356 Prof. A. M. Mayer's Researches in Acoustics* 



the mechanical appliances of our experiments ; for the average 

 difference in the measures of the duration of any one residual 

 sensation did not exceed the ^^o q °f a second. The perforated 

 disk made 3f revolutions to one of the driving-crank; and if the 

 disk has twelve perforations, then the above difference of -4-$^ 

 of a second is given by the difference between two observations, 

 in one of which the driving-crank made 30 revolutions in ten 

 seconds, and in the other made 29 revolutions in the same time. 

 It is evident that the apparatus readily detects this difference, 

 especially as I often ran it during thirty seconds to obtain the 

 number of beats striking the ear during one second. 



Before accepting as final the above determinations, I ascer- 

 tained that great differences in the intensities of the pulses had 

 little effect on the number of beats required to produce a conti- 

 nuous sensation. When a great increase in intensity was given 

 to the pulses, their number had to be slightly increased to pro- 

 duce the same continuous sensation as that experienced with 

 feebler pulses ; but the difference was barely measurable. It is 

 also important to remark that, after the blending of the pulses 

 has been once attained, a further increase in the velocity of the 

 disk does not change the character of the sensation. Extreme 

 velocities, of course, produce such violent agitations at the mouth 

 of the resonator as to render experimenting impossible. 



I have projected the above determinations into the accompa- 

 nying curve (fig. 2), placing on the axis of abscissae the numbers 

 of vibrations of the various sounds, as designated at the base of 

 the figure, and on the ordinates the corresponding durations of 

 their residual sensations. Thus has been obtained the full-lined 

 curve of the figure. The dotted curve is an equilateral hyperbola, 

 and expresses an assumed law — -that the durations of the resi- 

 dual sensations are inversely as the numbers of vibrations pro- 

 ducing them. In drawing the latter curve, I took the point 

 corresponding to the ordinate of Ut 3 as the basis of the assump- 

 tion. 



From the discussion of the curve of the experiments, we find 

 that the law connecting the pitch of a sound with the duration 

 of its residual sensation may be expressed thus, 



D =N?li ,+ - 0023 ' 



in which D equals, in fractions of a second, the duration of the 

 residual sonorous sensation corresponding to N number of vibra- 

 tions per second. 



We have already spoken of the difficulty of the determination 

 of the residual sonorous sensations by reason of the complex 

 character of the sound perceived when the vibrations of a tuning- 



