By a process entirely different, and by an independent course of reasoning, Mayer had, a few months previous to Joule, determined this equivalent to be 771·4 foot-pounds. Such a remarkable coincidence arrived at by pursuing different routes gives this value a strong claim to accuracy, and raises the Mechanical Theory of Heat to the dignity of an exact science, and its enunciators to the foremost place in the ranks of physical philosophers. In linking together the labours of the two remarkable men above alluded to, Prof. Tyndall remarks, that “Mayer’s labours have in some measure the stamp of profound intuition, which rose however to the energy of undoubting conviction in the author’s mind. Joule’s labours, on the contrary, are an experimental demonstration. Mayer _thought_ his theory out, and rose to its grandest applications. Joule _worked_ his theory out, and gave it the solidity of natural truth. True to the speculative instinct of his country, Mayer drew large and mighty conclusions from slender premises; while the Englishman aimed above all things at the firm establishment of facts.... To each belongs a reputation which will not quickly fade, for the share he has had, not only in establishing the dynamical theory of heat, but also in leading the way towards a right appreciation of the general energies of the universe.” But from these generalities we must pass to the application of the mechanical theory of heat to our special subject. We have learnt that every form of motion is convertible into heat. We know that the falling meteor or shooting star, whose motion is impeded by friction against the earth’s atmosphere, is heated thereby to a temperature of incandescence. Let us then suppose that myriads of such cosmical particles came into collision from the effect of their mutual attraction, or that the component atoms of a vast nebulous mass violently converged under the like influence. What would follow? Obviously the generation of an intense heat by the arrest of converging motion, such a heat as would result in the fusion of the whole into one mass. Mayer, in one of his most remarkable papers (“Celestial Dynamics”) remarks that the “Newtonian theory of gravitation, whilst it enables us to determine, from its present form, the earth’s state of aggregation in ages past, at the same time points out to us a source of heat powerful enough to produce such a state of aggregation—powerful enough to melt worlds: it teaches us to consider the molten state of a planet as the result of the mechanical union of cosmical masses, and to derive the radiation of the sun and the heat in the bowels of the earth from a common origin.”