HELMHOLTZ. 791 



which gives charm to it, was really due to its impurity; that if two 

 perfectly pure tones, generated by simple, pendular vibrations, agreed 

 in pitch and loudness, it would be quite impossible to distinguish them. 

 But practically, such toues are never produced; all ordinary tones are 

 composite, made up of the fundamental, which generally fixes the 

 nominal pitch 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. 

 Without 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 number, 

 in the composite whole. This beautiful hypothesis was illustrated and 

 established 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 universally 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 harmony. Why are certain combinations of 

 musical tones agreeable and others unpleasant? 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 accepted 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 permitted. 

 Helmholtz was actually engaged in the preparation of this and the 

 Sensations of Tone during the same years. No other man in the world 

 could have written these, for no other was at once an accomplished 

 physiologist, mathematician, and physicist. While I can not speak of 

 his contributions to the science of optics and ophthalmology, I must not 

 omit brief reference to his invention of the ophthalmoscope and the 

 ophthalmometer. Anxious to actually see what goes on in the eye, and 

 especially on the retina, that wonderful screen on which the image of 

 the visible world is focused, he invented the ophthalmoscope. The qual- 

 itative victory was followed 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 instru- 

 ments have been to ophthalmic surgery what the telescope and gradu- 

 ated circle have been to astronomy. So exact has the science of the 



