"Oliver Heaviside. An Appreciation : The Personal Equation : The Work of a Genius Elucidated"
A Guest Post by Oliver Lodge (1851-1940)
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For many years, Oliver Heaviside, The Man, by his friend Dr. G.F.C. Searle was the only biography available for Heaviside. Despite being revived and republished in 1987 by Ivor Catt, Searleās biography remains hard to find. Forrest Bishop generously made a scanned copy available online. After many decades of neglect, Oliver Heaviside has begun to receive well-deserved recognition. Paul Nahinās Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age, offers a technically rigorous recounting of Heavisideās work and life, and Basil Mahonās The Forgotten Genius of Oliver Heaviside: A Maverick of Electrical Science, is an excellent and accessible biography anyone can enjoy. So what unique content could I now offer on the life and work of this remarkable man? I went digging in the archives and found this - an obituary of Oliver Heaviside written by none other than Sir Oliver Lodge, last survivor of the āMaxwellians.ā Reprinted here from āOliver Heaviside. An Appreciation : The Personal Equation : The Work of a Genius Elucidated,ā The Electrician, February 13, 1925, p. 174, with a bit of light editing and some illustrations, is Lodgeās tontine of appreciation for his departed friend and colleague. The British spellings and superfluity of commas, colons, and semi-colons are reproduced as in the original.
OCCASIONALLY a remarkable genius arises we know not how nor whence. Such an one runs the risk of being misunderstood and neglected in his lifetime; partly perhaps because he has not gone through the ordinary processes of education, and has therefore not attracted the attention of his contemporaries in the regular way, and partly because his insight may be of an unorthodox and exceptional type, and his utterances personal and peculiar in style. He is also apt to be more or less in advance of his time, so that it is sometimes left to posterity to discover the brilliance and notable character of his achievement. Such an one was Waterston, who evolved the kinetic theory of gases years before the scientific world was ready to receive it ; with the result that his communication to the Royal Society on the subject was turned down by the referees ; and we are now told that among Waterston's Papers will be found other striking anticipations of the course of scientific progress, though they have not as yet been made public.
A Genius of Exceptional Ability.
Such an one again was Oliver Heaviside, a mathematical genius of exceptional ability, who flooded the columns of THE ELECTRICIAN with remarkable but ill-understood Papers, the value of which was, however, recognised long before his death (partly by Kelvin, partly by Fitzgerald, Dr. G. F. C. Searle, and others), but which for all practical purposes had been turned down by the telegraphic authorities of his time, and regarded as nonsense by no less a personality than Sir William Henry Preece, that genial orator, for many years engineer-in-chief to the Telegraphic Department of the British Post Office. Indeed I was told that a practical Paper by his brother, A. W. Heaviside, of Newcastle-on-Tyne, was rejected by the Society of Telegraph Engineers, because it embodied in more practical form the results of his brotherās mathematical researches. There is no doubt that Oliver Heaviside felt this neglect and contumely very keenly, and he gave expression to it in humorous and sarcastic fashion on many occasions.
All this is now ancient history, but reference to it cannot properly be omitted, for it loomed large in Heaviside's mind and saturates many of his lighter Papers. Besides, when serious mistakes are made, it is only just that for a time they should be remembered. Recognition, though tardy, came at lengthāāperhaps too late to be altogether consoling. The Royal Society made him a Fellow ; the Institution of Electrical Engineers awarded him their most distinguished medal ; and their President took the trouble to convey it personally to him at his solitary home in the depths of the country.
Part of the difficulty of recognising his achievements lay no doubt in his own personality ; he was of very retiring disposition with no social gifts. He lived alone, in what appeared to be a state of considerable poverty, cooking his own food, waiting on himself, and suffering from indifferent health. He was visited from time to time by occasional admirers of his genius, in his dismal lodgings at Kentish Town. But as soon as he began to be recognised he fled to Devonshire, and thence emerged no more ; never, so far as I know, attending the Royal Society, nor the Electrical Engineers, nor coming to hear the congratulations which might āā late in life āā have been showered on him ; and living to the end the life of a recluse.
