ELECTROLOGY. - Under this denomination is understood the systematic and, as far as possible, logical development of the science of electricity, independently of its great applications, which are reserved to electrotechnics. The division and the order of such a development evidently leaves a certain margin of arbitrariness. Before the discovery of voltaic electric currents, there were to be considered only the phenomena of the production and distribution of electricity under predominantly static conditions, and of the fields that such distributions produced. This is still the task of electrostatics, which in general is placed before the consideration of the other parts of electrology, that is, before the study of electric currents and of the complex phenomena by which they are produced and which they in turn produce.
It is not without interest to recall that at the end of the 19th century and in the first decades of the present century there arose a certain tendency to begin electrology outright with the study of electric currents, taken as the principal fundamental phenomenon, and then to consider electrostatics as a particular chapter of it. But, perhaps also as a consequence of certain views of modern physics, in which the consideration of the atom of pure electricity, that is, of the electron and its Coulomb field, is fundamental, the aforementioned tendency met with only partial success, for example, with the widely circulated treatise of R. W. Pohl.
I. ELECTROSTATICS
This branch of e. is essentially based (v. ELECTRICITY): 1) on the fact, confirmed by experience, of the existence of two kinds of electricity and of their well-known properties of attraction or repulsion quantitatively governed by Coulomb's law; 2) on the fact, likewise confirmed by experience, of the existence of insulating and conducting bodies; 3) on the hypothesis that in material bodies the two aforementioned kinds of electricity are in general contained in equal enormous quantities which, though subsisting distinctly in them, mutually cancel their external effects so that the aforementioned bodies turn out to be neutral to external observers; 4) on the hypothesis that in conducting bodies at least one of these two kinds of electricity moves under the influence of any electric field, however feeble.
An immediate consequence of the attraction of charges, however distributed, of electricity of different kinds and of the repulsion of analogous charges of electricity of the same kind is the very important phenomenon of electrification by influence or by induction, discovered around the middle of the 18th century. Let us consider its simplest case. Any conducting body, supported by a thread or by an insulating handle, is electrified by bringing electricity onto it. Owing to the repulsion exerted among all its parts, all this electricity moves to the surface of the body itself. Bringing this near another similarly insulated conductor in the neutral state, one observes that a part of its internal electricity of a kind contrary to that of the first body, which we shall call the inductor, moves to the part of its surface nearest to this one, while on the part of its surface farthest away an equal quantity of electricity of the same kind as that of the inductor accumulates. It is evident that if this latter part of the electricity is eliminated (e.g., by dispersing it to earth through our body by touching with a finger the surface where it is located), one will come into possession of a quantity of electricity of a kind contrary to that of the inductor body, transferable, at least in part, at will onto any other insulated conductor; and by repeating the operation, one will evidently be able to accumulate on suitably arranged conductors (on condensers) even considerable quantities of such electricity.
The machines for the production of static electricity all work on the basis of more or less systematic applications of the criterion just set forth and of a few other secondary expedients.
In the development of the theory of electric fields, electrostatics introduced and elaborated the very important notion of electric potential, coinciding with the one that Volta had ingeniously intuited and called electric tension. An electric charge in an electric field is always subjected to a force of a certain intensity, direction and sense; therefore an electric charge moving under the action of this force can perform work, whereas to force it to move in the opposite sense we would have to perform an analogous work. On the basis of this consideration we shall say that between two points P₁ and P₂ of an electric field there exists the potential difference V₁ - V₂ when a unit positive electric charge, moving from P₁ to P₂, can perform the work V₁ - V₂, or when to move an equal charge from P₂ to P₁ it is necessary to supply it with the same quantity of work; or again when, moving in an equal manner, a unit negative charge, the aforementioned productions or supplies of work are inverted. Since experience assures us that what precedes depends only on the extreme points P₁ and P₂ and is independent of the path followed by the charges, we can consider V₁ - V₂ the difference of potential energy between the points P₁ and P₂ of the system constituted by the electric charges determining the field, plus the aforementioned unit electric mass.
From what precedes it follows that potential is a quantity that we cannot define absolutely, but only by difference with respect to other analogous quantities, e.g., with respect to the potential V₃ of the earth. Let us add that, for the simple purpose of approximate clarification, it is often customary to say that the notion of electric potential stands to that of electricity as the notion of temperature stands to that of heat.
