# Amagat, Émile

# Amagat, Émile

(*b*. Saint-Satur, Cher, France, 2 January 1841; *d*. Saint-Satur, 15 February 1915)

*physics.*

Amagat became *docteur-es-sciences* at Paris in February 1872 and was then, successively, *agrégé*, professor of physics at the Facultè Libre des Sciences of Lyons, and examiner at the École Polytechnique. He was elected a corresponding member of the Acadèmie des Sciences on 5 May 1890, received from the Institut the Prix Lacaze pour la Physique in 1893, and became a full member of the Académie on 9 June 1902.

Amagat’s work dealt with fluid statics. At the time he began his work, Andrews had just announced the structure of a few isotherms of carbon dioxide at between 10° and 50° C. and up to 110 atmospheres, the region in which the product of pressure times volume is at a minimum for this compound. Andrews’ report was published in France in 1870, and his research was the only one, at the time, to use varying temperatures. From 1869 to 1872 Amagat studied the effect of temperatures up to 320° on the compressibility and expansion of gases. These studies led to his doctoral thesis.

Knowledge of liquids was even more limited. It was known that, except for water, the coefficient of compressibility increases with the temperature. Amagat published an extensive report on this subject in 1877, showing that this coefficient clearly decreases when pressure increases, which was contrary to the results reached by other experimenters.

There remained the search for the laws of the coefficients of compressibility, the coefficients of expansion under constant pressure and constant volume, the coefficients of pressure when both pressure and temperature are varied, and the limits toward which these laws tend when matter is more and more condensed by pressure. It was to this research that Amagat devoted the active phase of his career.

His first works were published between 1879 and 1882. They display the isotherms of a number of gases for temperatures between 0° and 100° and for pressures up to slightly more than 400 atmospheres (the limit that could be borne by the sturdiest glass tubes available).

The experimental data used as a base for this research were furnished by measurements taken in 1879 in a mine shaft at Verpilleux, near Saint–Étienne. Amagat determined by means of a column of mercury 327 meters high the compressibility of nitrogen up to 430 atmospheres. His results were universally adopted for the calculation of gas manometers. Until then only Regnault’s results had been available, and they went only to thirty atmospheres. As for Andrews, he had been content to apply Mariotte’s (Boyle’s) law up to 110 atmospheres, using a compressed-air manometer.

At the end of this first stage of his research Amagat realized that certain questions vital to the theory of fluids could be elucidated only by greatly increasing the limit of pressures. But having already gone beyond the possible resistance of glass tubes, he had to invent new experimental methods. At this point Amagat created his most ingenious apparatus, the manometer with free–moving pistons in viscous liquids; thus he was able to measure with certainty and regularity pressures above 3,000 atmosphereas. Using an idea that originated with Gally-Cazolat, Amagat constructed an apparatus that was a back-acting hydraulic press made gas-tight by means of a viscous liquid such as molasses or castor oil.

Amagat’s manometer served his own research and was also adopted in many military and firearms laboratories. The same apparatus, put in reverse, made it possible to create considerable pressures while measuring them. A remarkable application of this device is credited to Vieille in the adjustment of crushing cylinders for the creation of pressure in firearms.

Amagat’s own work, which had to do with gases and a fairly large number of liquids, was published between 1886 and 1893. After having constructed his network of isotherms (1887-1891), he spent the next two years extracting the experimental laws of fluid statics as they emerged from these results. Without the experimental data contributed by Amagat, many important theoretical works would have been impossible: research on liquids, Tait’s kinetic theory of gases, the works of Van Der Waals, the computation of coefficients in Sarrau’s formula (pressure and temperature in the detonation of explosives), and Sarrau’s application of his formula to oxygen, which made it possible to determine the critical temperature of this gas before it was liquefied by Wroblewski.

