Franklin's law of the conservation of electric charge

Franklin’s theory of the Leyden phial led to the doctrine that glass is impermeable to electricity. It was generalized by Aepinus[50] and his co-worker Johann Karl Wilcke (b. 1732, d. 1796) into the law that all non-conductors are impermeable to the electric fluid.

That this applies even to air they proved by constructing a machine analogous to the Leyden jar, in which, however, air took the place of glass as the medium between two oppositely charged surfaces.

The success of this experiment led Aepinus to deny altogether the existence of electric effluvia surrounding charged bodies:[51] a position which he regarded as strengthened by Franklin’s observation, that the electric field in the neighbourhood of an excited body is not destroyed when the adjacent air is blown away.

The electric fluid must therefore be supposed not to extend beyond the excited bodies themselves.

The experiment of Gray, to which we have already referred, showed that it does not penetrate far into their substance; and thus it became necessary to suppose that the electric fluid, in its state of rest, is confined to thin layers on the surfaces of the excited bodies.

This being granted, the attractions and repulsions observed between the bodies compel us to believe that electricity acts at a distance across the intervening air.

Two vitreously charged bodies repel each other. The force between two particles of the electric fluid must con Franklin’s one-fluid theory, which Aepinus adopted) be repulsive.

Since there is an attraction between oppositely charged bodies, the force between electricity and ordinary matter must be attractive. These assumptions had been made, as we have seen, by Franklin; but in order to account for the repulsion between two resinously charged bodies, Aepinus introduced a new supposition—namely, that the particles of ordinary matter repel each other.

This, at first, startled his contemporaries; but, as he pointed out, the “unelectrified” matter with which we are acquainted is really matter saturated with its natural quantity of the electric fluid, and the forces due to the matter and fluid balance each other; or perhaps, as he suggested, a slight want of equality between these forces might give, as a residual, the force of gravitation.

Assuming that the attractive and repellent forces increase as the distance between the acting charges decreases, Aepinus applied his theory to explain a phenomenon which bad been more or less indefinitely observed by many previous writers, and specially studied a short time previously by John Canton[52] (b. 1718, d. 1772) and by Wilcket[53]—namely, that if a conductor is brought into the neighbourhood of an excited body without actually touching it, the remoter portion of the conductor acquires an electric charge of the same kind as that of the excited body, while the nearer portion acquires a charge of the opposite kind.

This effect is known as the induction of electric charges. It had been explained by Canton and by Franklin[54] in terms of the theory of electric effluvia.

Aepinus showed that it followed naturally from the theory of action at a distance, by taking into account the mobility of the electric fluid in conductors; and by discussing different cases, so far as was possible with the means at his command, he laid the foundations of the mathematical theory of electrostatics.

Aepinus (lid not succeed in determining the law according to which the force between two electric charges varies with the distance between them; and the honour of having first accomplished this belongs to Joseph Priestley (b. 1733, d. 1804), the discoverer of oxygen.

Priestley was a friend of Franklin’s. Priestley had been informed by Franklin that he had found cork balls to be wholly unaffected by the electricity of a metal cup within which they were held. Franklin wanted Priestley to repeat and ascertain the fact.

On December 21, 1766, Priestley made experiments which showed that, when a hollow metallic vessel is electrified, there is no charge on the inner surface (except near the opening), and no electric force in the air inside.

He published this in 1767.[55] He says:

“This experiment shows that the attraction of electricity is subject to the same laws with that of gravitation. It is therefore according to the squares of the distances; since it is easily demonstrated that were the earth in the form of a shell, a body in the inside of it would not be attracted to one side more than another?”

This brilliant inference seems to have been insufficiently studied by the scientific men of the day; and, indeed, its author appears to have hesitated to claim for it the authority of a complete and rigorous proof. Accordingly we find that the question of the law of force was not regarded as finally settled for eighteen years afterwards.[56]

Electricity was raised to the position of an exact science by:

• Franklin’s law of the conservation of electric charge, and
• Priestley’s law of attraction between charged bodies

Both of them carried on a long and tenacious struggle with the reactionary influences which dominated the English Government in the reign of George 3rd. Both reluctantly exchanged their native flag for that of the USA.

The names of both have been held in honour by later generations, not more for their scientific discoveries than for their services to the cause of religious, intellectual, and political freedom.

The most celebrated electrician of Priestley’s contemporaries in London was the Hon. Henry Cavendish (b. 1731, d. 1810), whose interest in the subject was indeed hereditary, for his father, Lord Charles Cavendish, had assisted in Watson’s experiments of 1747.[57]

In 1771 Cavendish[58] presented to the Royal Society an “Attempt to explain some of the principal phenomena of Electricity, by means of an elastic fluid.”

The hypothesis adopted is that of the one-fluid theory, in much the same form as that of Aepinus. It was, as he tells us, discovered independently, although he became acquainted with Aepinus’ work before the publication of his own paper.

