Prof. A. M. Mayer's Researches in Acoustics. 525 



illuminated ; it has six distinct bright spots in it, beautifully 

 showing the six inflections in the curve. 



By sticking a pin in the centre of fig. 7 as an axis about 

 which revolves a piece of paper with a fine slit, the reader can 

 gain some idea of the complex motion which I have described. 



From the curves of figs. 4, 5, and 6 can similarly be repro- 

 duced their generating motions. Of course it is understood 

 that in all these cases the amplitudes of these vibrations are 

 enormously magnified when compared with the wave-lengths, 

 and that it is really only when the amplitudes of the elementary 

 pendulum-vibrations are infinitely small that the resultant 

 curves we have given can be rigorously taken as representing 

 what they purport to represent ; for the law of the " superposition 

 of displacements^ depends on the condition that the force with 

 which a molecule returns to its position of equilibrium is di- 

 rectly proportional to the amount of displacement, and this 

 condition only exists in the case of infinitely small displace- 

 ments; yet the law holds good for the majority of the pheno- 

 mena of sound. 



As a periodic vibration can alone produce in the ear the sen- 

 sation of sound, and as the duration of the period is always 

 equal to the least common multiple of the periods of the pen- 

 dulum-vibrations of the components, it follows that in the case 

 of a simple sound, or of a sound formed of an harmonic series, 

 the period equals the time of one vibration of the funda- 

 mental ; but in the case of any other combinations the duration 

 of the period of the recurring vibration increases with the com- 

 plexity of the ratio of the times of vibration of the components. 

 Thus the durations of the following combinations are placed after 

 them in fractions of a second — 



C 3+ C 4= 2 -k> ^+63=^03 + 13=^, C3 + E 3 +G3=^, 



C s + E 3 + G3 + C 4 = T y of a second. 



The above-mentioned facts suggest a curious physiological 

 inquiry, viz. Does it require a combination of sounds, simple 

 or composite, to remain on the ear the duration of an entire 

 period in order that it shall give the same sensation as is pro- 

 duced when the same combination is sounded continuously ? In 

 other words, will a portion of the recurring composite vibration 

 produce the same sensation as an entire period or several periods ? 

 The solution of this problem has been the object of a prolonged 

 experimental research ; but up to this time the results have been 

 so difficult of interpretation that I have not arrived at any cer- 

 tain knowledge on the subject. I shall, however, return to this 

 interesting but very difficult work. 



Stevens Institute, Hoboken, N. Jersey, U.S.A. 