II. THE ELECTRIC CURRENT AND ITS LAWS
If we place two insulated conductors charged with electricity and at different potentials in communication by means of even a very thin metallic wire, a uniform potential is immediately established throughout the entire system. In this case it is logical to suppose that in the wire there has been a flow of positive electricity in one direction or possibly of negative electricity in the other, or even simultaneously both flows, that is, what is briefly called an electric current; but an instantaneous electric current. Even by applying to the two conductors the electrical machines that had previously electrified them and brought them to their respective potentials, it is no longer possible to bring them back to those potentials and therefore to maintain permanently an appreciable current in the wire.
This is what, on the other hand, a voltaic pile does with the greatest ease, while establishing a difference of potential incomparably smaller than the preceding ones. As is well known, A. Volta, following long discussions concerning a phenomenon of an electrical nature brought to light by L. Galvani, who interpreted it through hypothetical electrical properties of living matter, succeeded in constructing a so-called chain, that is, a series of bodies in successive contacts, forming a closed circuit, in which conditions analogous to those of the chains that automatically came to be constituted in Galvani's experiments occurred. But while Galvani's chains always consisted, besides certain metallic elements, of an element that was held to be essential, consisting of living matter (the posterior part of the body of a freshly killed frog), Volta's chains consisted, besides the metallic elements, of an electrolyte (acidulated water) without any recourse to living matter. The closed chain, copper-electrolyte-zinc-copper, presented the impressive characteristic of possessing a permanent difference of potential between the copper and the zinc, which consequently implied the existence of an electric current circulating in the chain. Thus the first electric pile was discovered (1790).
In a short time numerous other types of piles were devised, which made it possible to have electric currents more intense than those that the primitive voltaic piles could supply, and thus the problem arose of measuring and studying these currents in their effects. But the most fundamental laws of currents were not arrived at until new and surprising discoveries of their effects made it possible to perfect considerably the means of research. In the first three decades of the 19th century the concepts of specific electrical resistance and of the electrical resistance of a given conductor, and of electromotive force, were clarified, and thus the very well-known laws of Ohm and Joule were arrived at, fundamental for currents in whatever form they present themselves.
III. MAGNETISM
Knowledge of the existence of the most evident among the phenomena we call magnetic goes back to the remotest antiquity; it is also certain that in the Far East uses of them for orientational purposes were made on the great magnet constituted by our earth more than ten centuries B.C. The first systematic studies in Europe were those of G. Gilbert (1600). Until that time, and still for more than two centuries thereafter, magnetism was interpreted with the hypothesis of the existence of two magnetic matters or fluids which in magnetized bodies gathered around the so-called poles; that is, with a mechanistic hypothesis of matters acting at a distance, which, especially after Coulomb's discovery of his well-known analogy with that valid for material masses and for electric ones, seemed to be as much as physics could desire.
But here it is of particular interest to recall that, at least after Gilbert, albeit in an indeterminate form, relations between magnetism and electricity were repeatedly foreseen in order to interpret some phenomenon that occurred in some discharge of electrical machines and in some fall of lightning, so much so that the Academy of Bavaria had already in 1774 (that is, even before the discovery of Coulomb's law) set as a prize competition the study of the analogies between electric forces and magnetic forces. But ideas on the subject began to become clear only after H. C. Oersted's discovery that magnetic needles are deflected by electric currents; a discovery which, refined by Biot and Savart and interpreted by Arago and above all by A. M. Ampère, not only determined the beginning of the vastest and most useful chapter of e., but raised the first and perhaps the gravest doubts concerning the reliability of mechanistic hypotheses in physical interpretations, precisely in the period when those hypotheses had reached the widest consensus and precisely in a chapter that seemed to owe its existence to them. But it is precisely from the adoption of laws incompatible with the mechanistic hypothesis that the most interesting developments of modern physics had their origin.
IV. ELECTROMAGNETISM
The deflecting force of every electric current on the poles of a magnetic needle, discovered by Oersted and by him obscurely interpreted as a conflict between electrical and magnetic tendencies, was immediately formulated quantitatively, still in the sense of actions at a distance, by Biot and Savart and interpreted by Arago as due to a magnetic field wrapped around the current; an interpretation that was also confirmed by means of a very well-known and simple experiment. On the basis of it, various types of apparatus were constructed (which were ultimately the first electromagnetic motors) which demonstrated that every magnetic pole tends to rotate around every rectilinear current in a plane normal to it and in a direction and sense depending on the nature of the pole and on the direction of the current; just as, in accordance with the third principle of Newtonian dynamics, apparatuses were constructed in which rectilinear conductors carrying a current tended to rotate around magnetic poles.