He was a voluminous correspondent, however, and both FitzGerald and myself received innumerable letters from his pen. Dr. Searle also must have received many, and probably continued to know him personally better than anyone else. He it is who would be able to tell us more about Heaviside's life and education. How he acquired his mathematical knowledge I do not know ; I hope that Dr. Searle does, and will tell us. But the outcome of his singular mind is embodied in several volumes of āElectrical Papersā (published by Macmillan in 1892) and other volumes on āElectromagnetic Theoryā (published by THE ELECTRICIAN Printing and Publishing Company, in 1893, 1899, and 1912). A recent reproduction of these last, in three volumes, with the same title, has been recently issued by Benn Brothers (now Ernest Benn, Ltd.).
The fact that these early Papers were accepted (I presume paid for) and published by THE ELECTRICIAN, for many years, redounds greatly to the credit of that organ ; for there could have been but few of its readers who really understood them : by the majority they must have been regarded with more or less awe, perhaps with some suspicion, but with certainly less than adequate attention.
Heaviside had, however, a peculiar vein of humour, and sometimes his writings amused, even though they did not edify. He had a wonderful instinct for grappling with the difficulties of a subject and giving it symbolic expression. Probably no one in his time had an equal grasp of the present and future outcome of Maxwell's theory. He expressed the generation of electric waves in his own style : he treated of the motion of electric charges at different velocities, including those which equalled or even hypothetically surpassed the velocity of light. Everything relating to electrical induction, and the energy of electric currents, and the forces and fluxes of energy in the electromagnetic field, the self-induction of wires and the generation of waves, was elaborately worked out in these early Papers. He invented a special system of vectorial algebra with which to deal with them. His mathematics often aroused the admiration of John Perry and other competent judges. And the three volumes on āElectromagnetic Theoryā may be taken as a summary of his matured views on these subjects.
It seems probable that workers on the science of the ether will make more use of his methods and results than they have at present done ; though the peculiarity of his modes of expression rather alienated, for a time, and perhaps even to this day, the majority of Cambridge mathematicians ; for, though there is much originality, there is little orthodoxy in his manner of presentation.
Cable Theory.
The chief subject on which his fame rests at present, the subject also which at the time aroused rather bitter controversy, was his development of the theory of cable signaling. This theory was (as all the world knows) begun by Kelvin ; and it may be truly said that Kelvin's theory of the propagation of pulses along cables, taking into full consideration their resistance and their capacity, rendered the Atlantic cable of 1865 and 1866 possible ; and it may be said that it was neglect of that theory which slaughtered the first cable in 1858. Kelvin's theory however, was incomplete ; it proceeded on the analogy of conduction of heat ; it applied Fourier's analysis of heat conduction to the electrical case ; and the results, though most helpful, indeed invaluable, were by no means the last word on the subject. Self-induction, though doubtless partially understood by Kelvin (he called it electro-dynamic capacity), was not introduced into his theory, it was probably considered a negligible factor for a long straight wire. Heaviside recast and remodelled the theory in the most general form ; he invented the terms āinductanceā and āreluctance,ā āreactance,ā āpermeance,ā āpermittance,ā and the like, on the lines of the term āresistanceā ; and some of these terms have come to stay. He showed that the propagation of signals along wires was in all essential respects identical with the laws of propagation of electric waves in free space. So that when I had the pleasure of detecting electric waves along wires, in or about 1888 at the same time as Hertz detected them in free space, Heaviside hailed both observations as practically one and the same though āā there is no doubt that Hertz's investigations eclipsed mine altogether, in thoroughness, as well as in practical results.
The Theory of Wave Transmission.
