_Energy._—Work thus understood is _mechanical energy_. It represents the lasting and objective effect of the mechanical activity independent of all the circumstances under which it was carried out. The same work may be done under very different conditions of time, velocity, force, and displacement. It is therefore the permanent element in the variety of mechanical aspects. Work, for example, in the collision of bodies when the motion of a body appears to be destroyed on impact with another, reappears as indestructible _vis viva_. This, then, is exactly what we call _energy_; and if we agree to give it this name, we may say that the conservation of energy is invariable throughout all mechanical transformations. _Distinction between Work and Force, and between Energy and Work._—The history of mechanics shows us what trouble has been taken and what efforts have been made to distinguish work (now mechanical energy) from force. It is worth while insisting on this distinction. It could be easily shown that force has no objective existence. It has no duration, no permanence. It does not survive its effect, motion. There is no conservation of force. It passes instantly from infinity to zero. It is a _vectorial magnitude_—that is to say, it involves the idea of direction. Work, on the other hand, is the real element; it is a _scalar magnitude_ involving the idea of opposite directions, indicated by the signs + and-. Work and force are heterogeneous magnitudes. Energy, and this is the only characteristic by which it is distinguished from work, is an _absolute magnitude_ to which we may not even give opposite signs. An example may perhaps throw these characteristics into relief—namely, the hydraulic press. We have on the platform exactly the work which has been done on the other side. The machine has only made it change its form. On the contrary, the force has been infinitely multiplied. We may, in fact, consider an infinite number of surfaces equal to that of a small piston, placed and orientated at will within the liquid; each, according to Pascal’s principle, will support a pressure equal to that which is exercised. As soon as we cease to support it, this infinity falls at once to zero. Now what real thing could pass instantly from infinity to zero?