=50. The Second Fundamental Principle.= Another fundamental discovery has been made in connection with the heat form of energy, which, like the law of conservation, relates to all forms of energy, but has found its first and most important application in heat. While the law of conservation answers the question, how much of the new form of energy is developed if a given quantity of energy changes, but gives no clue as to when such a change occurs, this second law asserts the condition under which such changes arise, and is therefore called the _second fundamental principle_. The discovery of this law antedates _Mayer's_ discovery of the law of conservation by about twenty years, and was made by a French military engineer, _Sadi Carnot_, who died soon afterward without having lived to see the recognition his great work obtained. _Carnot_ asked himself the question, Upon what does the action of the steam engine, which had just then come into use, depend? This led him first to the more general question of the action of heat engines in general. He found that no heat engine could work unless the heat dropped from a higher to a lower temperature, just as no water wheel can work unless the water flows from a higher to a lower level, and he determined the conditions which an _ideal heat engine_ must fulfil, that is, a machine in which the greatest possible value in work is obtained from heat. However, an ideal machine of this nature can be constructed in very different ways, and Carnot's discovery consists in the recognition of the fact _that the quantity of work obtained from the heat unit does not at all depend upon the peculiar construction of the ideal machine, but is determined solely by the temperature between which the heat transition takes place_. This follows from the following considerations: In the first place an ideal engine must be _reversible_, that is, it must be capable of working both ways, changing heat into work and work back into heat. Now, if we have two ideal engines between the same temperatures, and if we assume that engine A produces more work from the same quantity of heat than engine B, then let A move one way and let B move the other way with the work obtained from A. Since B produces less work from a given amount of heat, hence more heat from an equal amount of work, there will in the end be more heat at the higher temperature than was originally there. But experience teaches _that there is no means in nature by which heat in the absence of concomitant change could be caused to rise to a higher temperature_. Therefore an engine so constructed as to produce this result is impossible, And B cannot be of such a nature as to produce less work from the same quantity of heat than A.