But what impressed most was the fact that the forces acting between a magnetic pole and rectilinear electric currents, contrary to every mechanistic prediction, were not directed along the pole-current direction, but perpendicularly to the plane passing through the current and the pole. This was not comprehensible without supposing a particular intervention of the intervening medium. And it was probably to obviate this difficulty, in addition to the older one of interpreting actions at a distance, that H. Faraday arrived at his conception of lines of force in the medium, and then at the admission of an ever more important intervention of it in the unfolding of electric and magnetic phenomena.
Another surprising fact was that in the expression of Biot and Savart for the force with which a pole is solicited in the aforesaid direction depending on its intensity, on the intensity of the current and on their distance, the factor of proportionality, introduced a priori, turns out, by the necessary homogeneity of the equation, to have the dimensions and therefore the nature of a velocity; and that by employing any coherent system of units of measurement of the said quantities and performing an experiment, that velocity can be determined and turns out to be equal to the velocity c of light expressed naturally in that same system. This was the first approximation, at that time very mysterious, of an optical quantity to electrical and magnetic quantities.
As a brief complement to these fundamental remarks, it should be recalled that Ampère immediately surmised that actions analogous to the preceding ones must also occur between circuits carrying currents, and therefore discovered electrodynamic phenomena; that Faraday, aided by his lines of force, surmised the analogous existence of the phenomena of electromagnetic induction, by which, as the current of a circuit varies and therefore the quantity of the lines of force linked with it, various important repercussions must occur on other circuits (mutual inductions) and also on the inducing circuit itself (self-induction). These are the phenomena that on an enormous scale are employed today for the production of all direct and alternating currents, for all their transformations and in all electric motors; the phenomena that on a more modest scale led to the theoretical prediction and the production of electromagnetic waves and to their ever more numerous and surprising applications.
V. ELECTROMAGNETIC WAVES
Confirming Faraday's ideas concerning the participation in the unfolding of electromagnetic phenomena of the media in which are immersed the material bodies that until then had been their only seat, J. C. Maxwell set out to construct the general expression of the elementary law of the unfolding of those phenomena in any spatial element occupied by conducting or insulating matter, or even by void, and in any element of time. This was the broadest scientific synthesis that had ever been attempted. Maxwell, besides in some earlier publication, set it forth in 1870 in the first edition of his celebrated Treatise. Although the deductive procedures followed were not always rigorously consistent, and here and there appeared rather as strokes of genius than as logical deductions and thus would have surprised and even scandalized some devotee of extreme scientific exactness, Maxwell's theory imposed itself within a few years.
It is not possible to say briefly how one passes from the system of general differential equations to the concrete solutions of individual problems. But to be immediately convinced of the extraordinary power of the Maxwellian theory, and to acknowledge in it an imperishable merit, it will suffice to recall the particular case of them that led to the prediction of electromagnetic waves and to the electromagnetic theory of light.
The condition that Maxwell's equations correspond to electromagnetic phenomena, understood in their entirety, implied the intervention in them, besides of the quantities that were to be determined, that is, of the distribution with surface density of electricity on conductors ρ, and of the intensities of the electric and magnetic fields E and H as unknown functions, also of coefficients expressing certain fundamental properties, such as the conductivity σ of conductors, the dielectric power ε and the magnetic permeability μ of the media. There had moreover evidently to intervene that coefficient which we have seen insinuate itself mysteriously into the Biot and Savart expression of the electromagnetic law and turn out to be identifiable with the velocity of light. Now Maxwell, considering the particular case of the absence of conductors, and therefore of distributions of electric density equal to zero, observed that the perturbations of the intensities of the electric and magnetic fields E and H, which turned out to be everywhere interlinked with one another, propagated themselves transversely (that is, perpendicularly to the plane of those perturbations) with the velocity f_{eff} = ε, coinciding, that is, with the velocity of light. He therefore thought that the propagation of the transverse waves of light, which until then were considered to take place in an ether devised ad hoc and necessarily endowed with quite mysterious properties (v. ETERE), must instead take place in the far simpler ether that had to be posited as the basis of his theory. Everyone knows that the electromagnetic waves thus foretold were realized by H. Hertz eighteen years later (1888) and what part they play today in our daily life; that the electromagnetic theory of light replaced with notable advantage the previous theory of Fresnel and that in our customary macroscopic physics it is still fully valid.
Bibliography2 works
Paolo Strancio