March 14, 1^95] 



NA rURE 



47: 



for many years made it his habit to place every physical paper 

 published liy Helmhohz within the reach of En^^lish readers. 



And now, hiving brought you to the po^nt at which llelm- 

 holtz may be said lo have been fairly started on hii life's work, 

 let me first briefly describe his official career, before I consider 

 his work in greater detail. 



When his extraordinary abilities became evident, he was per- 

 mitted to sever his connection with the army. At tweniy-seven 

 years of age he became Teacher of Anatomy in ihe Academy of 

 Arts at Berlin. In the next year he was appointed Professor of 

 Anatomy and Physiology at Konigsberg, and he held similar 

 posts in the Universities of Bonn (1855-58) and Heidelberg 

 (1858-71). It was not till 1S71 that his early love for physics 

 was finally rewarded. When the chair of Physics was to be 

 filled in the University of the newly-founded German Empire, in 

 Berlin, it was (eh that even in Germany — the land of specialists — 

 no better occupant could be found than one who was then in his 

 fiftieth year, and had been all his life a teacher of anatomy and 

 physiology. The choice was universally approved and com- 

 pletely justified, and von Helmholtz held this post till his dfath. 



In this connection I am, by the kindness of .Sir Henry 

 Roscoe, enabled to show to you a relic of remarkable interest. It 

 is a photograph of the great teacher and investigator, taken at 

 the very last lecture that he delivered— that, namely, on July 



7. 1894- 



For some years, that is, from:the date of its foundation, von 

 Helmholtz was the president of the Physikalisch-Technische 

 Reichs-Ansialt in Chatlottenburg. This institution, founded 

 partly by the munificence of the late Dr. Werner Siemens, partly 

 by funds supplied by the State, has no precise analogue in this 

 country. It is devoted to the carrying out of systematic 

 researches on questions of fundamental importance to which a 

 long time must be devoted. 



The most characteristic work of Helmholtz was, as I have 

 already hinted, that in which his knowledge of physics and his 

 knowledge of anatomy were both directed to a common end. 

 He dealt in turns with the external physical phenomena, with 

 the mechanism of the organs which the phenomena affect, with 

 the relations between the mechanical effect on the organ and 

 the sensations which it excites, and, lastly, with the connection 

 between the sensations in those simple cases which can alone 

 be investigated in the laboratory, and the complex laws of 

 .^.-sthetics and art. 



The two books in which these problems were chiefly treated 

 were the "Physiological Optics," and the "Sensations of 

 .Sound." It is impossible to do more than lay before you a 

 sample which may afford some idea of the intricacy of the 

 problems with which he dealt, and of the pitfalls amongst 

 which he walked so warily. For this purpose I have chosen 

 one branch of his work on "Sound." 



I have deliberately selected that particul.ar portion which has 

 been most questioned, that on which the verdict of most of 

 those who have sat in judgment on his views has been against 

 him. 



In discussing this question I must give a general description 

 of the principal phenomena ; but if I were to attempt an 

 exhaustive catalogue of all the facts disputed and undisputed, 

 and of all the theories which have been based upon or upset by 

 them, not only would time fail me, but those who have not 

 given special attention to the subject would, I fear, become 

 hopelessly confused amid the chaos of opposing statements and 

 views. Another reason which urges me to be brief, is that a 

 few years ago Prof .Silvanus Thompson explained the whole 

 subject to the members of the Royal Institution, having kindly 

 consented to act as the mouthpiece of the celebrated instrument 

 maker, Konig, who has played so large a part in these con- 

 troversies. 



Among the chief achievements of Helmholtz was an ex- 

 planation of the physical ditTerence between pairs of notes 

 which we recognise as concords and discords respectively. 

 When two neighbouring notes are sounded, alternate swellings 

 .ind fallings off of the intensity are heard, which are calleii 

 beats. These produce an unpleasant effect, which depends 

 partly on their number, partly on the relative pitches of the 

 beating notes. When two notes beat badly, ihtry foim an in- 

 tolerable discord. When they become separated by a wider 

 interval, the beats are so rapid that they cease to be unpleasant. 



