We cannot yet actually measure chemical activity directly, but we know that chemical action may give rise to all other phenomenal modalities. It is their most ordinary source, and it is to it that industries appeal to obtain heat, electricity, and mechanical action. In the steam engine, for instance, the work that is received arises from the combustion of carbon by the oxygen of the air. This gives rise to the heat which vaporizes the water, produces the tension of the steam, and ultimately produces the displacement of the piston. The theory of the steam engine might be reduced to these two propositions: chemical activity gives rise to heat, and heat gives rise to motion; or to use the language to which the reader by now will be accustomed, chemical energy is transformed into thermal energy, and that into mechanical energy. It is a series of phases and of instantaneous changes, and the exchange is always affected according to a fixed rate. _The Measurement of Chemical Energy._—Our knowledge of chemical energy is less advanced than that of the energies of heat and sensible motion. We have not yet reached the stage of numerical verifications. We can only therefore affirm the equivalence of chemical and thermal energies without the aid of numerical constants, because we do not yet, in the present state of science, know how to measure chemical energy directly. Other known energies are always the product of two factors: the mechanical energy of position, or work, is measured by the product of the force _f_, and the displacement _s_; work = _fs_; the mechanical energy of motion, U = 1∕2_mv^2_, is measured by the product of the mass into half the square of the velocity. Thermal energy is measured by the product of the temperature and the specific heat; electric energy by the product of the quantity of electricity (in coulombs) and of the electromotive force (in volts). As for chemical energy, we guess that it may be valued directly according to Berthollet’s system, adopted by the Norwegian chemists, Guldberg and Waage, by means of the product of the masses and of a force, or co-efficient of affinity, which depends on the nature of the substances which are brought together, on the temperature, and on the other physical circumstances of the reaction. On the other hand, the researches of M. Berthelot enable us in many cases to obtain an indirect valuation in terms of the equivalent heat.