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 v_²; thus _v_² = 3 _p/ρ_, and _p_ and _ρ_ being known, we find _v_². 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. In the introduction to this paper Maxwell points out, while there was then no means of measuring the quantities which occurred in Clausius’ expression for the mean free path, “the phenomena of the internal friction of gases, the conduction of heat through a gas, and the diffusion of one gas through another, seem to indicate the possibility of determining accurately the mean length of path which a particle describes between two collisions. In order, therefore, to lay the foundation of such investigations on strict mechanical principles,” he continues, “I shall demonstrate the laws of motion of an indefinite number of small, hard and perfectly elastic spheres acting on one another only during impact.” Maxwell then proceeds to consider in the first case the impact of two spheres.