364 Prof. A. M. Mayer's Researches in Acoustics. 



ment of Young's hypothesis of three distinct sets of retinal 

 nerve-terminations ? The more we study the minute structure 

 of the retinal rods and cones, the further appears to remove an 

 understanding of the mode of operation of the sensory apparatus 

 of the eye. May not research in this direction be guided by the 

 hypothesis that the molecular constitution of the retinal rods 

 and cones is such that their molecules are severally tuned to the 

 vibrations corresponding to the colours red, green, and violet ? 

 This would lead us to look for effects of actinism on the retina 

 as showing the link existing between the transmitting and sen- 

 sory functions of the eye. Do not the facts of the known per- 

 sistence of chemical action, after it has been once initiated, and 

 the time which would be required for the retinal molecules to 

 recombine, or rearrange themselves, after the setherial vibrations 

 had ceased, comport with the known durations of the residual 

 visual sensations, and with the main facts of physiological 

 optics, better than the hypothesis that masses of the retinal 

 elements are set in vibration rather than their molecules ? 



5. Quantitative Applications of the Laws to the fundamental facts 

 of Musical Harmony. 



To show the full value of these laws in introducing quanti- 

 tative precision in the explanations of consonance and dis- 

 sonance would require an extended space ; we here present only 

 such application as will serve to show their importance in giving 

 clear and simple guides in reasonings in the physiological theory 

 of musical harmony. 



We have seen that 26 beats of the simple sound C v of 64 

 vibrations per second, give a continuous sensation ; therefore, to 

 determine the nearest consonant interval of this note, we have to 

 obtain a sound which will make with Cj the vibration-ratio of 

 64: 64 + 26. This would show that the nearest consonant in- 

 terval of C 1; on the natural scale, is its fourth plus § of a semi- 

 tone. The duration of the residual sensation of Ut 4 is -j-|- of a 

 second; hence, to determine by our law the nearest consonant 

 interval of Ut 4 , we must combine with it a note which will give 

 with Ut 4 the vibration-ratio of 512 : 512 + 130. This note is 

 the E above C 4 — that is, its major third. In the following Table 

 we give the determinations of the nearest consonant intervals of 

 the Cs throughout five octaves* : — 



* We have, for simplicity of illustration, determined the above intervals 

 on the basis of the pitch of the lower note ; but as the beats are produced 

 by the conjoined action of the two sounds, it would have been more accu- 

 rate to have taken, as a second approximation, the mean pitch of the two 

 sounds. Thereby the above determinations would be somewhat changed 

 for lower, but not perceptibly for higher notes. 



