QUANTITATIVE ESTIMATES OF SENSORY EVENTS 283 



' terminal stimuli.' Merkel's results suggested that this mid-point lay 

 nearer the arithmetic than the geometric mean of the terminal values, while 

 Angell found the opposite to be true. Angell's result is in accordance with 

 the requirements of Weber's law and Fechner's derivatives ; Merkel's, on 

 the other hand, would seem to support Plateau's ' quotient-hypothesis ' 

 described by Brown and Thomson (7) as the ' one-time chief rival of the 

 Weber-Fechner law.' This theory postulated direct proportionality between 

 the just noticeable difference of sensation and that of stimulus, and at one 

 time had many supporters, though later Plateau himself repudiated it. 

 The Merkel-Angell controversy attracted a good deal of attention, e.g., 

 from Ament (3), who showed that the values of the mid-stimulus were a 

 function of both the ratio between and the absolute values of the terminal 

 stimuli. 



The work of the Leipzig group was summed up by Wundt himself (60), 

 who believed that hearing was the sense-department in which Weber's law 

 was of the widest application. At the same time he admitted that the 

 method of mean gradation seemed to yield mean values closer to the 

 arithmetic than to the geometric mean. 



Though not strictly belonging to the same group, the work of Hoefer (22) 

 and Keller (24) may conveniently be included in the present section. 

 Hoefer studied auditory differential sensitivity among individuals suffering 

 from psychoses and functional neuroses. SulDnormal sensitivity was found 

 only in a few cases, though flagging of attention was often evident. Keller, 

 using a modification of Mosch's method, found that Weber's law held good, 

 with a mean value of about t'o> ^s against the figure of J usually found by 

 previous investigators. Keller also believed that the Gaussian law of error 

 did not hold in psycho-physical experiments, so that methods involving its 

 application were to be avoided. 



(iii) All the work discussed so far was concerned with unpitched sounds. 

 Wien (59) was the first, by nearly twenty years, to work with tones. These 

 were produced by electrically-driven tuning-forks of three frequencies, and 

 the intensity range was much the greatest of any in the early researches. 

 A resonator, covered with the membrane of an aneroid barometer, served 

 as an artificial ear-drum, by means of which the relative amplitudes of 

 vibrations could be measured with great accuracy. Wien's work is remark- 

 able not only in respect of its pioneer use of tones, but also in that on the 

 basis of his results he drew up an empirical equation for the diiference 

 threshold, which, in its integrated form, gave a curve for the relation between 

 stimulus and sensation surprisingly similar to that recently adopted as a 

 standard by the American Standards Association (4). 



Deenik (ii) extended Wien's frequency range, and experimented with 

 organ-pipes as well as with electrically-driven tuning-forks. In the case 

 of the former the subject himself adjusted the intensity of the variable until 

 a difference was noticeable. Unfortunately Deenik's intensities were not 

 so conveniently graded as Wien's, and in general his interest was con- 

 centrated rather on differences of sensitivity as a function of frequency. It 

 is worth mentioning, however, that Deenik found that the finest thresholds 

 were in the region of 2,000 cycles ; this corresponds quite well with the 

 point at which recent work has shown that the widest range exists between 

 the upper and lower thresholds of hearing. 



(iv) The present section marks the beginning of work with vacuum-tube 

 oscillators. Unless otherwise stated, it is to be assumed in sections (iv) 

 and (v) that some form of oscillator was used in all the studies reported. 



Like Deenik, Guernsey (19) was chiefly interested in the variation of the 

 intensity threshold with pitch. Her point of maximum sensitivity, how- 



