# Supplement to the Fourth, Fifth, and Sixth Editions of the Encyclopædia Britannica/Æpinus (Francis Ulrich Theodore)

​ÆPINUS, (Francis Ulrich Theodore) eminent in the mathematics, and in natural philosophy, was born at Rostock in Lower Saxony, in 1724, and died at Dropt in Livonia in 1802. We regret that our means of information do not enable us to communicate any particulars in regard to his personal history; but we shall give some account of his contributions to science, and these, after all, form the most interesting memorials of a philosopher’s life.
The work by which he is best known, is entitled, Tentamen Theoriæ Electricitatis et Magnetismi, published at Petersburgh in 1759. It appeared under the sanction of the Imperial Academy, to which the theory had been in part communicated; and it is said on the title page to be Instar Supplementi Comment. Acad. Petropolitanæ. The work indeed merited this distinction, as being the first systematic and successful attempt to apply mathematical reasoning to the subjects of electricity and magnetism. Already the theory of Franklin, with regard to the former, was very generally received, and was supposed to afford a satisfactory explanation of the phenomena. But though it seemed sufficient for this purpose in ​the common and somewhat loose manner in which the matter had hitherto been treated, it was not certain that the same would hold when the conclusions were accurately and mathematically deduced. To apply this test was what Æpinus undertook, and what he has executed in a manner very satisfactory and complete. He has treated very fully, and perhaps has nearly exhausted what may be called the statics of electricity and magnetism, or the equilibrium of their forces. A great field yet remains, where the motion of the electric fluid is to be considered, and its distribution over the surfaces of bodies of a given figure; where greater difficulties are to be encountered, and where the latest improvements of the integral calculus in the hands of La Place and Poisson have begun to be applied. The investigations of Æpinus in their own department led to very satisfactory results, and the exact agreement between them and the phenomena actually exhibited was extensively observed. Notwithstanding this agreement, we cannot consider the theory of positive and negative electricity as being yet sufficiently established. Though the assumption on which it is founded appear very simple at first, it is found more complex on a nearer inspection. The assumption is, that a fluid resides in the surfaces of all the bodies termed electrics, which is highly elastic, and strongly attracted, at the same time, by the particles of the body, and that while this fluid remains equally diffused over the surface of the body, no phenomenon whatever gives any information of its existence. By certain mechanical operations, however, the equilibrium of this fluid may be destroyed; the fluid may be accumulated at one end, or on one side of a body, and entirely withdrawn from the opposite. It is when an electric is brought into this state that it exhibits the phenomena of electricity, between which, and the calculus instituted on the suppositions just laid down, Æpinus has everywhere remarked the most exact agreement. One great difficulty, however, still remains. The negative ends of two electrified bodies repel one another, just as much as the ends which are reckoned positive. But such an effect cannot result from the mere absence of a substance; when the electric fluid is withdrawn, if repulsion still continue, it must arise from the mutual action of the particles of the body itself. Thus it would appear, that, in the absence of the electric fluid, the tendency of the particles of matter is to repel one another. This is an essential part of the theory; and it is not accurate to say, that the doctrine of Franklin or Æpinus supposes no more than the existence of an elastic fluid diffused over the surfaces, and strongly attracted by the particles of bodies. It supposes, besides, that these particles, in the absence of this fluid, mutually repel one another. This not only takes away from the simplicity of the hypothesis, but it is obviously a very unnatural, not to say a contradictory supposition; because, when the electric matter is removed, how comes it to pass that the particles of the body, notwithstanding their mutual repulsion, still cohere together as firmly as before? This difficulty is acknowledged by Æpinus himself; but it would seem that the theory had taken a strong hold of his mind before he was aware of this consequence from it, so that he became by degrees reconciled to a supposition which appeared to him a first not a little incongruous. This must not surprise us: It is not always that, even among philosophers, we meet with the candour, or perhaps we should say the courage, with which Newton suspended his belief in his own great discovery, the principle of universal gravity, as long as the erroneous opinion then existing, about the magnitude of the earth, made the moon's motion in her orbit appear inconsistent with the descent of falling bodies.
Another remark, made by Æpinus himself, involves in it a difficulty which should have induced him to view his theory with considerable diffidence. Though he considers the difference of the two electricities to be the same as between excess and defect, or to consist in this, that the fluid which is deficient in the one part is in excess in the other, he admits that no phenomenon points out on which side the excess, or on which the defect lies. This is a strong indication that the difference is not of the kind supposed. We are not left at a loss to tell whether cold is the absence of a substance which we call heat, or heat the absence of a substance which we call cold. If there were just as much reason for asserting the one of these propositions as the other, one would certainly be inclined to reject both. The same should be done with respect to electricity and magnetism.
