.

The second statement is that Professor Quincke's results were different from mine, that he observed sometimes an increase, sometimes a diminution, of the velocity of light whose plane of polarization is parallel to the lines of force. Our results are not really inconsistent. The phenomena were different because the physical actions examined were different, perhaps as widely different as conduction and convection in the somewhat similar experimental question of the conduction of heat in fluids. JOHN KERR.

Glasgow, 18th June, 1894.

XV. Notices respecting New Books.

Electromagnetic Theory. By OLIVER HEAVISIDE.

("The Electrician" Printing and Publishing Company.)

THIS THIS work consists largely of definitions and summaries, and it may be considered as giving something like a bird's-eye view of the more theoretical and recondite portions of electromagnetic science dealt with in Mr. Heaviside's previous, and most valuable, work, Electrical Papers.'

Omitting a comparatively short introduction, the present work may be said to contain three long chapters, whose titles are: "Outline of Electromagnetic Connections," "The Elements of Vectorial Algebra and Analysis," and "Theory of Plane Electromagnetic Waves."

Within the limits of an ordinary review it would be impossible to follow Mr. Heaviside in detail in his exposition of the processes at work in the electromagnetic field, even if my knowledge were so complete as to enable me to do justice to every portion of the abstruse and elaborate work for which Mr. Heaviside is so well known. I must therefore confine my remarks to comparatively few of the interesting and important questions so ably dealt with by him; and it will, no doubt, be better if I select chiefly those portions of the work in which he appears in opposition, sometimes rightly and sometimes wrongly (according to my judgment) to prevailing views.

A reader of Mr. Heaviside's writings is at once struck by the extraordinary style which distinguishes him from every other English writer on Mathematics or Physics; and the impression which is produced by this style is often the reverse of pleasing. There is a complete absence of the conventionalities which are generally recognized as proper to the writing of a scientific treatise. Mr. Heaviside is the Walt Whitman of English Physics; and, like the so-called "poet," he is certain to raise aversion to his peculiarities. A few typical instances must suffice for quotation. Thus, in p. 142, he pays a well-deserved tribute to printers in the words" Compositors are very intelligent, read mathematics like

winking, and carry out all instructions made by the author." Again (p. 203), when defining the potential produced at any point of space by a vector, he says, "We may use the same definition when it is a vector that has to be potted, or potentialised. Thus, if A is the potential of C, then A pot CΣ C/4πr." Again (p. 352), when discussing the magnetic flux relations, he presents us with the ethical maxim, "Different men have different opinions -some like apples, some like inions'! We can easily imagine the difficulty of some thoroughly zealous and painstaking German translator of this work in his attempt to render this scientific principle into good German. In vain does he consult his English dictionaries for the word "inions"; until, perhaps, after a week's labour, the happy solution occurs to him that "inions " is a misprint for "ions," which are, of course, preferred to apples by those endowed with electrical tastes,-and then the truth of the principle becomes at once obvious.

It was pleasant to find in a previous work that Mr. Heaviside attaches due importance to clearness of expression, and even to grammatical accuracy. In a passage in which he severely criticises the language of a well-known experimentalist, he very truly says "The first step to the understanding of a writer is to find out what he means." Now, if I am not mistaken, this passage affords a key to Mr. Heaviside's peculiar style, and supplies, to a great extent, a justification of it. So far as my own experience of English writers is concerned, it is not a great exaggeration to say that by far the greater portion of my time is occupied in the work of ascertaining the meaning of the author and in overcoming the difficulties of ambiguous language. The intrinsic difficulties of the subject demand, in general, a comparatively short time. Thus, the typical English writer in opening up a mathematical discussion on (say) an electromagnetic field, in some portions of which there are wires conveying electrical currents, there being in other portions magnets, dielectrics, conductors, &c., will usually assume the following shroud of vagueness: "Letv be the velocity, C the current, E the electromotive force, K the specific inductive capacity, V the potential, μ the permeability, B the induction, D the displacement, H the magnetic force, L the inductance, T the kinetic energy, &c., &c." After every one of which we exclaim "Of what?" But in vain, the typical author considers that he has bargained to give us the whole bundle of facts and nothing more. In the grave and stilted Scientific Treatise, or Solemn Homily, there must be no touch of imagination to increase the interest of the reader, nor any digression for the purpose of anticipating a misunderstanding, however natural.

