The Point-atoms of Ruđer Josip Bošković: The Key to the Fields of Michael Faraday

For the coming New Year, one of the themes that I will focus on is the replacement of the very productive research program of Wilhelm Eduard Weber in the middle of the nineteenth century, including the co-invention of the telegraph with Karl Gauss, and the development of a full electrodynamical theory, complete with a planetary model of the atom, by the electrodynamics of James Clerk Maxwell. This story is very convoluted, and involves many actors, both in the UK and in Germany, including such names as Michael Faraday, William Thomson (later Lord Kelvin), Hermann Helmholtz and Heinrich Hertz.

Weber’s and Clerk Maxwell’s electrodynamics are based on completely different paradigms. All of Weber’s work assumed action-at-a-distance, and he can be considered to be the last of a chain of researchers working within this paradigm: Isaac Newton, Charles Augustin de Coulomb, André-Marie Ampère, and Wilhelm Eduard Weber. As for Clerk Maxwell, he mathematized the electrical and magnetic fields posited by Faraday. In this post, therefore, it is only fitting that I focus on one aspect: the metaphysical principles behind Faraday’s fields.

Ruđer Josip Bošković.

One of the recurring themes of modern science is how often there are attempts to make matter, space or time, or even all three, disappear, as if these were all illusions. We can see below, in the writings of Faraday, that he was not content with the idea of physical atoms interacting at a distance across a vacuum. Therefore, he went searching for a solution with the eighteenth-century Jesuit scholar from Ragusa (now Dubrovnik) Ruđer Josip Bošković (commonly known by the English name Roger Joseph Boscovich and the Italian name Ruggiero Giuseppe Boscovich), who attempted to synthesize a compromise between the bodies of Newton and the monads of Gottfried Leibniz, by introducing non-material extensionless point atoms that are simply centers of forces. Here is Faraday writing in 1844:

I am not ignorant that the mind is most powerfully drawn by the phenomena of crystallization, chemistry and physics generally, to the acknowledgement of centres of force. I feel myself constrained, for the present hypothetically, to admit them, and cannot do without them, but I feel great difficulty in the conception of atoms of matter which in solids, fluids and vapours are supposed to be more or less apart from each other, with intervening space not occupied by atoms, and perceive great contradictions in the conclusions which flow from such a view.

If we must assume at all, as indeed in a branch of knowledge like the present we can hardly help it, then the safest course appears to be to assume as little as possible, and in that respect the atoms of Boscovich appear to me to have a great advantage over the more usual notion. His atoms, if I understand aright, are mere centres of forces or powers, not particles of matter, in which the powers themselves reside. If, in the ordinary view of atoms, we call the particle of matter away from the powers a, and the system of powers or forces in and around it m, then in Boscovich's theory a disappears, or is a mere mathematical point, whilst in the usual notion it is a little unchangeable, impenetrable piece of matter, and m is an atmosphere of force grouped around it.

In many of the hypothetical uses made of atoms, as in crystallography, chemistry, magnetism, &c., this difference in the assumption makes little or no alteration in the results, but in other cases, as of electric conduction, the nature of light, the manner in which bodies combine to produce compounds, the effects of forces, as heat or electricity, upon matter, the difference will be very great. [pp.289-290, my emphasis]¹

Faraday was not just ill at ease with the physical atoms interacting across a vacuum of Newton, but also of the physical aether assumed by Cristiaan Huygens, Robert Young and Augustin-Jean Fresnel to explain the properties of light. For Faraday, the aether should be understood in a Boscovichian manner. Here is Faraday writing in 1846:

I suppose we may compare together the matter of the æther and ordinary matter (as, for instance, the copper of the wire through which the electricity is conducted), and consider them as alike in their essential constitution; i.e. either as both composed of little nuclei, considered in the abstract as matter, and of force or power associated with these nuclei, or else both consisting of mere centres of force, according to Boscovich's theory and the view put forth in my speculation; for there is no reason to assume that the nuclei are more requisite in the one case than in the other. It is true that the copper gravitates and the æther does not, and that therefore the copper is ponderable and the æther is not; but that cannot indicate the presence of nuclei in the copper more than in the æther, for of all the powers of matter gravitation is the one in which the force extends to the greatest possible distance from the supposed nucleus, being infinite in relation to the size of the latter, and reducing that nucleus to a mere centre of force. The smallest atom of matter on the earth acts directly on the smallest atom of matter in the sun, though they are 95,000,000 of miles apart; further, atoms which, to our knowledge, are at least nineteen times that distance, and indeed, in cometary masses, far more, are in a similar way tied together by the lines of force extending from and belonging to each. What is there in the condition of the particles of the supposed æther, if there be even only one such particle between us and the sun, that can in subtilty and extent compare to this?

