284 REPORTS ON THE STATE OF SCIENCE, ETC. 



ever, was located somewhat higher — between 3,000 and 7,000 cycles, results 

 varying for different observers. 



Mackenzie (33) made use of a princijjle similar to that of optical flicker. 

 Mackenzie found that if two frequencies alternated in the ear at a fairly 

 rapid rate, the interruptions of the louder were more conspicuous than 

 those of the weaker. It was possible to adjust the intensities until the two 

 tones appeared equally interrupted ; at this point the respective loudnesses 

 were taken as equal. A comparison of the physical values of the tones 

 thus balanced showed that except at weak intensities, where room-noise 

 was held to have an interfering effect, the relative sensitivity of the ear was 

 invariable over the whole hearing range. 



Knudsen (29) also used an alternation method, whereby two intensities 

 of the same tone were alternated at the rate of about fifty changes per 

 minute, the difference between them being decreased or increased until 

 the ' flutter ' ceased or began to be apparent. The value of the difference 

 threshold was shown to decrease continuously with rise in intensity, until 

 a constant value was reached. The point at which the curve flattened in 

 this way was shown to vary for different frequencies, but on the whole the 

 value of the threshold seemed to be independent of frequency. Knudsen 

 also drew up a generalised equation intended to serve as a truer expression 

 of differential sensitivity, and showed that computed values of the threshold 

 based on this formula agreed fairly well with his experimental results. 



Knudsen's results share with those of Riesz (46) the distinction of having 

 been used by subsequent investigators as the basis of theoretical considera- 

 tions and calculations. Riesz measured differential intensity sensitivity by 

 determining for a tone of given frequency and intensity the minimal intensity 

 to which a second tone, differing from the first by 3 cycles per second, had 

 to be raised to make the beats just perceptible. Twelve observers each 

 worked with seven tones ranging from 35 to 10,000 cycles ; the whole 

 range of intensities, from the absolute threshold to near the threshold of 

 feeling, was covered. The general conclusion as regards Weber's law was 

 that it held at all frequencies for intensities above 10® times the absolute 

 threshold value. Curves showing the difference threshold plotted against 

 a logarithmic intensity scale seem to confirm this, unless the threshold axis 

 is itself logarithmic, in which case the curves do not seem to flatten per- 

 ceptibly at any point of the intensity scale. This observation, however, is 

 based on replotting some of the data of smoothed curves, and as such is no 

 doubt open to question. 



Telford and Denk (55) confirmed Riesz's results rather closely for one 

 frequency (800 cycles). The form of the curve obtained was almost 

 identical with those of Riesz, but the apparatus used was such as to make 

 measurement of intensities in terms of db level impossible. Further, for 

 some reason not very apparent, thresholds were calculated from the formula 

 (1 2^ — Ii^)/Ii^, where Ij and 1 2 were the lower and higher intensities 

 respectively. 



(v) The work of Macdonald and Allen (32, 2) shows a departure from 

 recent practice in that the sounds studied were variator tones, of which 

 the intensities were measured in terms of blowing pressure. The authors 

 follow Merkel and others in their recommendation that the reciprocal of 

 the threshold be used as a measure of sensitivity, so that a higher numerical 

 value would indicate heightened sensitivity. The main finding was that 

 Weber's law did not hold, since a plot of the reciprocal of the threshold, 

 against intensity fell into two distinct parts. A new empirical equation 

 was suggested as holding good (with appropriate changes of constants) for 

 hearing not only under normal conditions, but also under conditions of 



