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he hesitated to accept it. The exchange of the wooded banks of the Neckar for the muddy shores of the Spree was unwelcome to him, and he was impelled to make it only, it is said, by the prevision that the practice of vivisection would be in a manner, forced upon him if he continued in the physiological line. This was the turning-point of his

Until then he had been officially a physiologist, incidentally a physicist. Thenceforward he professed physics, thus realising at the age of fifty his juvenile aspirations. He occupied the chair of Magnus to the end, but added to his professorial duties in 1887 others of a more onerous character. In that year the Physico-Technical Institute, endowed by Werner von Siemens, was founded by the German Government at Charlottenburg.

Helmholtz became its first director. He rose to the occasion by displaying a completely new range of faculties. His administrative abilities proved to be of a high order. A large staff obeyed his instructions; an extensive organisation depended upon his guidance. He regulated its working with a commanding insight, a grasp of details, a steady patience, and an invincible firmness which were equally beyond praise and expectation.

Nor did his original labours suffer interruption. Only their scope was modified. They were now directed chiefly to electrical and hydro-dynamical topics, the treatment of which at last brought to the front his vast mathematical resources. Occasional excursions into these territories he had already made. At Königsberg, in 1851, he determined the duration of induced electrical currents, as a parergon to his researches on nervous conductivity. In 1869 he published an account of some experiments on electrical oscillations, and fixed, in 1871, a lower limit for the propagation-rate of electro-magnetic induction. His further contributions to the science were numerous and varied. In the Faraday lecture delivered by him at the Royal Institution, April 5, 1881, he sounded their Leitmotiv. The great fundamental problem,' he said, 'which Faraday called up anew for discussion, was the existence of forces working directly at a • distance, without any intervening medium. Its solution was the primary object Helmholtz had in view.

Did a medium veritably exist ? Was electrical action carried on intelligibly by means of stresses and strains in a real although intangible substance, or unintelligibly, magically, across void space ? Long and laborious investigations finally satisfied him that Faraday's divinatory instinct had guided him to the truth that as regards electrical processes the root of the matter is in the medium. The manner of its constitution is another and a still more subtle question, which he did not pretend to answer; but he set on foot suggestive inquiries as to its relations with ponderable matter, thus preparing the way for that complete theory of them which science demands from the future.

The novel idea of electrical convection originated with Helmholtz in 1876. It means that the bodily transport of a charged conductor has the same effect as a current through a stationary conductor. The experimental proof of this equivalence was wrought out in Helmholtz's laboratory by Henry Rowland, of Baltimore, eminent as a solar spectroscopist. "Convection 'promises to be of vital importance in new views about magnetisation. The extension to electrodynamics of the mechanical principle of least action came later. It was achieved in a series of papers, beginning in 1886, and closing with his final communication to the Berlin Academy, June 14, 1894. Another, and not the smallest, of Helmholtz's services to electrical science was indirectly rendered. For it was he that inspired the labours of Heinrich Hertz. Hertz was his favourite pupil. 'I have ever regarded him, he wrote after his early death, as the one who had penetrated furthest into my own circle of ' scientific thought, and it was to him that I looked with 'the greatest confidence for the further developement and • extension of my work.' By a prize question, proposed in 1879, Helmholtz deliberately set Hertz upon the track which led to his great discovery of electrical ether-waves, and he reported on it to the Academy in 1888, in highly impressive terms, and with a countenance glowing with satisfaction. Few deplored his loss more keenly. He saw in him, as it were, typified, 'the victory of the soul over the opposing * powers of nature.' 'In him we found all the qualities * required for the solution of the hardest problems in science. · Heinrich Hertz appeared predestined to disclose new vistas • into the unpenetrated depths of nature; but all these hopes 6 were crushed by the insidious disease which destroyed the life we esteemed so valuable.'

He was nearing his own end when he wrote these lines. Hertz died on the first, Helmholtz did not live to see the last day of 1894.

* Helmholtz, preface to Hertz’s ‘Principles of Mechanics,'translated by Jones and Walley. 1899.

His promotion of dynamical knowledge consisted first in giving the widest possible application to the principle of least action, next and most conspicuously in his researches on vortex motion in fluids. Here he struck a rich lode overlooked even by Lagrange. So far only a small part of its contents has been brought to light; yet it sufficed to alter profoundly our conceptions of nature. The results obtained by Helmholtz were employed by Lord Kelvin in his vortex-ring' theory of matter; from them Professor Fitzgerald evolved a 'vortex-sponge’ hypothesis of the ether. Neither probably corresponds closely with actual facts, but each represents an intrepid attempt to scale an eminence. It was at any rate shown that ultimate atoms might be absolutely unlike Dalton's hard, round entities, arbitrarily assumed to be indivisible. Ideas respecting them acquired elasticity and variety, and an untrodden field of possibilities was seen to stretch away to an indefinite horizon.

