At the meeting of the British Association at Ipswich, in 1851, a paper by J. J. Waterston of Bombay, on “The General Theory of Gases,” was read. The following is an extract from the Proceedings:—
The author “conceives that the atoms of a gas, being perfectly elastic, are in continual motion in all directions, being constrained within a limited space by their collisions with each other, and with the particles of surrounding bodies.
“The vis viva of these motions in a given portion of a gas constitutes the quantity of heat contained in it.
“He shows that the result of this state of motion must be to give the gas an elasticity proportional to the mean square of the velocity of the molecular motions, and to the total mass of the atoms contained in unity of bulk” (unit of volume)—that is to say, to the density of the medium.
“The elasticity in a given gas is the measure of temperature. Equilibrium of pressure and heat between two gases takes place when the number of atoms in unit of volume is equal and the vis viva of each atom equal. Temperature, therefore, in all gases is proportional to the mass of one atom multiplied by the mean square of the velocity of the molecular motions, being measured from an absolute zero 491° below the zero of Fahrenheit’s thermometer.”
It appears, therefore, from these extracts that the discovery of the laws that temperature is measured by the mean kinetic energy of a single molecule, and that in a mixture of gases the mean kinetic energy of each molecule is the same for each gas, is due to Waterston. They were contained in his paper of 1846, and published by him in 1851. Both these papers, however, appear to have been unnoticed by all subsequent writers until 1892.
Meanwhile, in 1848, Joule’s attention was called by his experiments to the question, and he saw that Herapath’s result gave a means of calculating the mean velocity of the molecules of a gas. For according to the result given above, p = ⅓ ρ v²; thus v² = 3 p/ρ, and p and ρ being known, we find v². Thus for hydrogen at freezing-point and atmospheric pressure Joule obtains for v the value 6,055 feet per second, or, roughly, six times the velocity of sound in air.
Clausius was the next writer of importance on the subject. His first paper is in “Poggendorff’s Annalen,” vol. c., 1857, “On the Kind of Motion we call Heat.” It gives an exposition of the theory, and establishes the fact that the kinetic energy of the translatory motion of a molecule does not represent the whole of the heat it contains. If we look upon a molecule as a small solid we must consider the energy it possesses in consequence of its rotation about its centre of gravity, as well as the energy due to the motion of translation of the whole.
Clausius’ second paper appeared in 1859. In it he considers the average length of the path of a molecule during the interval between two collisions. He determines this path in terms of the average distance between the molecules and the distance between the centres of two molecules at the time when a collision is taking place.
These two papers appear to have attracted Maxwell’s attention to the matter, and his first paper, entitled “Illustrations of the Dynamical Theory of Gases,” was read to the British Association at Aberdeen and Oxford in 1859 and 1860, and appeared in the Philosophical Magazine, January and July, 1860.