It is this characteristic of some of our writers which renders a treatise on the same subject, and with the same scope, by a French author such a welcome relief. In the latter we almost invariably find vagueness, ambiguity, and an illogical order of thought conspicuously absent; and very possibly it is this consideration that has induced Mr. Heaviside to throw over the orthodox style of

writing-though, in so doing, he has occasionally allowed his illustrations and his language to fall into an opposite extreme.

As everyone knows, Mr. Heaviside has advocated many changes in scientific nomenclature, and has already succeeded in getting some of them adopted. The present volume teems with them; but he does not appear (p. 34) to expect success for a very large number.

It is an unfortunate (perhaps an unavoidable) circumstance that, on the appearance of any new branch of science, there is sure to be started a system of nomenclature which, with the advance of knowledge, is soon perceived to be unscientific and misleading. The science of Electricity is far from being an exception to this rule. Its most conspicuous term, Electromotive Force, is thoroughly misleading; and this term Mr. Heaviside replaces, very happily, by the term "Voltage" (p. 26); for, that which is usually called the "electromotive force along any path" is, in reality, the lineintegral of the [tangential compt. of the] electric force-intensity from the beginning to the end of that path, and this Mr. Heaviside habitually describes as the Voltage along the path. Analogously, the same integral for the magnetic force-intensity he calls the Gaussage-which, as he takes the trouble to inform us, is “ pronounced Gowsage, after Gauss (pronounced Gowce)"-this latter to replace the absurd "magnetomotive force." Can we imagine the typical English author taking so much trouble to set us right? Mr. Heaviside is usually most scrupulously precise and accurate; but, for a moment, he forgets this characteristic when, at the end of p. 26, he continues :-"The Voltage or the Gaussage along a line is the sum of the effective electric or magnetic forces along the line the effective component being merely the tangential component of the real" [i. e. the resultant] "force." He knows well that the sum of such quantities (infinite in number, and each of finite magnitude) is infinite. The unskilful "practician" should be told that he is not to take the sum of such components, but the sum obtained by multiplying each of them by the element of length of the curve, and then adding these products together. And is there not a little slip of the same nature at the top of p. 151 (and elsewhere), where the surface-integral of induction is written ΣNB instead of NBdS?

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With regard to another term in very common use with the practicians, viz., "lines of force," Mr. Heaviside is justly severe, more particularly in Vol. II. of his Papers' (p. 328), where he says "It is quite painful to read of magnetic resistance to lines of force." The worst of this matter with regard to lines of force is that a line of force, in the strict Euclidian sense of a line (length without breadth) is a mathematical reality with which the mathematicians cannot dispense, while the unit tube of force is also a reality, and quite distinct from the line; so that when the practician talks of the number of lines of magnetic force passing through a given surface, either he employs the notion of tubes while talking of lines, or—and this is, perhaps, what generally happens-he is

talking simple mathematical nonsense, and picturing to himself a charged electric body or a magnetic pole from a fairly large number (!) of points on whose surface emanate lines, which may pretty well occupy the space immediately round the body, but which diverge so much from each other at a short distance from it, that space is there practically devoid of lines. The surface of the body, thus conceived, strongly resembles the head of a pepper-caster, while a much more accurate representation would liken it to the surface of a golf ball.

In the same way, another glaring absurdity is visited with just severity (p. 109),- "The utterly vicious misuse of pressure to indicate E.M.F. or voltage, by men who are old enough to know better, and do."

