The Conservation of Energy

A polar division of attraction and repulsion is observed in the phenomena of static electricity and magnetism.

Whatever hypothesis may be adopted of the modus operandi of these two forms of motion, in view of the facts no one has any doubt that attraction and repulsion, in so far as they are produced by static electricity or magnetism and are able to develop unhindered, completely compensate one another, as in fact necessarily follows from the very nature of the polar division.

Two poles whose activities did not completely compensate each other would indeed not be poles, and also have so far not been discovered in nature.

For now, we will ignore Galvanism because it uses chemical reactions which makes it more complicated.

Instead, let us investigate the chemical processes of motion themselves.

Two parts by weight of hydrogen combine with 15.96 parts by weight of oxygen to form water vapour. It creates heat of 68,924 heat units.

Conversely, 17.96 parts by weight of water vapour are decomposed into 2 parts by weight of hydrogen and 15.96 parts by weight of oxygen by removing 68,924 heat units.

The same thing holds for all other chemical processes.

Thus:

• combination gives off motion
• decomposition needs motion

As a rule:

• repulsion is the active side, needing the addition of motion
• attraction is the passive side, producing a surplus of motion and giving off motion.

The modern theory declares that energy is:

• set free during the combination of elements
• bound up during decomposition.

Helmholtz declares:

Helmholtz insists that, in chemistry and mechanics, force consists only in attraction. Therefore force is:

• the exact opposite of energy
• identical with repulsion.

Hence we, no longer use the simple forms of attraction and repulsion. Instead, we use a whole series of sub-forms wherein universal motion goes through winding up and running down processes. These, in opposition to each other, manifest as attraction and repulsion.

These manifold forms of appearance are comprehended under the single expression of motion.

On the contrary, they themselves prove in action that they are forms of one and the same motion by passing into one another.

• mechanical motion of masses passes into heat, into electricity, into magnetism
• heat and electricity pass into chemical decomposition
• chemical combination in turn develops heat and electricity and, by means of the latter, magnetism
• heat and electricity produce once more mechanical movement of masses.

These changes take place in such a way that a given quantity of motion of one form always has an exactly fixed quantity of another form.

It is irrelevant which form the motion takes or is measured in, whether it is for measuring mass motion, heat, electromotive force, or the motion in chemical processes.

My basis is the theory of the “conservation of energy” established by J. R. Mayer [1] in 1842. This has led to fundamental concepts of “force”, “energy”, and “work”.

“Energy” is the word used for repulsion.

Helmholtz uses the word “force” to express attraction.

One could regard this as a mere distinction of form, inasmuch as attraction and repulsion compensate each other in the universe.

Accordingly, it would appear a matter of indifference which side of the relation is taken as positive and which as negative, just as it is of no importance in itself whether the positive abscissae are counted to the right or the left of a point in a given line. Nevertheless, this is not absolutely so.

We are not concerned here with the universe, but with phenomena on the earth and conditioned by:

• the earth’s position in the solar system, and
• the solar system in the universe.

At every moment, however, our solar system gives out enormous quantities of motion into space, and motion of a very definite quality, viz. the sun’s heat, i.e. repulsion.

But our earth itself allows of the existence of life on it only owing to the sun’s heat, and it in turn finally radiates into space the sun’s heat received, after it has converted a portion of this heat into other forms of motion.

Consequently, in the solar system and above all on the earth, attraction already considerably preponderates over repulsion. Without the repulsive motion radiated to us from the sun, all motion on the earth would cease.

If tomorrow the sun were to become cold, the attraction on the earth would still, other circumstances remaining the same, be what it is to-day.

As before, a stone of 100 kilogrammes, wherever situated, would weigh 100 kilogrammes. But the motion, both of masses and of molecules and atoms, would come to what we would regard as an absolute standstill. Therefore it is clear that for processes occurring on the earth to-day it is by no means a matter of indifference whether attraction or repulsion is conceived as the active side of motion, hence as “force” or “energy.”

On the contrary, on the earth to-day attraction has already become altogether passive owing to its decisive preponderance over repulsion; we owe all active motion to the supply of repulsion from the sun. Therefore, the modern school - even if it remains unclear about the nature of the relation constituting motion - nevertheless, in point of fact and for terrestrial processes, indeed for the whole solar system, is absolutely right in conceiving energy as repulsion.

The expression “energy” by no means correctly expresses all the relationships of motion, for it comprehends only one aspect, the action but not the reaction. It still makes it appear as if “energy” was something external to matter, something implanted in it. But in all circumstances it is to be preferred to the expression “force.”

As conceded on all hands (from Hegel to Helmholtz), the notion of force is derived from the activity of the human organism within its environment.

We speak of muscular force, of the lifting force of the arm, of the leaping power of the legs, of the digestive force of the stomach and intestinal canal, of the sensory force of the nerves, of the secretory force of the glands, etc. In other words, in order to save having to give the real cause of a change brought about by a function of our organism, we fabricate a fictitious cause, a so-called force corresponding to the change. Then we carry this convenient method over to the external world also, and so invent as many forces as there are diverse phenomena.

