" (written in 1823).
In 1824 a new truth was formulated from which was to be developed a doctrine which was to overturn, to a great extent, natural philosophy as conceived by Newton and Bosco\-ich and carried out by Laplace and liis disciples. However, Sadi Carnot (1796-1832), the author of this new truth, still assumed the cor- rectness of the theorv- of caloric. He proposed to extend to heat-engines the principle of the impossi- bility of perpetual motion recognized for engines of unchanging temperature, and was led to the following conclusion: In order that a certain quantity of caloric may produce work of the kind that human industry requires, this caloric must pass from a hot to a cold body; when the quantity of caloric is given, as well as the temperatures to which these two bodies are raised, the useful work produced admits of a superior limit independent of the nature of the substances which transmit the caloric and of the device by means of which the transmission is cfTected. The moment that Carnot formulated this fertile truth, the founda- tions of the theorj' of caloric were shaken. However, in the hj-pothesis of caloric, how could the generation of heat by friction be ex-plained? Two bodies rubbed together were found to be just as rich in caloric as they had been; therefore, whence came the caloric evolved by friction?
As early as 1783 Lavoisier and Laplace were much