In this memoir Cavendish makes no assumption regarding the law of force between electric charges, except that it is “inversely as some less power of the distance than the cube”; but he evidently inclines to believe in the law of the inverse square.

He shows it to be “likely, that if the electric attraction or repulsion is inversely as the square of the distance, almost all the redundant fluid in the body will be lodged close to the surface, and there pressed close together, and the rest of the body will be saturated”; which approximates closely to the discovery made four years previously by Priestley.

Cavendish did, as a matter of fact, rediscover the inverse square law shortly afterwards; but, indifferent to fame, he neglected to communicate to others this and much other work of importance.

The value of his researches was not realized until the middle of the nineteenth century, when William Thomson (Lord Kelvin) found in Cavendish’s manuscripts the correct value for the ratio of the electric charges carried by a circular disk and a sphere of the same radius which had been placed in metallic connexion. Thomson urged that the papers should be published; which came to pass [59] in 1879, a hundred years from the date of the great discoveries which they enshrined. It was then seen that Cavendish had anticipated his successors in several of the ideas which will presently be discussed—amongst others, those of electrostatic capacity and specific inductive capacity.

In the published memoir of 1771 Cavendish worked out the consequences of his fundamental hypothesis more completely than Aepinus; and, in fact, virtually introduced the notion of electric potential, though, in the absence of any definite assumption as to the law of force, it was impossible to develop this idea to any great extent.

One of the investigations with which Cavendish occupied himself was a comparison between the conducting powers of different materials for electrostatic discharges. The question hall been first raised by Beccaria, who had shown[60] in 1753 that when the circuit through which a discharge is passed contains tubes of water, the shock is more powerful when the cross-section of the tubes is increased.

Cavendish presented a memoir to the Royal Society in 1775,[61]:

“From some experiments, iron wire conducts about 400 million times better than rain or distilled water. The electricity meets with no more resistance in passing through a piece of iron wire 400,000,000 inches long than through a column of water of the same diameter only one inch long. Sea—water, or a solution of one part of salt in 30 of water, conducts 100 times, or a saturated solution of sea—salt about 720 times, better than rain-water.”

The experiments were published in the volume edited in 1879. In it, the method of testing by which Cavendish obtained these, results was simply that of physiological sensation, but the figures given in the comparison of iron and sea—water are remarkably exact.

While the theory of electricity was being established on a sure foundation by the great investigators of the eighteenth century, a no less remarkable development was taking place in the kindred science of magnetism, to which our attention must now be directed.

The law of attraction between magnets was investigated at an earlier date than the corresponding law for electrically charged bodies. Newton,[62] in the Principia, says: “The power of gravity is of a different nature from the power of magnetism, For the magnetic attraction is not as the matter attracted. Some bodies are attracted more by the magnet, others less; most bodies not at all. The power of magnetism, in one and the same body, may be increased and diminished; and is sometimes far stronger, for the quantity of matter, than the power of gravity; and in receding from the magnet, decreases not in the duplicate, but almost in the triplicate proportion of the distance, as nearly as I could judge from some rude observations,”

The edition of the Principia which was published in 1742 by Thomas Le Seur and Francis Jacquier contains a note on this corollary, in which the correct result is obtained that the directive couple exercised on one magnet by another is proportional to the inverse cube of the distance.

The first discoverer of the law of force between magnetic t poles was John Michell (b. 1724, d. 1793), at that time a young Fellow of Queen’s College, Cambridge,[63] who in 1750 published A Treatise of Artificial Magnets; in which is shown an easy and expeditious method of making them superior to the best natural ones. In this he states the principles of magnetic theory as follows[64]:—

“Wherever any Magnetism is found, whether in the Magnet itself, or any piece of Iron, etc., excited by the Magnet, there are always found two Poles, which are generally called North and South; and the North Pole of one Magnet always attracts the South Pole, and repels the North Pole of another; and vice versa.”

This is of course adopted from Gilbert.

“Each Pole attracts or repels exactly equally, at equal distances, in every direction.” This, it may be observed, overthrows the theory of vortices, with which it is irreconcilable.

“The Magnetical Attraction and Repulsion are exactly equal to each other.” This, obvious though it may seem to us, was really a most important advance, for, as he remarks, “Most people, who have mention’d any thing relating to this property of the Magnet, have agreed, not only that the Attraction and Repulsion of Magnets are not equal to each other, but that also, they do not observe the same rule of increase and decrease.”

“The Attraction and Repulsion of Magnets decreases, as the Squares of the distances from the respective poles increase.”

This great discovery, which is the basis of the mathematical theory of Magnetism, was deduced partly from his own obscrvations, and partly from those of previous investigators (e.g. Dr. Brook Taylor and P. Musschenbroek[errata 1]), who, as he observes, had made accurate experiments, but had failed to take into account all the considerations necessary for a sound theoretical discussion of them,