232 THE POPULAR SCIENCE MONTHLY. 



in its various physical connections, and especially in relation to the 

 theory of music. These researches are described in papers contained 

 in the American Journal of Science and Arts, and several of his impor- 

 tant conclusions have been incorporated in the English edition of 

 Helmholtz's " Sensations of Tone as a Physiological Basis for a The- 

 ory of Music." Mr. Alexander J. Ellis, F. R. S. (the translator of 

 the above work), has also recently published a lecture which he deliv- 

 ered before the London Musical Association, on the application of 

 Prof. Mayer's discoveries to the elucidation of the fundamental prin- 

 ciples of musical harmony. 



The chief claims of Prof. Mayer in regard to his recent acousti- 

 cal results may be concisely summed up as follows : 



1. He discovered that, by using the phenomena of sympathetic 

 vibration, one can show that the translation of a vibrating body 

 causes it to give sonorous waves, differing in length from those pro- 

 duced by the same vibrating body when stationary. 



2. He first succeeded in actually detecting the different phases of 

 vibration in the air surrounding a sounding body, and thereby meas- 

 ured the lengths of its waves ; and first experimentally explored in 

 the free air the exact form of any wave-surface ; and he has deter- 

 mined the forms of these envelopes around a sounding body with 

 as much facility as one can obtain the form of the surface of a pal- 

 pable body in the dark. 



3. He devised a simple and accurate method of measuring the 

 wave-lengths of sound in air and in gases, and was the first to meas- 

 ure with precision the relative intensities of sounds by means of 

 manometric flames. 



4. He first approximately determined the mechanical equivalent 

 of an aerial sonorous vibration. 



5. He obtained in an experiment all the conditions required in 

 " Fourier's theorem," and thus first gave an exact experimental con- 

 firmation of it. 



6. He has devised and used Jive new methods of sonorous analy- 

 sis for the decomposition of a compound sound into its elementary 

 simple tones. He also first, by means of a rotating disk, reproduced 

 the vibratory motions of a molecule of air, when it is animated with 

 the resultant action of the six elementary vibrations forming a musi- 

 cal note. 



7. He first discovered, by delicate experiment, that the fibrils of 

 the antennae of the male mosquito vibrate sympathetically to notes 

 which have the range of pitch of the sounds given out by the female 

 mosquito. He also showed first how an insect may determine the 

 direction of sounds by means of his antenna?. 



8. He discovered that the terminal auditory nerve-fibrils vibrate 

 half as often in a given time as the membrane of the tympanum and 



