The first law of energetics, that of the conservation of energy, is analogous to Lavoisier's principle in chemistry, the conservation of matter. The sign of equality which unites the terms of a chemical equation expresses the fact that after every chemical reaction the same total mass of matter is present as before the transformation. This is also true of energy; after every transformation we find exactly the same total quantity of energy as before it. This, however, tells us nothing as to the conditions of the transformation, or the causes, _i.e._ the anterior phenomena, which determined such transformation. The second principle of energetics, that of Carnot, enunciated in 1824, deals with the conditions under which a transformation of energy is possible. A mass of water at a certain height represents a quantity of potential energy equal to the product of its weight by its height; but this energy cannot produce mechanical work unless the water is allowed to fall. Consider two lakes at the same altitude and of the same capacity, one of which is entirely landlocked, while the other has an open channel leading to the sea. Each lake represents the same quantity of potential energy, but the energy of the landlocked lake is useless, it cannot be {103} transformed; whereas the other lake whose water can run into the sea realizes the conditions necessary for utilization, viz. the transformability of its energy. The same may be said of all forms of energy; a heat engine can only act as a transformer, change heat into work, if there is a difference of temperature between its source and its sink; an electric motor can only work if there is a fall of potential between the entrance and the exit of the electric current. Energy presents itself to us as the product of two factors, weight and height in the waterfall, quantity and temperature in the heat engine, current intensity and potential in the electric motor. In considering these two factors we may note that one factor is always a quantity (Q) and the other an intensity (I). This latter expresses some sort of difference of position or condition, the height of the weight, a difference of temperature in the heat engine, of pressure in the gas engine, or of electric potential in the dynamo or electric furnace. There can be no current of energy without this difference of potential, and therefore no transformation from one form of energy to another. The second law of thermodynamics, Carnot's law, may therefore be enunciated thus: "Energy cannot be transformed without a fall of potential." We may also derive this principle from a consideration of the formula of efficiency, the ratio of the work done by the transformer to the work done on the transformer. Efficiency = energy transformed / total energy absorbed