The investigations of Æpinus, however, are by no means rendered useless, even if the theory of positive and negative electricity, or of positive and negative magnetism be exchanged for that of two elastic fluids, each attracting the other, and both attracted by the particles of bodies. Most of his investigations may be easily accommodated to this supposition, and, therefore, they are, fortunately for themselves and for their author, of a more permanent nature than the principles from which they were deduced.
It is to be added to this, that Æpinus was the first who saw the affinity between electricity and magnetism, in its full extent, and perceived the light that these two mutually cast on one another. He instituted a regular series of experiments on the nature of the Tourmaline, on which he wrote a small treatise, published in 1762. He is to be regarded also as the inventor of the Condenser of Electricity, and of the Electrophorus, of which he gave the complete theory.
A very excellent view of the theory of Æpinus was published at Paris by M. Haüy, in 1787, in 8vo. The same author has, however, adopted the theory of the two fluids in his own treatise, Leçons de Physique. There is a remarkable coincidence between Æpinus’s work on electricity and magnetism, and that of Mr Cavendish, given in the Philosophical Transactions for 1771, p. 584. The principles from which they set out, and the conclusions at which they arrive, are in a great measure the same. It appears, however, quite certain, that Mr Cavendish knew nothing of the work of the Russian philosopher till his own was completed. His mode of proceeding is more geometrical, and in some parts he has gone farther.
The researches of Æpinus were not confined to the subjects now mentioned, but extended to most of the branches of natural philosophy. Beside the treatise ​on the Tourmaline, he published, in 1762, a work, in 4to, On the distribution of heat at the surface of the earth; a work which, though translated into French, has hardly, we believe, made its way into this country, and of which we are therefore unable to speak from our own knowledge. He is also the author of many valuable memoirs on different subjects in pure mathematics, in astronomy, mechanics, optics, meteorology, contained in the 7th, 8th, 9th, 10th, and 12th volumes of the Novi Commentarii Petropolitanæ, and in the volumes of the Berlin Memoirs, for 1755, 1756. In a memoir contained in the last of these is the first account of his experiments on the Tourmaline, which were conducted with great accuracy and judgment, and do honour to the author as a man of a sound and philosophical understanding, well instructed in the true principles of inductive investigation. Indeed, notwithstanding the objections we have made to his theories of electricity and magnetism, we must acknowledge that this is the general impression produced by the perusal of his works. He appears to have been well acquainted with practical astronomy, and sometimes to have had the charge of the Imperial Observatory. He made improvements on the Micrometer and the Reticulum, and wrote a memoir on the effects of parallax in the transit of a planet over the sun; a difficult subject, and one rendered at that time (1764) peculiarly interesting, on account of the transit of Venus which was just past, and that which was soon expected. (Novi Com. Pet. Tom. X. p. 433.) In the same volume he has a memoir on the subject of accidental colours, which at that time had hardly been treated of by any author but Buffon; and another on the affinity between electricity and magnetism. In the 12th volume he notices, we believe for the first time, the electric property of the Brasilian emerald. He was not aware that this emerald is in reality the green Tourmaline (Brogniart, Tom. I. p. 418.); a variety of that mineral on which he had already exercised his ingenuity with so much success.
It is rare, in an advanced state of science, to have the satisfaction of making a new discovery with regard to a subject quite elementary, and one that has been long a subject of attention. This, however, happened to Æpinus with respect to the Lever, and to the simplest kind of lever—that which has equal arms; of which he has demonstrated a new property in the 8th volume of the Commentaries above referred to. It is this:—If a lever, with equal arms, be acted on at its opposite ends by forces, in a given ratio to one another, and having their directions parallel to straight lines given in position, and if these forces be resolved each into two, one at right angles to the lever, and the other in the direction of it: in the case of equilibrium, the sum of the two forces, having the same direction with the lever, will be the greatest possible. This theorem, remarkable for its simplicity, and for illustrating the connection between the equilibrium of bodies, and certain problems concerning the maxima or minima of variable quantities, occurred when he was pursuing some of his inquiries concerning magnetism. He seems not to have been very fortunate, however, in his investigation, which is more complex than is necessary, as the proposition admits of a geometrical demonstration, remarkable for its simplicity. (L.)