VI. On a general law of density in saturated vapours

• Published in: Philosophical Transactions of the Royal Society of London
• Format: Article in Journal/Newspaper
• Language: English
• Published: The Royal Society 1852
• Subjects: General Medicine; Carbonic acid
• Online Access: http://dx.doi.org/10.1098/rstl.1852.0007; https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1852.0007

The relation between the pressure and temperature of vapours in contact with their generating liquids has been expressed by a variety of empirical formulæ, which, although convenient for practical purposes, do not claim to represent any general law. Some years ago, while examining a mathematical theory of gases, I endeavoured to find out from the French Academy’s experiments, if the density of steam in contact with water followed any distinct law with reference to the temperature measured from the zero of gaseous tension. [By Rudberg’s experiments, confirmed by Magnus and Regnault, this zero is —461° in Fahr. scale, or —273°·89 in the Centigrade scale. Temperatures reckoned from this zero I shall call G temperatures to save circumlocution .] If t represents the G temperature, Δ the density of a gas or a vapour, and p its elastic force, the equation t Δ = p . . . . . . . . . . . . . . . (1.) represents the well-known laws of Marriotte and of Dalton and Gay-Lussac. The function that expresses a general relation between p and t in vapours must include a more simple function, expressing a general relation between Δ and t . The proper course, therefore, seemed to be to tabulate the quotients p/t from the experiments of the Academy and to project them into a curve. Now, for reasons connected with the vis viva theory of gases, which represents the G temperature as a square quantity, I projected these densities as ordinates to the square root of the G temperatures as abscissæ , and the curve traced out was of the parabolic kind, but of high power. To reduce this, because density is a cubic quantity, I tabulated their cube roots and set them off as ordinates to the same abscissæ. The result was gratifying, for the familiar conic parabola made its appearance. To ascertain whether this curve was exactly the conic parabola, I tabulated the square root of these ordinates, corresponding with the sixth root of the densities, and laid them off as new ordinates to the same abscissæ. The result is shown in the accompanying Chart, Plate VII., under the title French Academy's Steam . The observation's are denoted by dots thus•, and it will be remarked that they range with great precision in a straight line, any slight divergence being sometimes to the right and sometimes to the left; precisely as might be expected from small errors of observation. Other series of experiments on steam were projected in a similar manner; and it was found that although no two exactly agreed with each other, yet that each set ranged in a straight line nearly. The vapours of ether, alcohol, and sulphuret of carbon were tried in the same way, and found to conform to the same law. I have since added to the Chart M. Avogadro’s observations on the vapour of mercury, which will be found remarkably in accordance; also Dr. Faraday’s experiments on liquefied gases, given in the Philosophical Transactions for 1845. Of these, olefiant gas (No. 1, p. 160) is remarkably in accordance; also the nitrous oxide (No. 2, p. 168), ammonia, cyanogen, sulphurous acid, and carbonic acid at the upper part of its range. Muriatic acid, sulphuretted and arseniuretted hydrogen do not show the same regularity. The coordinates of the points being the square root of the G temperature and the sixth root of the densities, the equation to the straight line that passes through the points expresses the sixth root of the density in terms of the square root of the G temperature.