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 important conclusions have been incorporated in the English edition of Helmholtz's “Sensations of Tone as a Physiological Basis for a Theory of Music.” Mr. Alexander J. Ellis, F. R. S. (the translator of the above work), has also recently published a lecture which he delivered before the London Musical Association, on the application of Prof. Mayer's discoveries to the elucidation of the fundamental principles of musical harmony.
The chief claims of Prof. Mayer in regard to his recent acoustical 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 produced 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 measured the lengths of its waves; and first experimentally explored in the free air the exact form of any wave-surface; and he has determined the forms of these envelopes around a sounding body with as much facility as one can obtain the form of the surface of a palpable 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 measure with precision the relative intensities of sounds by means of manometric flames.
4. He first approximately determined the mechanical equivalent of an aërial sonorous vibration.
5. He obtained in an experiment all the conditions required in “Fourier's theorem,” and thus first gave an exact experimental confirmation of it.
6. He has devised and used five new methods of sonorous analysis 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 musical note.
7. He first discovered, by delicate experiment, that the fibrils of the antennæ 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 antennæ.
8. He discovered that the terminal auditory nerve-fibrils vibrate half as often in a given time as the membrane of the tympanum and
