Optimal thought and optimal fitness through reason, logic, science, passion, and wisdom.
The Origin of the Concept of “Potential Energy” 2
The Origin of the Concept of “Potential Energy” 2

The Origin of the Concept of “Potential Energy” 2

In “On the general law of the transformation of energy” (The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Series 4, Volume 5, 1853 – Issue 30), William John Macquorn Rankine (C.E., F.R.S.E., F.R.S.S.A.) introduced the term “potential energy” into science in 1853:

In this investigation the term energy is used to comprehend every affection of substances which constitutes or is commensurable with a power of producing change in opposition to resistance, and includes ordinary motion and mechanical power, chemical action, heat, light, electricity, magnetism, and all other powers, known or unknown, which are convertible or commensurable with these. All conceivable forms of energy may be distinguished into two kinds; actual or sensible, and potential or latent.

Actual energy is a measurable, transferable, and transformable affection of a substance, the presence of which causes the substance to tend to change its state in one or more respects; by the occurrence of which changes, actual energy disappears, and is replaced by.

Potential energy, which is measured by the amount of a change in the condition of a substance, and that of the tendency or force whereby that change is produced (or, what is the same thing, of the resistance overcome in producing it), taken jointly.

If the change whereby potential energy has been developed be exactly reversed, then as the potential energy disappears, the actual energy which had previously disappeared is reproduced.

The law of the conservation of energy is already known, viz. that the sum of the actual and potential energies in the universe
1s unchangeable.

The object of the present investigation is to find the law of the transformation of energy, according to which all transformations of energy between the actual and potential states take place.


Interesting that, in his “On the Origin of Force” (1865), John Herschel was opposed to the term “potential energy:”

It will perhaps be objected to this, that the principle so generally cited, and now so universally recognized as a dominant one in physics — that of the “conservation of force” – stands opposed to any, even the smallest amount of arbitrary change in the total of “force” existing in the universe. This principle, so far as it rests upon any scientific basis as a legitimate conclusion from dynamical laws, is no other than the well-known dynamical theorem of the conservation of vis viva (or of “energy” as some prefer to call it)[5] supplemented to save the truth of its verbal enunciation, by the introduction of what is called “potential energy” [Rankine, 1853], a phrase which I cannot help regarding as unfortunate, inasmuch as it goes to substitute a truism for the announcement of a great dynamical fact.

No such conservation, in the sense of an identity of total amount of vis viva at all times, and in all circumstances, in fact, exists. So far as a system is maintained by the mutual actions and reactions of its constituent elements at a distance (i.e., by force), vis viva may temporarily disappear, and be subsequently reproduced between certain limits. Collision, indeed, between its ultimate atoms, regarded as absolutely rigid, and therefore inelastic (for that which cannot change its figure can have no resilience), cannot take place without producing a permanent destruction of it, which there exists no means of repairing. And here we may remark that, this being the case, to ascribe to such atoms any magnitude becomes not only superfluous, but embarrassing. The system of Boscovich has to be accepted in its integrity, if absolute permanence is to be one of the conditions insisted on; and they come to be considered as mere localizations of inertia and such other attributes, including the centralization of force – if any other than this there be – which belong to our notion of material substance. The conservation of energy, then, is in effect no conservation at all in any strict sense of the term, unless so supplemented.[6]

It is a fact dynamically demonstrable that the total amount of vis viva in any moving system abandoned to the mutual reaction of its particles, while depending at every instant of time, solely for its magnitude, on the then relative situation of those particles (or being, in algebraical phrase, a function of their mutual distances), has a maximum value which it cannot exceed, and a minimum below which it cannot descend. Let its state then be what it will, there is sure to be a certain amount of vis viva by which its actual falls short of its extreme possible value; and to say that the amount of this deficiency added to the actual present amount will make up the maximum, is neither more nor less than a truism: whether expressed in so many words, or by saying that the potential together with the actual energy of the system is invariable; or, again, in other words, that when certain changes have taken place in the relative situations of the parts of the system, what it has lost in actual it has gained in potential energy.

When in speaking of a mechanical combination we say that what is lost in time is gained in power, though equally a translation in ordinary language of a dynamical equation, the terms used refer to different modes of viewing the expenditure of force. But in the case before us they stand in their nakedness of similar meaning and convey to the mind no equivalence available for any purpose of reasoning. If, indeed, we could be assured, a priori, that the system is one of simple or compound periodicity in which a certain lapse of time will restore every molecule to identically the same relative situation with respect to all the rest; we should then be sure that in the nature of things there would take place periodically, so to speak, a winding up from a lower to a higher state of potential energy, to be subsequently exchanged for newly-created vis viva. But as we can have no such a priori assurance, can only assume such restoration to be possible, and can see no means of effecting it, if possible, otherwise than by foresight and prearrangement; the one equally with the other is an unknown function, variable within unknown limits, and susceptible of fluctuations to an unknown extent, nor can we have any, the smallest, right to assert that what is expended in the one form is, necessarily, laid up in reserve for further use in the other. It would be very difficult, I apprehend, to show whether in the winding up of a clock, or the building of a pyramid, taking into consideration all the various modes in which vis viva disappears and reappears in the expenditure of muscular power, the evolution of animal heat, the consumption of the materials of our tissues (laying aside all question as to the evolution of force from intellectual effort), the propagation of vibratory motion, and a thousand other modes of transfer; the total vis viva of this our planet is increased or diminished. That it should remain absolutely unchanged during the process is in the last degree inconceivable. The amount of vis viva latent in the form of heat or molecular motion in the sun and planets in our immediate system may bear, and probably does bear, a by no means inappretiable ratio to that more distinctly patent in the form of bodily motion in the periodical circulation of the planets round the sun, and the sun and planets round their axes. The latter amount fluctuates to and fro according to laws easily calculable; but the former we have no means whatever of computing, and to what extent, or within what limits, it may be variable, we are altogether ignorant.


It is unfortunate that Herschel was corrupted by a bad epistemology (ibid):

What is it that we ought to understand by the theory of any natural phenomenon! This is a question not without its importance when we are told, as we so frequently are, that it is useless to inquire into causes: that, in fact, causes are to us as though they were not; seeing that all we can ever attain to is the observation and registry of constant laws of phenomenal sequence in other words, that phenomenon succeeds phenomenon, event event, according to certain rules, which are all we have any business to inquire into.


Leave a Reply

Your email address will not be published. Required fields are marked *