§ 1. Object of this Paper.—In a paper on the Mechanical Action of Heat, which I sent to the Royal Society of Edinburgh in December 1849, and which was read in February 1850, it was shown, that if sensible or thermometric heat consists in the motion of molecular vortices supposed to be arranged in a particular way, and combined in a particular way with oscillatory movements, the principles of thermodynamics, and various relations between heat and elasticity, are arrived at by applying the laws of dynamics to that hypothesis. The object of the present paper is to show how the general equation of thermodynamics, and other propositions, are deduced from the hypothesis of molecular vortices, when freed from all special suppositions as to the figure and arrangement of the vortices, and the properties of the matter that moves in them, and reduced to the following form:—That thermometric heat consists in a motion of the particles of bodies in circulating streams, with a velocity either constant or fluctuating periodically. This, of course, implies that the forces acting amongst those particles are capable of transmitting that motion.