Helmholtz left his mark in passing, so to speak, upon meteorology. He not only lectured on water-spouts, and traced out mathematically the movements of the air, but originated what may be termed the wave-theory of cloudformation. It was suggested to him by the spectacle of a great floccular area lying beneath and around the RighiKulm. The oceanic analogy was obvious; and as oceanwaves are raised by the friction of wind with water, so it might plausibly be inferred that atmospheric waves must be generated by the gliding, one over the other, of airstrata, differing in density because of their different temperatures. Then, with the listing of each crest, a condensation of aqueous vapour would, under favourable circumstances,

Considerable support has been lent to this rationale by observations from balloons; and it has lately been transplanted to solar physics with a view to solving the enigma of the photospheric cloud-shell.

Among other topics treated of by the Admirable Crichton of modern science '* were the 'anomalous dispersion of light, tidal friction, glacier-motion, aeronautics, human locomotion. He threw out the idea of cigar-shaped balloons; and, from telescopic observations at his laboratory window, of pedestrians in the streets of Königsberg, detected several mistakes made by Weber in his analysis of the movements of the limbs. His corrections were long afterwards verified by instantaneous photography. As a more serious task, he

* Rücker, Lecture at the Royal Institution, March 8, 1895. VOL. CXCII. NO. CCCXCIV.

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improved the theory of the microscope, and fixed the minimum visible at the top of an inch. The limitation is due to diffraction, or the shattering of the light-waves at the edges of the objects under scrutiny. Helmholtz ascribed to geometrical axioms merely an experiential value, and he was one of those who keep an open mind regarding the number of dimensions in space.

As a popular lecturer, Helmholtz has never been surpassed. He had indeed, in Germany, the arena almost to himself, the dignity of science, as it seemed to most of bis contemporaries, requiring its seclusion within the halls of universities. Its wide diffusion struck him, on the contrary, as a prime desideratum. His expositions were not of the facile kind. Admirably lucid, they were, none the less, pitched too high for the purpose of simple intellectual diversion. They demanded, and amply deserved, sustained attention. He drew his audience, as has been well said, up to his level, instead of letting himself down to theirs. Hence his discourses were of lasting value. They could afford to dispense with the charm of the spoken word. They appealed to deliberate readers quite as effectively as to cultivated hearers. They belong, in short, to the best class of general scientific literature. Their circulation in print has, accordingly, been very large. They were issued in two series, extending over thirty-seven years; and the final address, delivered on the occasion of his Jubilee in 1891, has a special interest from its autobiographical character. The title of the latest English edition is included among the headings to this article.

Helmholtz married in 1849 Olga von Velten, of Potsdam. She died in 1859, leaving a son and daughter. Both survive. The former is an engineer at Munich, the latter became the wife of Dr. Branco, the Suabian geologist. Another son and daughter were the offspring of a second marriage contracted in 1861 with Anna von Mohl, a lady of high position in Würtemberg. Great hopes were entertained of a brilliant future for Robert von Helmholtz. His career seemed likely to furnish a worthy sequel to his father's; but he died in 1889, when scarcely seventeen years of age, his renown unfulfilled.' The daughter married a son of Werner von Siemens.

Helmholtz led a quiet domestic life, enlivened by the sedate gaiety of thronged musical receptions. The best

* Kronecker, 'The Electrician,' August 28, 1891.

artists in Berlin esteemed it an honour to perform at his house; and he himself sang tastefully, and played Bach's fugues on a magnificent piano, presented to him by the Steinways of New York in recognition of his services to musical art. He was a frequenter, too, of the Bayreuth Festivals, and usually proceeded thence to the Engadine, where he revelled in Alpine scenery and cogitated over Alpine problems. His first trip to this country, in 1854, was in many ways memorable to him.

'England,' he wrote to his friend Carl Ludwig, ‘is a great land, and one feels there what a magnificent thing civilisation is, and how the minutest conditions of life bear its impress. In comparison with London, Berlin and Vienna are mere villages. To describe London is impossible; it must be seen with one's own eyes before one can attempt to form an estimate of it. A visit to London marks an epoch in one's life; after such a visit, one learns to judge human actions on a scale hitherto unknown.' *

Three weeks' sight-seeing were not enough-according to his strenuous view of his duty as a tourist-to show him half the big town; but he met Faraday, Stokes, Sabine, Grove, Airy, Andrews, Rowan Hamilton, stayed with Bence Jones at Folkestone, where he picked up his early associate, Du Bois Reymond, and attended the meeting of the British Association at Hull. He then

Spent eight days in Scotland, to feast on nature. Edinburgh,' he continues, is a jewel among cities. The Scotch Highlands have a peculiar majesty, from their proximity to the Atlantic Ocean; but they are, on the whole, barren and monotonous, and not to be compared with the Alps. I saw Fingal's Cave in beautiful weather, then unceasing rain compelled me to return. I travelled home vid Hull and Hamburg, and arrived with a very empty purse.'

With Lord Kelvin he formed subsequently a close and lasting friendship, and was often hospitably received by him at Glasgow. An eavesdropper with a phonograph might surreptitiously have made a fortune by recording their conversations; but none, to the world's loss, was at hand. We may be sure that they left no stone of the cosmos unturned in their eager search for truth.

Imperial favours were freely bestowed upon this illustrious German. The Emperor William admitted him to private colloquies; the ennobling preposition was added to his bourgeois name in 1883; he was on terms of intimacy with the Crown Prince and Princess (the present Empress

+ M'Kendrick, loc. cit. p. 90.

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