The theory of the transmission of waves along free aerial wires is simple enough. The equations are much the same as for waves anywhere : they are given in my āPhilosophical Magazineā Paper for August, 1888, near the end of a disquisition on lightning conductors. But Heaviside did not stop at waves along aerial wires : he applied the theory to impulses along cables, where the combination of capacity and resistance exercised its deleterious effect, and constituted the great difficulty in efficient signalling. He showed that by taking self-induction into account, the results could be much more accurately expressed, and further, that self-induction was not the hindrance or bugbear which Sir William Preece thought it was, but that it was the most essential help. And, indeed, without inductance it is difficult to see now how any transmission theory could be satisfactory. Heat has no rate of propagation : it is merely diffusion ; and Kelvin's theory of cable signalling was entirely on diffusion lines. The waves, as it were, soaked through, and the time of arrival was quite indefinite ; it depended merely on how sensitive the receiving instrument could be. If you had to signal by heat, along a rod of copper, to a thermometer at one end, by applying to the other end, first a flame and then a block of ice, alternately, so that the distant thermometer could experience pulses of temperature and respond to the signals (which in imagination might be dots and dashes), no rate of propagation could be specified. An infinitely sensitive thermometer would feel the influence at once ; any practicable thermometer would feel it after considerable delay. But the delay could be reduced by making the thermometer still more sensitive : and that is what Kelvin did ; his mirror galvanometer and syphon-recorder were instruments far more sensitive than any of their predecessors : and accordingly the very beginnings of diffusion were felt, and could be stopped, before had accumulated, by an opposition pulse. That was, and to some extent still is, the system of cable signalling.
The Effect of Inductance.
But when inductance is taken into account it is seen there is a definite velocity involved āā viz., the velocity of light. No instrument could respond instantaneously, even if infinitely sensitive. True waves are passing along the cable, greatly modified by the distortional effect of diffusion, which has the effect of transmitting waves at different paces, and smoothing out sharp signals ; after the same sort of fashion as a coach spring smooths out the bumps and irregularities of a road. Such smoothing out is to some extent tolerable, when dots and dashes, and especially when right and left deflections, are used. A dash is not suitable for transmission, it lasts too long ; but right and left deflections, that is positive and negative signals, may be quite brief āā the briefer the better, for then there is nothing to accumulate ; the positive pulse is curbed by the immediately following negative pulse. All this was applied by Fleeming Jenkin and other telegraphic experts ; but no one contemplated the possibility of telephonic speech through a long cable, even after the telephone had been invented. The smoothing out of consonants would reduce them to nonsense ; and on Lord Kelvin's theory speech would be unintelligible and impossible of transmission on any cable longer than, say, that across the Irish Sea.
But Heaviside's theory modified all that : he showed that the effect or tendency of inductance was to add momentum to the signals, to give them a real speed, to wipe out much of deleterious effect of capacity, to transmit waves of all lengths at the same speed ; so that if only sufficient inductance could be employed, signals could be transmitted even along a cable of Atlantic length without distortion. He gave in fact the theory of the distortionless cable. [More on that from Hackaday].
He showed also that a certain amount of leakage, lateral escape of electricity, would improve the signals : it would weaken it, of course, but the attenuation might be more than compensated by the absence of distortion.
The Influence of the Magnetic Field.
Put into words, by way of exposition of one aspect of the theory, one may say that for the transmission of true waves āā not diffusion waves like heat, but waves like light, waves such as exist in free ether, and approximately along an aerial line āā the electric and the magnetic energies are required to be equal. If one overpowers the other we have distortion, varying rates of transmission, or no rate of transmission at all, nothing but diffusion if the overpowering is excessive. In Kelvin's theory it was excessive, because the inductance was considered zero, that is to say, the magnetic field was neglected ; the electric field alone was taken into account. Heaviside pointed out that the magnetic field was really doing the work, though greatly overpowered by the electric, especially in cables of large capacity. By adding self-inductance, magnetic energy could be increased and made more equal to the electric energy ; by leakage the overplus of electric energy could be still further reduced, though less economically. If the two energies could be made quite equal we should have true distortionless waves, with every feature of the signal reproduced at the far end, subject to nothing but attenuation.
