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 common ground. The doctrine of least action was first propounded by Maupertius in 1744. Two years later he proclaimed it to be a universal law of nature, and the first scientific proof of the existence of God. It was weakly supported by him, violently attacked by König of Leipzig, and keenly defended by Euler. Lagrange's conception of the principle of least action became the mother of analytic mechanics, but his statement of it was inaccurate, as has been remarked by Josef Bertrand in the third edition of the Mécanique Analytique. The form of the principle of least action, as it now exists, was given by Hamilton, and was extended to electrodynamics by F. E. Neumann, Clausius, Maxwell, and Helmholtz. To subordinate the principle to all reversible processes, Helmholtz introduced into it the conception of the "kinetic potential." In this form the principle has universal validity.

An offshoot of the mechanical theory of heat is the modern kinetic theory of gases, developed mathematically by Clausius, Maxwell, Ludwig Boltzmann of Munich, and others. The first suggestions of a kinetic theory of matter go back as far as the time of the Greeks. The earliest work to be mentioned here is that of Daniel Bernoulli, 1738. He attributed to gas-molecules great velocity, explained the pressure of a gas by molecular bombardment, and deduced Boyle's law as a consequence of his assumptions. Over a century later his ideas were taken up by Joule (in 1846), A. K. Krönig (in 1856), and Clausius (in 1857). Joule dropped his speculations on this subject when he began his experimental work on heat. Krönig explained by the kinetic theory the fact determined experimentally by Joule that the internal energy of a gas is not altered by expansion when no external work is done. Clausius took an important step in supposing that molecules may have rotary motion, and that atoms in a molecule may move relatively to each other. He assumed that the force acting