Applying the methodology: assumptions and their consequences

To get a good grasp of Maxwell’s methodology in 1861, it may be beneficial to analyze at length the assumptions Maxwell made and the results he obtained as he set them down in concluding Part 11 of the paper. We focus principally on issues relevant to methodology and consistency, and we follow Maxwell’s summary point by point. We begin with point (1):

(1) Magneto-electric phenomena are due to the existence of matter under certain conditions of motion or of pressure in every part of the magnetic field, and not to direct action at a distance between the magnets or currents. The substance producing these effects may be a certain part of ordinary matter, or it may be an aether associated with matter.47

Maxwell began by asserting that electromagnetic phenomena are not “due to” action at a distance. In contrast to Maxwell’s view in Station 1, action at a distance is no longer considered equivalent to lines of force: “due to” is the language of causation, not the terminology of analogy. Maxwell’s confidence in the unifying concept of lines of force had grown substantially. But, interestingly, here he associated the lines with matter, be it ordinary or aetherial. This belief, that matter is the carrier of electromagnetic phenomena, is not even considered in Station 1. Clearly, at the outset of this summary Maxwell is unequivocal in seeking a physical account of the phenomena.

Concepts are neither right nor wrong (neither true nor false); they are to be judged by their usefulness in some context. It follows that the concept of action at a distance is either helpful or not in accounting for electromagnetic phenomena. We note that Maxwell asserted that action at a distance has no physical reality; by contrast, lines of force are physical.

What is the ontological status of the molecular vortices whose interactions represent these lines of force? Maxwell is unambiguous: lines of force are physical. For Maxwell, the explanandum is “lines of force,” while the explanans is “molecular vortices.” Maxwell was willing to consider alternatives to these vortices, but not to the lines of force—the object of his inquiry.

(2) The condition of any part of the field, through which lines of magnetic force pass, is one of unequal pressure in different directions, the direction of the lines of force being that of least pressure, so that the lines of force may be considered lines of tension.48

The lines of force are in fact lines of tension; this makes them physical.

(3) This inequality of pressure is produced by the existence in the medium of vortices or eddies, having their axes in the direction of the lines of force, and having their direction of rotation determined by that of the lines of force.

The expression “produced by the existence” is physical talk: Maxwell did not hesitate to assert that vortices exist in the medium. The remaining issue, as far as Maxwell is concerned, is the size of the vortices: “it is probably very small as compared with that of a complete molecule of ordinary matter.”49 This claim makes no sense if the vortices are not real. That is, the claim regarding size presupposes that the vortices are real.

(4) The vortices are separated from each other by a single layer of round particles, so that a system of cells is formed, the partitions being these layers of particles, and the substance of each cell being capable of rotating as vortex.50

In this passage Maxwell referred to substance: the rotating vortex is material and has a clearly defined boundary to form a distinct rotating cell. In sum, we have here a physical system that obeys the laws of mechanics.

In (5) Maxwell began by describing the motion of the particles which form the layer that separates the vortices from each other (see point (4)). The irregular motions of the particles result in heat, and in effect “these particles ... play the part of electricity.”51 According to this hypothesis the motion of translation constitutes an electric current, and the tangential pressures created by the irregular motion of the particles, constitutes electromotive force. Clearly, Maxwell’s analysis is physical, not formal.

Maxwell confessed that the analysis is “awkward”:

The conception of a particle having its motion connected with that of a vortex by perfect rolling contact may appear somewhat awkward. 1 do not bring it forward as a mode of connexion existing in nature, or even as that which 1 would willingly assent to as an electrical hypothesis. It is, however, a mode of connexion which is mechanically conceivable, and easily investigated, and it serves to bring out the actual mechanical connexions between the known electromagnetic phenomena; so that I venture to say that any one who understands the provisional and temporary character of this hypothesis, will find himself rather helped than hindered by it in his search after the true interpretation of the phenomena?2

This is a revealing passage. Maxwell began on a negative note, namely, he stated that he did not claim that this “mode of connexion” exists in nature; indeed, he did not even propose it as “an electrical hypothesis.” The hypothesis of molecular vortices was intended to do more epistemic work than just serve as an illustration; it was supposed to give an idea of the way the phenomena might be produced in nature—it was clearly explanatory, not illustrative. But Maxwell never meant to suggest that this is the true description of the phenomena. He considered the scheme of molecular vortices a “provisional” hypothesis that succeeded in many ways in accounting for the phenomena. But Maxwell had an epistemic problem here: he embarked on a search for an explanation, something which he had not done in Station 1. He now stated that the goal was to find “the true interpretation” of the phenomena, assuming it would be mechanical. Maxwell insisted on the provisional status of the hypothesis he put forward; nevertheless, in his view it is likely to help in the search for the true interpretation.

Point (6) elaborates on the mechanical relation between electric current and the vortices: the discussion offers a physical account of electromotive forces based on this mechanical relation. In the remaining two points another physical account is offered, namely, the results of relative motions. In points (7) and (8) Maxwell drew consequences regarding the forces which arise from the relative motions of electromagnetic elements, be they rotational or translational.53

Overall, the concluding pages of Part 11 of the paper on physical lines of force is a tour de force where Maxwell took advantage of a mechanical illustration to draw consequences for electromagnetic phenomena. It is noteworthy that, when Maxwell recapitulated the assumptions he had made and the results he had obtained, he offered verbal descriptions rather than algebraic equations.

In Part 1 and Part II of Station 2 Maxwell displayed a consistent approach which he distinguished from the methodology he had applied in Station 1. There he took a formal-analogical approach while here, in Station 2, as the title of the paper indicates, he took a physical approach, proposing a hypothesis based on a mechanical illustration.54

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