Sect. 4.—Force of Steam.
THE experiments on the elastic force of steam made by the French Academy are fitted in an especial manner to decide the question between rival formulæ, in consequence of the great amount of force to which they extend; namely, 60 feet of mercury, or 24 atmospheres: for formulæ which give results almost indistinguishable in the lower part of the scale diverge widely at those elevated points. Mr. Waterston[10] has reduced both these and other experiments to a rule in the following manner:—He takes the zero of gaseous tension, determined by other experimenters (Rudberg, Magnus, and Regnault,) to be 461° below the zero of Fahrenheit, or 274° below the zero of the centigrade scale: and temperatures reckoned from this zero he calls “G temperatures.” The square root of the G temperatures is the element to which the elastic force is referred (for certain theoretical reasons), and it is found that the density of steam is as the sixth power of this element. The agreement of this rule with the special results is strikingly close. A like rule was found by him to apply generally to many other gases in contact with their liquids.
[10] Phil. Trans. 1852.
But M. Regnault has recently investigated the subject in the most complete and ample manner, and has obtained results somewhat different.[11] He is led to the conclusion that no formula proceeding by [607] a power of the temperature can represent the experiments. He also finds that the rule of Dalton (that as the temperatures increase in arithmetical progression, the elastic force increases in geometric progression) deviates from the observations, especially at high temperatures. Dalton’s rule would be expressed by saying that the variable part of the elastic force is as at, where t is the temperature. This failing, M. Regnault makes trial of a formula suggested by M. Biot, consisting of a sum of two terms, one of which is as at, and the other is bt: and in this way satisfies the experiments very closely. But this can only be considered as a formula of interpolation, and has no theoretical basis. M. Roche had proposed a formula in which the force is as az, z depending upon the temperature by an equation[12] to which he had been led by theoretical considerations. This agrees better with observation than any other formula which includes only the same number of coefficients.
[11] Mém. de l’Institut, vol. xxi. (1847). M. Regnault’s Memoir occupies 767 pages.
[12] The equation z = t⁄1 + mt.
Among the experimental thermotical laws referred to by M. Regnault are, the Law of Watt,[13] that “the quantity of heat which is required to convert a pint of water at a temperature of zero into steam, is the same whatever be the pressure.” Also, the Law of Southern, that “the latent heat of vaporization, that is the heat absorbed in the passage from the liquid to the gaseous consistence, is constant for all purposes: and that we obtain the total heat in adding to the constant latent heat the number which represents the latent heat of steam.” Southern found the latent heat of the steam of water to be represented by about 950 degrees of Fahrenheit.[14]
[13] See Robison’s Mechanical Philosophy, vol. ii. p. 8.
[14] Ib. p. 160.