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Some other terms put forward by Mr. Heaviside do not seem to be so helpful. For example, the ratio of electric displacement to electric force at any point of a dielectric he proposes to call the permittivity" of the medium, because it indicates "the capacity for permitting electric displacement." But a capacity for permitting is no more identified with electric displacement than with magnetic; and hence there is nothing definitely suggestive in the word. It can scarcely be doubted that "coefficient of electric elasticity," as applied to its reciprocal, in accordance with usage in the general theory of Elasticity, is a better term—and it is, in fact, explicitly used by Maxwell, vol. i., art. 60; but, unfortunately, Mr. Heaviside expressly rejects this helpful term, which does not tax the memory, on the ground (see 'Papers,' Vol. II. p. 328) that "the prefixing of adjectives is just one of those things that we should try to avoid in a convenient terminology." On the contrary, I think, when the prefixing of an adjective secures clear and proper definition, it should be adopted.

The system of nomenclature is carried somewhat too far. We do not want a name for every coefficient, and a wholly different name for its reciprocal; the list soon becomes too formidable; and it is a little amusing to find Mr. Heaviside, after telling us at p. 21 that c in the equation D=cE is the "permittivity" of the medium, telling us at the top of p. 24 that "e is the coefficient of compliance, or the compliancy"-as if he thought that c still required a little artistic touching. But "compliance" and " compliancy" fail in helpfulness just as much as" permittance" and permittivity." The truth is that the problem to describe an assigned quality of a body in a single, perfectly definite, and appropriate word no more admits of a solution than does at an arbitrary moment in a game of Chess the corresponding problem to play and mate in one move.

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Many people will, perhaps, think that in the word "forcive," for a system of forces, conciseness is again a little overdone.

It must be noted as worthy of commendation that Mr. Heaviside systematically and in explicit terms always identifies the magnetic induction at any point in a medium with a flux or displacement, and thereby removes whatever obscurity is contained in Maxwell's

general use of the term, besides bringing the subject more into line with the theory of strain and stress in general. "So far we have considered the two forces, electric and magnetic, producing four fluxes, two involving storage and two waste of energy "(p. 25), the existence of one of these fluxes (namely, the magnetic conduction current) being quite problematical, but nevertheless postulated (as appears farther on) for the purpose of giving formal completeness to the cross connexions of electric and magnetic phenomena, and allowing us to dispense with Maxwell's Vector Potential.

Thus, in Mr. Heaviside's notation, the systematic, concise, and fundamental equations of the electromagnetic field are simply the following:

in which p and o at a point are volume-densities of electrification and "magnetification," q is the vector of velocity at the point if the medium is moving, K is the magnetic conduction current at the point, the other quantities being pretty generally recognizable, while K, g, σ are all of doubtful existence (see more particularly p. 539 of Vol. II. of the Papers').

With regard to Mr. Heaviside's notation for vectors-viz., Clarendon type-it may be said that its adoption is impossible for the simple reason that we cannot use it, or anything like it, in our manuscript work; unless, indeed, in addition to pen, ink, and pencil, we keep beside us a camel's-hair brush with a plate of indian ink, and then paint in our vectors when they occur in the work, after the slow manner of the Chinese. Mr. Heaviside is conscious of this difficulty, and he suggests (p. 142) that in manuscript work we should have some distinctive mark for vectors, such as a suffix; so that the vector of electric force-intensity might be written E. There are two objections to this: firstly in the case of such a vector, for example, as that of intrinsic electric force in a medium, for which Mr. Heaviside uses e, (in Clarendon type) we should be obliged to write e in MS.-which is intolerable, as are also B1, &c.; and secondly it is very undesirable to have our ordinary work (with which we are most concerned, and to which we become most accustomed) written in one language, while our books are written in another; there is a loss of time generated by the unfamiliarity involved in the process. At the same time, Clerk Maxwell's terrible German letters are not to be tolerated for a moment. Perhaps a horizontal bar over the letters is the best, though this is not good.

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We are now brought to the consideration of certain other peculiarities of Mr. Heaviside's work. Maxwell was, apparently, the