In Hegel’s time natural science (with the exception perhaps of heavenly and terrestrial mechanics) was still in this naive state, and Hegel quite correctly attacks the prevailing way of denoting forces (passage to be quoted).[2] Similarly in another passage:

“It is better (to say) that a magnet has a Soul (as Thales expresses it) than that it has an attracting force; force is a kind of property which is separable from matter and put forward as a predicate - while soul, on the other hand, is its movement, identical with the nature of matter.” (Geschichte der Philosophie [History of Philosophy], I, p. 208.)

To-day we no longer make it so easy for ourselves in regard to forces. Let us listen to Helmholtz:

“If we are fully acquainted with a natural law, we must also demand that it should operate without exception…. Thus the law confronts us as an objective power, and accordingly we term it a force. For instance, we objectivise the law of the refraction of light as a refractive power of transparent substances, the law of chemical affinities as a force of affinity of the various substances for one another. Thus we speak of the electrical force of contact of metals, of the force of adhesion, capillary force, and so on. These names objectivise laws which in the first place embrace only a limited series of natural processes, the conditions for which are still rather complicated…. Force is only the objectivised law of action…. The abstract idea of force introduced by us only makes the addition that we have not arbitrarily invented this law but that it is a compulsory law of phenomena. Hence our demand to understand the phenomena of nature, i.e. to find out their laws, takes on another form of expression, viz. that we have to seek out the forces which are the causes of the phenomena.” (lLoc. cit., pp. 189 - 191. Innsbruck lecture of 1869.)

Firstly, it is certainly a peculiar manner of “objectivising” if the purely subjective notion of force is introduced into a natural law that has already been established as independent of our subjectivity and therefore completely objective.

At most an Old-Hegelian of the strictest type might permit himself such a thing, but not a Neo-Kantian like Helmholtz. Neither the law, when once established, nor its objectivity, nor that of its action, acquires the slightest new objectivity by our interpolating a force into it; what is added is our subjective assertion that it acts in virtue of some so far entirely unknown force. The secret meaning, however, of this interpolating is seen as soon as Helmholtz gives us examples: refraction of light, chemical affinity, contact electricity, adhesion, capillarity, and confers on the laws that govern these phenomena the “objective” honorary rank of forces.

“These names objectivise laws which in the first place embrace only a limited series of natural processes, the conditions for which are still rather complicated.”

And it is just here that the “objectivising,” which is rather subjectivising, gets its meaning; not because we have become fully acquainted with the law, but just because this is not the case. Just because we are not yet clear about the “rather complicated conditions” of these phenomena, we often resort here to the word force. We express thereby not our scientific knowledge, but our lack of scientific knowledge of the nature of the law and its mode of action.

In this sense, as a short expression for a causal connection that has not yet been explained, as a makeshift expression, it may pass for current usage.

Anything more than that is bad. With just as much right as Helmholtz explains physical phenomena from so-called refractive force, electrical force of contact, etc., the medieval scholastics explained temperature changes by means of a vis calorifica and a vis frigifaciens and thus saved themselves all further investigation of heat phenomena.

And even in this sense it is one-sided, for it expresses everything in a one-sided manner. All natural processes are two-sided, they rest on the relation of at least two effective parts, action and reaction. The notion of force, however, owing to its origin from the action of the human organism on the external world, and further because of terrestrial mechanics, implies that only one part is active, effective, the other part being passive, receptive; hence it lays down a not yet demonstrable extension of the difference between the sexes to non-living objects. The reaction of the second part, on which the force works, appears at most as a passive reaction, as a resistance. This mode of conception is permissible in a number of fields even outside pure mechanics, namely where it is a matter of the simple transference of motion and its quantitative calculation. But already in the more complicated physical processes it is no longer adequate, as Helmholtz’s own examples prove. The refractive force lies just as much in the light itself as in the transparent bodies. In the case of adhesion and capillarity, it is certain that the “force” is just as much situated in the surface of the solid as in the liquid. In contact electricity, at any rate, it is certain that both metals contribute to it, and “chemical affinity” also is situated, if anywhere, in both the parts entering into combination. But a force which consists of separated forces, an action which does not evoke its reaction, but which exists solely by itself, is no force in the sense of terrestrial mechanics, the only science in which one really knows what is meant by a force. For the basic conditions of terrestrial mechanics are, firstly, refusal to investigate the causes of the impulse, i.e. the nature of the particular force, and, secondly, the view of the one-sidedness of the force, it being everywhere opposed by au identical gravitational force, such that in comparison with any terrestrial distance of fall the earth’s radius = (infinity).

But let us see further how Helmholtz, “objectivises” his “forces” into natural laws.

