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Helmholtz's brief but stimulating instructions. He himself was on one occasion taught by him, with patient care, to fashion a myograph out of a cigar- box, some knittingneedles, cork, sealing-wax, and glass-plates.* It was a long job, but, doubtless, a most remunerative one as regards technical training.

Dr. M'Kendrick remarks, in the useful little work named at the head of this article, that,

Helmholtz did not, like many, lose time in doing second-rate work that others, perhaps, could have done better. His scientific instinct appeared to guide him often into what are termed virgin-fields. Thus he had the great satisfaction of collecting the first-fruits, and he usually gathered so well as to leave little for others who came after him. Hence the researches and discoveries that were announced in rapid succession were always epoch-making, and always in a special sense his own. (P. 59.)

His first performance at Königsberg was the measurement of the transmission-rate of nervous impulses. It was generally regarded half a century ago as all but instantaneous. Johannes Müller despaired of its experimental determination. The conditions of the problem appeared to be such as to baffle anv available method. Helmholtz solved it by the aid of an ingeniously devised myographion,' a small induction coil, and a frog's leg. The batrachian speed for motor action proved to be 90 feet a second, the human speed 115 to 130 feet. Sensory impressions are more difficult to manage. Their investigation demands the cooperation of an intelligent subject; it is hence practicable only in man. Modifying his arrangements accordingly, Helmholtz found that nervous stimulation travels to the brain at rates varying from 160 to 320 feet a second. Its velocity is increased by heat, diminished by cold, and changes with electrical conditions. Possibly it is different in different individuals, but we cannot agree with Dr. MʻKendrick that the phenomenon of personal equation' is referable to this cause. In Dr. Maskelyne's time an assistant lost his place at the Royal Observatory because he noted star-transits a second later than the Astronomer Royal. The defect was ineradicable: he could not hurry up his perceptions. Bessel in 1823 first recognised such diversities as a source of error to be eliminated from observations, and, by systematising, rendered them innocuous to

* The Electrician, August 21, 1891.

accuracy. They probably depend upon brain-quality, not upon nerve-conductivity.

* In 1851,' Dr. M‘Kendrick tells us (p. 71), 'Helmholtz conferred an inestimable benefit on bumanity, and handed his name on to posterity, by the invention of the ophthalmoscope. Had be done little else in his long life-time, his name would never be forgotten; and yet the invention of this instrument took its origin, not in any profound investigation, but in the desire to exhibit a physiological phenomenon to his students.'

Here we ineet one of the felicities of his mental constitution. Teaching is not to most men a stimulating pursuit. Rather it tends to cramp the originative faculty, and to clip the wings of genius. Time devoted to it counts negatively, as a rule, in a career of research. Not so with Helmholtz. The process of imparting knowledge to others showed him how to seek it for himself. Between him and his pupils a sort of reciprocal action arose. Their intellectual needs were the beacons of his advance. Some of his largest inquiries and finest contrivances sprang from the fecund inspirations of the lecture-room. The search for means to expound ascertained truths set him upon the track of many previously unknown. As he himself said long afterwards :

• A teacher in a university is subject to excellent discipline, in that he is obliged each year, not only to give at least an outline of the whole of his science, but also to convince and satisfy the clear heads among his hearers, some of whom will be the great men of the next generation. This necessity was most beneficial to myself. In preparing my lectures, I was led to devise the method of measuring the velocity of the nervous impulse, and also to the conception of the ophthalmoscope. This instrument became the most popular of my scientific achievements; but good fortune, rather than any personal merit, favoured me in its invention.'

Cats' eyes notoriously "shine in the dark,' and so, in varying degrees, do the eyes of men and other animals. But no light is emitted by them. The property depends upon the presence of a reflective apparatus behind the lenses. Helmholtz turned it to account for the purpose of seeing into the eye. Delicate contrivances were needed; but his precise intuition of their nature, combined with iron perseverance, enabled him to realise them successfully. When Von Graefe, the great ophthalmologist, first surveyed the fundus of the living human eye, its optic disc and blood-vessels all distinctly visible, it is related that his

face flushed with excitement, and he cried, “Helmholtz

co has unfolded to us a new world. What remains to be ““ discovered ?")* His enthusiasm was scarcely excessive. Diseases of the eye had until then been treated quite casually. No diagnosis of them was feasible. Now at last ophthalmic medicine assumed a scientific character, to the untold benefit of humanity. Charles Babbage seems to have very nearly anticipated Helmholtz in the invention of the ophthalmoscope. His instrument, shown privately to Wharton Jones, was, however, never brought to perfection.f

The publication of Helmholtz's great work on ‘Physio* logical Optics'occupied ten years (1856–1866). It embodied a surprising variety of novel and authentic results. The secret of visual accommodation was shown in it to consist in alterations of curvature in the crystalline lens, according to the distance of the objects viewed. Coloursensation was largely treated of, the mechanism of binocular vision was laid bare, the causes of colour-blindness were discussed from the standpoint of specific nervous sensibility. As an optical physiologist Helmholtz was the direct successor of Thomas Young.