Perhaps I am in error in thinking the idea generally formed of the æther is that its nuclei are almost infinitely small, and that such force as it has, namely its elasticity, is almost infinitely intense. But if such be the received notion, what then is left in the æther but force or centres of force? As gravitation and solidity do not belong to it, perhaps many may admit this conclusion; but what are gravitation and solidity? certainly not the weight and contact of the abstract nuclei. The one is the consequence of an attractive force, which can act at distances as great as the mind of man can estimate or conceive; and the other is the consequence of a repulsive force, which forbids for ever the contact or touch of any two nuclei; so that these powers or properties should not in any degree lead those persons who conceive of the æther as a thing consisting of force only, to think any otherwise of ponderable matter, except that it has more and other forces associated with it than the æther has. [pp.448-449, my emphasis]²

So what was Boscovich’s model? His major work was the Philosophiæ Naturalis Theoria (A Theory of Natural Philosophy³), first published in Vienna in 1758, then in Venice in 1763. Here is a summary from the Synopsis of the Whole Work:

From this [Art. 7] until Art. 11, I explain the Theory itself: that matter is unchangeable, and consists of points that are perfectly simple, indivisible, of no extent, & separated from one another; that each of these points has a property of inertia, & in addition a mutual active force depending on the distance in such a way that, if the distance is given, both the magnitude & the direction of this force are given; but if the distance is altered, so also is the force altered; & if the distance is diminished indefinitely, the force is repulsive, & in fact also increases indefinitely; whilst if the distance is increased, the force will be diminished, vanish, be changed to an attractive force that first of all increases, then decreases, vanishes, is again turned into a repulsive force, & so on many times over; until at greater distances it finally becomes an attractive force that decreases approximately in the inverse ratio of the squares of the distances. This connection between the forces & the distances, & their passing from positive to negative, or from repulsive to attractive, & conversely, I illustrate by the force with which the two ends of a spring strive to approach towards, or recede from, one another, according as they are pulled apart, or drawn together, by more than the natural amount. [p.17, my emphasis]

The nature of these point atoms is explained further at the beginning of Part I:

7. The primary elements of matter are in my opinion perfectly indivisible & non­ extended points; they are so scattered in an immense vacuum that every two of them are separated from one another by a definite interval; this interval can be indefinitely increased or diminished, but can never vanish altogether without compenetration of the points themselves; for I do not admit as possible any immediate contact between them. On the contrary I consider that it is a certainty that, if the distance between two points of matter should become absolutely nothing, then the very same indivisible point of space, according to the usual idea of it, must be occupied by both together, & we have true compenetration in every way. Therefore indeed I do not admit the idea of vacuum interspersed amongst matter, but I consider that matter is interspersed in a vacuum & floats in it. [pp.37,39, my emphasis]

So Faraday, as he developed his concepts of fields and lines of force, deliberately and consciously was working with a non-material metaphysics based on the work of Boscovich. The difference with Weber’s work is striking. We will see later that Boscovich greatly influenced numerous other researchers.

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1. Michael Faraday. A speculation touching Electric Conduction and the Nature of Matter. To Richard Taylor, Esq., Jan. 25, 1844. In Experimental Researches in Electricity, London: Richard and John Edward Taylor, vol.II, pp.284-293, 1844.

2. Michael Faraday. Thoughts on Ray-vibrations. To Richard Phillips, Esq., April 15, 1846. In Experimental Researches in Electricity, London: Richard Taylor and William Francis, vol.III, pp.447-452, 1855.

3. Roger Joseph Boscovich, A Theory Of Natural Philosophy. Latin-English Edition. From the text of the first Venetian edition published under the personal superintendence of the author in 1763. London: Open Court Publishing, 1922.