286 REPORTS ON THE STATE OF SCIENCE, ETC. 



times less than lo seconds considerable fluctuations (of an irregular 

 character) were found within the range represented. 



The present writer (49) carried out short series of experiments with 

 various instruments, (a) Since watch- tick experiments had apparently 

 not been performed since the time of Renz and Wolf, it was decided to 

 see what improvements could be made on their procedure. Four in- 

 tensities were studied, upper and lower binaural thresholds being obtained 

 for each of four subjects. A stop-watch which could be operated noise- 

 lessly was used. Marked individual differences were found, and only a 

 very crude approximation to constancy over a limited range, (b) Three 

 subjects participated in some experiments with Wundt's fall-phonometer ; 

 a lower threshold was found for two heights, using both time-orders. 

 Individual differences were again noted, but an overall average of about 

 o*2 seemed to be indicated, this value falling between those obtained by 

 the Leipzig group on the one hand, and Keller (24) on the other, (c) Lower 

 thresholds for four subjects were found by the method of Limits, using a 

 valve-maintained tuning-fork (frequency 512 cycles), devised by K. J. W. 

 Craik. The sound was suitably amplified, and heard in a moving-coil 

 loudspeaker. The following are some of the conclusions reached : 

 (i) Weber's law did not hold, even for a limited stimulus-range ; the value 

 of the threshold increased at both extremes, and varied continuously 

 throughout ; (2) Individual differences with respect both to fineness of 

 discrimination and to shape of curve were found ; (3) Although curves 

 for each subject remained fairly constant in shape, marked day-to-day 

 variations in sensitivity seemed to occur. 



The psycho-physical method commonly known as ' Mean Gradation ' 

 acts as a convenient link between the Weber's law investigations and the 

 recent work on the construction of sensation scales, since it can conveniently 

 be used in either connection. The present writer carried out a series of 

 experiments with this method, the purpose being to repeat, with variations, 

 the work of Merkel and Angell. The instrument used was the tuning-fork 

 described above. The stimulus ratios were i : 10 and i : 100 — rather 

 higher than those studied by Merkel and Angell. Each ratio was judged 

 by two subjects at three intensity levels, spaced at intervals of 20 db. Some 

 difficulty was experienced in finding a criterion of ' nearness ' to either 

 mean, but taken all over, the results seemed to favour a closer correspon- 

 dence of the estimated with the geometric mean. 



More systematic work using the same method was carried out by Gage 

 (17), who was interested in the following problem : If a mid-stimulus 

 value Xs be found between extremes Xi and X;^, and further mid-values 

 X2 and Xi be then found between X^ and X3 and X^ and X^, then a mid- 

 value Xs between X2 and X4 should, if a sensation scale is to mean anything, 

 coincide with X3. (This would hold irrespective of whether the mid-values 

 coincided with the geometric or the arithmetic mean.) Gage found that 

 the required correspondence did not occur, discrepancies of 5 and 6 db 

 being obtained over a range of 40 db. Newman, Volkmann and Stevens 

 (41), on the other hand, repeated Gage's work, introducing certain refine- 

 ments in the procedure, and reduced the discrepancies between X3 and 

 X3' to o-i8 to 0-36 db over a range of 20 db, which actually, in terms of 

 loudness values, was a greater interval than Gage's. The authors therefore 

 concluded that the method of ' bisection ' (as it is now generally called) 

 could after all be used as the basis of a loudness scale. 



Other work on loudness scales has been done by a variety of methods, 

 which, grouped together, may be said to constitute the most satisfactory 

 and satisfying approach to the stimulus-sensation relationship. In the 