Having been forced to study the elasticity of glass in order to gauge the variations in volume of the containers holding the fluids studied, in 1889–1890 Amagat broadened his study until it embraced the elasticity of solids in general, starting with a verification of the general formulas of elasticity. As a correlative study he had to determine the compressibility of mercury. As early as 1876 and 1882 he had done research on the elasticity of rarefied gases. Amagat found that air, hydrogen, and carbon dioxide follow Mariotte’s law at pressures as low as 1/10,000 atmosphere.

Amagat then turned to various special studies related to his general research: interior pressure of fluids; negative interior pressure; laws regulating the specific heats of fluids at different temperatures and pressures, and their relationship; verification of Van Der Waals’ law of corresponding states, according to which the equation of the state of all gases can be represented by a single function in which critical temperature, pressure, and volume appear as parameters; solidification of liquids by pressure: determination of the density of liquefied gases and of their saturated vapor; the atomic volume of oxygen and of hydrogen; the interaction of oxygen and mercury; the differential equation of the speed of sound in gases; and the relations between the coefficients of the formulas of Coulomb (magnetism), Laplace, and Ampère; “The Laplace formula connects those of Coulomb and of Ampère but only by employing an almost constant factor that experience alone can determine.”

## BIBLIOGRAPHY

Amagat presented all accounts of his work to the Academie des Sciences; his papers are listed in the following indexes to the *Comptes rendus* of the Acadèmie: for Vols. **62-91** (12 papers); **92-121** (48 papers); **122-151** (18 papers); and **152-181** (4 papers). Individual papers are “Compressibilitè de l’air et de l’hydrogè;ne à des tempèratures élevées,” in *Annales de chimie et de physique*, 4th series, **28** (1873), 274-279; “Dilatation et compressibilité des gaz ä diverses températures,’ *lbid.*, **29** (1873), 246-285; “Recherches sur l’élasticitè de l’air sous de faibles pressions,” lbid., 5th series. **8** (1876), 270-278; “Recherches sur la compressibilité des liquides,” lbid., **11** (1877), 520-549; “Sur l’équation différentielle de la vitesse du son,” in *Journal de physique*, 1st series, **9** (1880), 56-59; “Mémoire sur la compressibilité des gaz aux fortes pressions. Influence de la température,” in *Annales de chimie et de physique*, 5th series, **22** (1881), 353-398; “Mémoire sur la compressibilité de l’air et de l’acide carbonique de I atm. à 8 atm. et de 10° à 300°,’ ibid., **28** (1883), 456-464; “Mémoire sur la compressibilité de l’air, de l’hydrogène et de l’acide carbonique raréfiés,” lbid., 464-480; “Sur une forme nouvelle de la fonction φ(pvt) = 0,” ibid., 480-507; “Sur la dètermination du rapport , in *Journal de physique*, 2nd series, **4** (1885), 174-177; “Mémoires sur l’èlasticité des solides et la compressibilitè du mercure,” in *Annales de chimie et de physique*, 6th series, **22** (1891); “Sur la dé termination de la densité des gaz et de leur vapeur saturée, éléments du point critique de l’acide carbonique,” in *Journal de physique*, 3rd series, I (1892), 288-298; “Sur le déplacement de la tempèrature du maximum de densité de l’eau par la pression et le retour aux lois ordinaires sous l’influence de la pression et de la tempèrature,” *lbid.*, 3rd series, **2** (1893), 449–459; “Mémoires sur l’élasticité et la dilatation des fluides jusqu’aux trés hautes pressions,” in *Annales de chimie et de physique*, 6th series, **29** (1893), 68-137 and 505-574, 2 articles; “Pressions intèrieures dans les fluides et forme de la fonction °(pvt) = 0,” in *Journal de physique*, 3rd series **3** (1894), 307-316; and “Sur les chaleurs specifiques des gaz et les propriétés des isothermes.” *ibid.*, 3rd series, **5** (1896). 114-123.

No general study has been made of Amagat’s life or his work. See, however, *Notice sur les travaux scientifiques de M. E. H. Amagat*... (Paris, 1896), which, although published anonymously, was written by Amagat himself to be presented to the Académie des Sciences at the time of his candidature, in accordance with traditional practice.

Jacques Payen

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**Amagat, Émile**