The inverse process, the conversion of heat into work, required investigation, and it is this that constitutes the science of thermodynamics. It was the subject of the celebrated _Réflexions sur la Puissance Motrice du Feu, et sur les Machines Propres à Développer cette Puissance_, published in 1824 by Sadi Carnot, an uncle of the late President of the French Republic. Only a few copies of this essay were issued, and its text was known to very few persons twenty-four years later, when it was reprinted by the Academy of Sciences. Its methods and conclusions were set forth by Thomson in 1849 in a memoir which he entitled, "An Account of Carnot's Theory of the Motive Power of Heat." Numerical results deduced from Regnault's experiments on steam were included; and the memoir as a whole led naturally in Thomson's hands to a corrected theory of heat engines, which he published in 1852. Carnot's view of the working of a heat engine was founded on the analogy of the performance of work by a stream of water descending from a higher level to a lower. The same quantity of water flows away in a given time from a water wheel in the tail-race as is received in that time by the wheel from the supply stream. Now a heat engine receives heat from a supplying body, or source, at one temperature and parts with heat to another body (for example, the condenser of a steam engine) at a lower temperature. This body is usually called the refrigerator. According to Carnot these temperatures corresponded to the two levels in the case of the water wheel; the heat was what flowed through the engine. Thus in his theory as much heat was given up by a heat engine to the body at the lower temperature as was received by it from the source. The heat was simply transferred from the body at the higher temperature to the body at the lower; and this transference was supposed to be the source of the work.[17] The first law of thermodynamics based on Joule's proportionality of heat produced to work expended, and the converse assumed and verified _a posteriori_, showed that this view is erroneous, and that the heat delivered to the refrigerator must be less in amount than that received from the source, by exactly the amount which is converted into work, together with the heat which, in an imperfect engine, is lost by conduction, etc., from the cylinder or other working chamber. This change was made by Thomson in his second paper: but he found the ideas of Carnot of direct and fruitful application in the new theory. These were the cycle of operations and the ideal reversible engine.