From light he proceeded to sound-from the study of the eye to the study of the ear. His treatise on " Tone

Sensations, published in 1863, revolutionised the subject. Lord Kelvin assigns to it a unique position in the literature of philosophy.’I It includes, as he says, ' mathematical and experimental investigations on the inanimate external · influences concerned in sound, investigations of the anatomical structure of the ear in virtue of which it perceives sound, and applications to the philosophical foundation of the musical art.' And Clerk Maxwell, in the Rede lecture for 1878, pronounced Helmholtz, by a series of daring • strides,' to have effected a passage over that untrodden 'wild between acoustics and music—that Serbonian bog ' where whole armies of scientific musicians and musical ' men of science have sunk.'s

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He had rare qualifications for the enterprise. That inner sense for music which the abstrusest speculations cannot give, and which roasting in sulphur' cannot remove, was his by nature; he took double-first rank as a physicist and physiologist; his experimental instinct was sure; and he had a reserve of mathematical power that lent impetus to

* M'Kendrick, loc. cit. p. 83.

Ibid. p. 77.
† Proc. R. Society, vol. lvii. p. 40.
f Life of Maxwell, Campbell and Garnett, p. 363.

every movement of his mind. Yet his attempt to bridge the gap between science and art had but a scanty measure of success. No one, however, doubts that the enjoyment of music is based on sensations of the simplest kind, and of these Helmholtz found the true physiological explanation. He showed that discords offend the ear through an actual roughness of the vibrations producing them, very much as a harsh surface grates upon the touch. The obnoxious effect is due to sub-audible beats,' resulting from the interference of the dissonant notes or their overtones. The nerves are distressed by an uncomfortable feeling of discontinuity; they demand the repose of the smooth flow given by harmonious combinations.

But this rationale of discords and concords does not touch the real problem of æsthetic preferences. Rising out of the material relations of music there is something that transcends them. For the divine enters into everything that is human. This supernal element mingles with our pleasure in listening to the commonest folk-tune; it confronts us in the poignant pathos of Millet's ' Angelus,' in the haunting sadness of Tennyson's ' Down the Valley of 'Cauterets; ' it overwhelms us in great architecture, in the Hallelujah Chorus, in the Tannhäuser' overture. Yet it evades, and must always evade, analysis ; the progress of science can bring us no nearer to a knowledge of its essence. On this point Helmholtz was under no delusion. These • phenomena of agreeableness of tone,' he remarked, 'as • determined solely by the senses, are of course merely the • first step towards the beautiful in music. And he rose to enthusiasm in describing how the stream of sound' carries with it into the hearer's soul unimagined moods • which the artist has overheard from his own, and finally • raises him up to that repose of everlasting beauty of which . God has allowed but few of His elect favourites to be the • heralds.

The detection of the part assignable to beats' in music was, however, only one of his many contributions to physiological acoustics. His investigation of vowel-sounds was a masterpiece. His predecessors, Wheatstone, Willis, and Donders, had shown their connexion with the varied developement of overtones ; Helmholtz gave the clinching proof, spoke the ultimate word on the subject. Following up analysis with synthesis, he decomposed the human voice,

* Popular Lectures on Scientific Subjects, vol. i. p. 93.

by means of his resonators,' into its elementary tones, then reproduced the different vowels by combinations of tuning-forks, each representing a constituent vibration. Further, the whole question of timbre' (Klangfarbe) was first exhaustively treated by him. Pure tones he found to be as difficult of reproduction as pure colours. One set of sound-waves is superposed upon another; the main disturbance starts half a dozen minor ones, and the diversified groups thus formed strike the ear as differences of quality, the actual corresponding objective fact being the variety in shape of the compound wave, resulting from the amalgamation of many simple waves of sundry periods. Hence the dissimilarity in effect between notes of the same pitch on the violin and fute, on the piano, the harp, or the human voice. The apparatus used by Helmholtz in these curious inquiries was supplied by Maximilian, King of Bavaria. Expenses were involved far beyond the modest means of a university professor.

The book be was royally aided to prepare appeared in an English translation by Mr. A. J. Ellis in 1875. Its merits can scarcely be exaggerated. It is many-sided, far-reaching, profound. We have done no more than pick out a few specimens from the stores of knowledge it contains. Nevertheless, its express purpose was not attained. The author adventured in it to interpret art-theories from the side of natural science.* They undeniably remained in statu quo. For this purpose the mechanism of the ear was vainly explored. The marvels of aural anatomy help in no way to elucidate questions connected with musical form or musical expression; it signifies nothing, as regards them, whether or no vibrators exist in the cochlea, what may be the function of the basilar membrane,' or how Corti's lyre of three 'thousand strings’t is concerned in transmitting the impulsions of the air. All that can be said is that, by the sagacity and thoroughness of the research, the 'so far and

no farther' was prescribed to the ambition of expounding art on the basis of sensation.

The Chair of Physics at Berlin became vacant by the death of Magnus, March 4, 1871. The choice of a successor to him lay between Kirchhoff and Helmholtz, and Kirchhoff was retained at Heidelberg by Grand Ducal authority. Helmholtz was then the inevitable man for the post. Yet

* Einleitung, October 1862.
+ Tyndall, Lectures on Sound, p. 409.

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