Among other examples, that of the coiled spring which is unwound is particularly suitable for showing this fundamental character of the idea of mechanical energy, an idea which is the clearest of all. Machines are only transformers and not creators of mechanical energy. They only change one form into another. In the same way, too, a stream of water or the torrent of a mountainous region may be utilized for setting in motion the wheels and the turbines of the factories situated in the valley. Its descent produces the mechanical work which would be a creation _ex nihilo_ if we do not connect the phenomenon with its antecedents. We look on it as a simple restitution, if we think of the origin of this water which has been transported and lifted in some way to its level by the play of natural forces—evaporation under the action of the sun, the formation of clouds, transport by winds, etc. And we here again see that a complex energy has been transformed, in its first phenomenal condition, into _potential energy_, and that this potential energy is always expended in the second phase without loss or gain. _The Different Kinds of Mechanical Energy; of Motion, of Position._—There are as many forms of energy as there are distinct categories of phenomena or of varieties in these categories. Physicists distinguish between two kinds of mechanical energy—energy of motion and energy of position. The energy of position presents several variants—energy of distance, which corresponds to force: of this we have just spoken; energy of surface, which corresponds to particular phenomena of surface tension; and energy of volume which corresponds to the phenomena of pressure. Energy of motion, _kinetic energy_, is measured in two ways: as work (the product of force and displacement, W = _fs_) or as _vis viva_ (half the product of the mass into the square of the velocity U = _mv^2_∕2.)[9] [9] We therefore notice that the measures of force and work bring in mass, space, and time. The typical force, weight, is given by w = mg. On the other hand, we have by the laws of falling bodies _v_ = _gt_; _s_ = 1∕2_gt^2_; whence _g_ = 2_s_∕_t^2_; _w_ = _m_(2_s_∕_t^2_); or, if F be the force, M the mass, L the space described, and T the time, we have F = MLT^{-2}, which expresses what are called the dimensions of the force—that is to say, the magnitudes with their degree, which enter into its expression. We may thus easily obtain the dimensions of work:— _Work_ = _f_ × _s_ = _mv^2_∕2 = ML^2T^{-2}. § 4. THERMAL ENERGY.