Febeuaky 7, 1896.] 



SCIENCE. 



193 



of the whole, and a series, more or less 

 complete and extended, of overtures or 

 harmonics, the vibration frequencies of 

 which are two, three, four or some other 

 multiple of that of the fundamental. With- 

 out these, the fundamental, though pure, 

 was plain, dull and insipid ; with them it, 

 formed a composite with quality, soft it 

 may be, or brilliant or rich or harsh, or any 

 of the thousand things which may be said 

 of a tone. Which it was and what it was, 

 was determined by the relative proportions 

 of the several overtones, indefinite in num- 

 ber, in the composite whole. This beauti- 

 ful hypothesis was illustrated and estab- 

 lished by innumerable experiments, and it 

 was proved that the form of the air wave was 

 the quality of the tone, and that this form 

 originated in the mode of vibration of the 

 sounding body, which was almost uni- 

 versallj' not simple, but complex. But, the 

 most important work of Helmholtz along 

 this line was the extension of this theory 

 to the solution of a problem more than two 

 thousand years old, proposed, in fact, by 

 the Greek, Pythagoras. It meant nothing 

 less than the physical explanation of har- 

 mony. Why are certain combinations of 

 musical tones agreeable and others un- 

 pleasant ? — and, indeed, the answer to this 

 tells as well, why a certain succession of 

 tones, as in a musical scale, is likely to be 

 generally acceptable to the human ear. 

 Lack of time will only permit me to say 

 that in the interference and consequent 

 beating of certain of the overtones or upper 

 partials, of two fundamentals, Helmholtz 

 found the explanation of their dissonance, 

 and that while in certain particulars his 

 theory as originally published has been 

 criticised, it is in general universally ac- 

 cepted and admitted to be one of the most 

 splendid contributions to modern science. 



I am warned, also, that I must not speak 

 of that other great work, the Physiological 

 Optics, as I would so gladly do if time per- 



mitted. Helmholtz was actually engaged 

 in the preparation of this and the ' Sensa- 

 tions of Tone ' during the same years. No 

 other man in the world could have written 

 these, for no other was at once an accom- 

 plished physiologist, mathematician and 

 physicist. While I cannot speak of his 

 contributions to the science of optics and 

 ophthalmology, I must not omit brief refer- 

 ence to his invention of the ophthalmoscope 

 and the ophthalmometer. Anxious to ac- 

 tually see what goes on in the eye, and es- 

 pecially on the retina, that wonderful 

 screen on which the image of the visible 

 world is focussed, he invented the ophthal- 

 moscope. The qualitative victory was fol- 

 lowed by the quantitative, in the invention 

 of the ophthalmometer, by means of which 

 accurate measurements of the various 

 curved surfaces in the eye could be made. 

 These two instruments have been to oph- 

 thalmic surgery what the telescope and 

 graduated circle have been to astronomy. 

 So exact has the science of the eye become 

 through their use that it is not great exag- 

 geration to say that one may now have a 

 disordered eye repaired, corrected and set 

 going with little more uncertainty than 

 attends the performance of the same duty 

 for an ill-conditioned chronometer. Had 

 Helmholtz accomplished nothing except the 

 invention of these instruments he would 

 have been entitled to the thanks of all 

 mankind, on account of the comfort they 

 have added to life and the pajn and suffer- 

 ing they have prevented. 



If I had devoted all of the time allotted 

 to me to a simple enumeration of the con- 

 tributions to human knowledge made by von 

 Helmholtz during fifty years of marvellous 

 intellectual activity I must have left my 

 task incomplete, but I must not close with- 

 out reference to one or two of these, more 

 purely physical in their character and 

 equally stamped with the genius of their 

 author. 