An important note from the Aetherczarā¦ The previous paragraph expresses a truly critical point and one Iāve only seen Oliver Lodge make. Electromagnetic waves, whether in free space or guided on a transmission line, always have equal amounts of electric and magnetic energy. A mathematically equivalent way of expressing this condition is to say that the field impedance of the wave is identical to the characteristic impedance of the propagation channel, 376.7 ohm for free space, potentially quite different for a transmission line. In cases of interference or distortion - as Lodge indicates - the energy gets out of balance and therefore slows down. I am also indebted to historian Bruce J. Hunt for pointing this out to me.
Such a state of things can only be approximated to in practice. Silvanus Thompson advocated the construction of cables added inductances, so as to carry out into practice Heavisideās views ; and everyone knows that Prof. Pupin, in America, succeeded in influencing capitalists to make such cables according to his design ; and they were found to have just the properties predicted for them. Moreover, in America successful enterprise has gone further. They really have long-distance telegraphy there (they say that we have not got any long distances, and therefore have not attended to it so fully) ; they apply extra inductance to their land lines. And in that way I am told that the General Electric Co. (or perhaps it is the Western Electric Co., I am not sure) by applying extra inductance at regular intervals along their extensive continental lines, find it possible to transmit clear and distinct telephonic speech from New York to California, and beyond.
Practical Results of Heaviside's Theory.
I am now trespassing on subjects concerning which practical experts are more fully informed than myself. But I have said enough to indicate that these interesting and extensive developments (of which we have not as yet by any means heard the last) owe their origin and inception to the genius and perspicacity of the subject of this memoir. That he failed to derive any pecuniary benefit (at least as far as I know) is to be lamented ; but under the present system of scientific recognition (or non-recognition) it was probably inevitable. It was not an easy matter to help Heaviside pecuniarily : I believe that FitzGerald, and probably others, tried once or twice ; but he had a pride which discouraged such attempts. A Government pension he was ultimately prevailed on to accept, provided it was so put as to recognise his work for Science, so as to remove from it anything of an eleemosynary character.
He has left his name on the atmosphere in the form of a āHeaviside layer,ā which is considered responsible for the transmission of electric waves to the Antipodes round the curvature of the earth.
Another little excursion of his is noted in the āPhilosophical Magazineā for January, 1925, where a Japanese professor describes a method for making an electret by electrising a dielectric, on the analogy of magnetising a permanent magnet ; and finds that his idea was anticipated by Oliver Heaviside in āElectrical Papersā Vol. i, Ā§xii, under the title āElectrisation, Natural Electret.ā
Heaviside was fond of tracing magnetic analogies to electric phenomena : hence his name āreluctanceā for the magnetic analogue to resistance. He even introduced a pseudo-magnetic coefficient in some equations, so as to make them more symmetrical and therefore more pleasing to mathematicians. His theory of the distortionless cable is very complete and beautiful ; he knew how to avoid reflections at distant ends and how to design a cable of any desired properties. His brother worked practically, and accumulated data, in the same direction ; but he was suppressed.
I do not think the man was unhappy ; though at one time he was rather embittered by the misunderstanding and hostility of those in authority āā an attitude which a genial man like Sir William Preece would have been the first to lament had he been better informed. Heaviside lived an independent, self-contained life : and no doubt his insight into Nature (whether recognised by his contemporaries or not) must have given him moments of sincere pleasure. The least we can do now is to recognise his genius, and wish that it had been earlier recognised and more widely known.
Next time: 4.1 Heaviside, Poynting, & Energy Flow: "When Energy Goes From Place to Place, It Traverses the Intermediate Space"
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