The sense of dissonance produced by many of these wider 

 intervals, such as the seventh (4 : 7), requires further explana- 

 tion. In general, the fundamental musical note is only the first 



NO. 1324, VOL. 51] 



and loudest of a series of so-called partials, whose vibration 

 frequencies are 2, 3, 4, &c. , times that of the fundamental, 

 and the consonance and dissonance of two notes is shown to 

 depend on the presence or absence of beats between important 

 members of these series. Thus in the case of the seventh the 

 frequencies of the octave of the lower note and that of the 

 upper note would be in the proportion 8 : 7, which are 

 sufficiently near to make the beats very prominent and 

 disturbing. 



In cases where the notes are pure, that is, are not accom- 

 panied by upper partials, the explanation of dissonance is 

 based upon another phenomenon. 



When two notes are sounded simultaneously a third tone is 

 often perceived, the frequency of which is equal to the differ- 

 ence of their frequencies. The number of vibrations of this 

 tone is equal to the number of beats, and as there has been con- 

 troversy as to whether the beats when they become rapid can 

 produce a note, and if so, whether this note is or is not the same 

 thing .as the difference tone, it is necessary to distinguish 

 between the two. This distinction is to be found in the mode 

 of their production ; but for the moment it is sufficient to re- 

 member that they may be distinguishable, and to reserve for 

 them two name=, viz. the beat-note, and the first difference 

 tone respectively. 



Helmholtz drew attention to the fact that together with the 

 difference tone there is also produced a note, the frequency of 

 which is equal to the sum of those of the two primaries, and this 

 he called the first summation-tone. 



Together with these he believed that there existed summation 

 and difference tones of higher orders, the whole series being 

 included under the name of combination tones. Our sense of 

 dissonance between pure notes was explained as dependent on 

 beats produced by the combination tones. 



Up to the time of Helmholtz it was generally thought that 

 these tones were produced in the ear itself, and had no objec- 

 tive existence in the external air. They are thus often called 

 subjective, but as that adjective is usually reserved for impres- 

 sions produced in the brain itself, it is better to say that they 

 were regarded as c.ir-made. Helmholtz himself gave a theory, 

 which showed that it is probable that a membrane like the 

 drum-skin of the ear, which is forced out of shape by pressure, 

 and that bones, like those in the ear, which can rattle, would, 

 if acted upon by two notes, manufacture by their own proper 

 movements all the varied combinational tones which his theory 

 postulated. He therefore believed that combinational tones 

 were largely ear-made, 



V'ou will observe that his theory of discord is quite unaffected 

 by the question whether the combination tones are or are not 

 sometimes objective. Provided only they are produced at all, 

 it is immaterial whether they are produced in the ear itself. 

 Von Helmholtz admitted that the phenomena we observe are in 

 most cases ear-made tones ; but h-.' also asserted that they were 

 sometimes objective, and could set bodies tuned to vilirate with 

 them in resonant motion. Ibis latter statement has been 

 denied with singular unanim.ily, sometimes, I think, without 

 due regard to the limitations which Helmholtz himself placed on 

 the conditions under which the objective character of the notes 

 can be realised. 



All ordinary calculations .is to the production and mingling 

 of different waves of sound are based upon the supposition that 

 the displacements of the particles of air, or other body through 

 which the sound is travelling, are very small. If this is so, the 

 force which tends to restore each disturbed particle to its 

 ordinary position of equilibrium is accurately proportional to 

 the amount of the displacement. 



In von Helmholtz' view, objective combination tones were 

 in general produced when the disturbance was so great that 

 this condition was no longer fulfilled. Violence is of 

 the essence of the explanation. Hence the siren, where 

 both sets of holes open into the .same small wind- 

 chest — the harmonium, in which two reeds alternately cIjsc 

 and open slits in the same enclosure, are the instruments best 

 suited to produce them. Of these the siren is the more efficient. 

 Von Helmholtz convinced himself that the coml)inatinn tones 

 produced by the harmonium are for the most part ear-made. 

 He expressly slated that "when the places in which the two 

 tones are struck are entirely separate and have no mechanical 

 connection, as, for example, if they come from two singers, two 

 separate wind instruments, or two violins" — to which wc may 

 add two tuning-forks — " the reinforcement of the combinational 



