You will have been wondering when the principle of conservation of energy would enter the scene. In fact, it has been skulking in the wings for some time. FOURIER used a special case of it; in notes written subsequently to his treatise, CARNOT came around to it; CLAPEYRON stated it clearly but made no use of it. The authors of the early nineteenth century saw no conflict between using the vis viva theory for physics (i.e. popular explanation of how things really are) and the caloric theory for mathematics (i.e. calculation of the phenomena). According to the vis viva theory, heat was simply a vibratory motion of the smallest parts of bodies, but this idea was thought ill adapted to calculate anything. According to the caloric theory, something named “heat”, which could perfectly well be explained as a manifestation of the intestine motion of the smallest parts of bodies, was conserved in total quantity as it was transferred from one body to another. If addition of caloric was the agent by which the parts were made to vibrate, then for the mathematical theory it was defter to discuss the transfer of that agent rather than the fine structure of the intestine motion to which it gave rise. Thus, so long as nothing specific was required as the outcome, it was not hard to believe in both theories at once.