In a lecture of 1854 (loc. cit.., p. 119) he examines the “store of working force” originally contained in the nebular sphere from which our solar system was formed. “In point of fact it received an enormously large legacy in this respect, if only in the form of the general force of attraction of all its parts for one another.” This indubitably is so. But it is equally indubitable that the whole of this legacy of gravitation is present undiminished in the solar system to-day, apart perhaps from the minute quantity that was lost together with the matter ’ We should now call this potential energy. which was flung out, possibly irrevocably, into space. Further, “The chemical forces too must have been already present and ready to act; but as these forces could become effective only on intimate contact of the various kinds of masses, condensation had to take place before they came into play.” If, as Hclmholtz does above, we regard these chemical forces as forces of affinity, hence as attraction, then again we are bound to say that the sum-total of these chemical forces of attraction still exists undiminished within the solar system.

But on the same page Helmholtz gives us the results of his calculations “that perhaps only the 454th part of the original mechanical force exists as such” - that is to say, in the solar system. How is one to make sense of that? The force of attraction, general as well as chemical, is still present unimpaired in the solar system. Helmholtz does not mention any other certain source of force. In any case, according to Helmholtz, these forces have performed tremendous work. But they have neither increased nor diminished on that account. As it is with the clock weight mentioned above, so it is with every molecule in the solar system and with the solar system itself. “Its gravitation is neither lost nor diminished.” What happens to carbon and oxygen as previously mentioned holds good for all chemical elements: the total given quantity of each one remains, and “the total force of affinity continues to exist just as powerfully as before.” What have we lost then? And what “force” has performed the tremendous work which is 453 times as big as that which, according to his calculation, the solar system is still able to perform? Up to this point Helmholtz has given no answer. But further on he says:

“Whether a further reserve of force in the shape of heat was present, we do not know.” - But, if we may be allowed to mention it, heat is a repulsive “force,” it acts therefore against the direction of both gravitation and chemical attraction, being minus if these are put as plus. Hence if, according to Helmholtz, the original store of force is composed of general and chemical attraction, an extra reserve of heat would have to be, not added to that reserve of force, but subtracted from it. Otherwise the sun’s heat would have had to strengthen the force of attraction of the earth when it causes water to evaporate in direct opposition to this attraction, and the water vapour to rise; or the heat of an incandescent iron tube through which steam is passed would strengthen the chemical attraction of oxygen and water, whereas it puts it out of action. Or, to make the same thing clear in another form: let us assume that the nebular sphere with radius r, and therefore with volume 4/3(pi)r³ has a temperature t. Let us further assume a second nebular sphere of equal mass having at the higher temperature T the larger radius R and volume 4/3(pi)R³. Now it is obvious that in the second nebular sphere the attraction, mechanical as well as physical and chemical, can act with the same force as in the first only when it has shrunk from radius R to radius r, i.e. when it has radiated into world space heat corresponding to the temperature difference T - t. A hotter nebular sphere will therefore condense later than a colder one; consequently the heat, considered from Helmholtz’s standpoint as an obstacle to condensation, is no plus but a minus of the “reserve of force.” Helmholtz, by pre-supposing the possibility of a quantum of repulsive motion in the form of heat becoming added to the attractive forms of motion and increasing the total of these latter, commits a definite error of calculation.

Let us now bring the whole of this “reserve of force”, possible as well as demonstrable, under the same mathematical sign so that an addition is possible. Since for the time being we cannot reverse the heat and replace its repulsion by the equivalent attraction, we shall have to perform this reversal with the two forms of attraction. Then, instead of the general force of attraction, instead of the chemical affinity, and instead of the heat, which moreover possibly already exists as such at the outset, we have simply to put - the sum of the repulsive motion or so-called energy present in the gaseous sphere at the moment when it becomes independent. And by so doing Helmholtz’s calculation will also hold, in which he wants to calculate “the heating that must arise from the assumed initial condensation of the heavenly bodies of our system from nebulously scattered matter.” By thus reducing the whole “reserve of force” to heat, repulsion, he also makes it possible to add on the assumed “heat reserve force”. The calculation then asserts that 453/454 of all the energy, i.e. repulsion, originally present in the gaseous sphere has been radiated into space in the form of heat, or, to put it accurately, that the sum of all attraction in the present solar system is to the sum of all repulsion, still present in the same, as 453: 1. But then it directly contradicts the text of the lecture to which it is added as proof.

If then the notion of force, even in the case of a physicist like Helmholtz, gives rise to such confusion of ideas, this is the best proof that it is in general not susceptible of scientific use in all branches of investigation which go beyond the calculations of mechanics. In mechanics the causes of motion are taken as given and their origin is disregarded, only their effects being taken into account. Hence if a cause of motion is termed a force, this does no damage to mechanics as such; but it becomes the custom to transfer this term also to physics, chemistry, and biology, and then confusion is inevitable. We have already seen this and shall frequently see it again.