"Between Bernoulli and Maxwell... Euler, d'Alembert, Lagrange and Hamilton expounded Newton's dynamics] in more and more general forms, until at last all [mechanical] processes... were seen as conforming to... the Principle of the Conservation of Energy, and the Principle of Least Action. This mathematical drive... continued, overflowing beyond... mechanics... [and into] processes involving nonmechanical factors: heat, electricity, vitality, and chemical change... The most comprehensive exposition was given in 1847 by Hermann von Helmholtz... In 1848, J. P. Joule [demonstrated that]... whether he produced heat by the passage of an electric current, or by mechanical effort, the conversion took place at fixed, measurable rates. ...[I]t was natural to look again for an explanation ...Perhaps the production of heat by friction merely transferred mechanical energy from a visible level to an invisible one... the increased motion of the molecules... Clausius and Maxwell turned this view... into a fully-developed branch of mathematics (...from 1857 to 1866.) ...[H]eat theory had been united into the general theory of 'matter in motion'... the random agitation of vast numbers of invisibly-small particles."