QUANTITATIVE ESTIMATES OF SENSORY EVENTS 289 



reference tone was constructed. This relation was found to be more 

 satisfactory than simply adopting the decibel scale as a loudness scale, but 

 it still conflicted with introspectional evidence as regards loudness. A 

 method whereby observers adjusted tones to half an original loudness 

 was therefore substituted ; the procedure was progressively repeated 

 six times, and estimates of quarter loudness gave a fairly good check ; 

 thirty-four subjects took part. The authors go on to describe the applica- 

 tion of their scale to the assessment of total noise by an aural balance 

 method. This was held to give better estimates of loudness than methods 

 of frequency analysis, the use of which, it was said, might give discrepancies 

 of anything up to 40 per cent, when compared with direct noise-meter 

 readings. 



At the discussion following the original reading of the paper just discussed, 

 various numerical relations approximating to the authors' scale were pro- 

 posed. A friend of the present writer, however, has suggested an ex- 

 ponential equation : L (loudness) = 100 e •°5'^-5 (where x stands for 

 sensation level in db) ; this, though not accurate, especially at the lower 

 end, corresponds as well as any of the other suggested formula, and is 

 more in line with the results of Ham and Parkinson, and of the present 

 writer (49), who experimented on loudness estimation with the tuning-fork 

 apparatus already referred to in two places. The procedure most closely 

 resembled that of Richardson and Ross. Estimates of fractional and 

 multiple loudness were made separately. For the former the unit intensities 

 were — 30 and — 20 db attenuation on the instrument ; for the latter 

 — 30 and — 40 db. Three subjects took part, and while considerable 

 fluctuations were seen in the results of all three, those of each individual 

 always showed more resemblance to his other estimates than to those of 

 the others. Accordingly it was possible and necessary to draw distinct 

 smoothed curves for each observer, so that real individual differences seemed 

 to have been established. A full mathematical analysis of the curves was 

 not attempted, but it was apparent that some at least were of exponential 

 form. Checks by the ' {b) ' method (see p. 286) gave rather inconclusive 

 results. One further point, however, is of greater interest, namely, that 

 fractional estimation or judgment did not seem to give curves of the same 

 form as multiple estimation. This may have been due to the limited 

 number of estimations made, but it bears out the remarks on the non- 

 comparability of results of different methods stressed by Riesz (47), Abbott 

 (1), and others. The fullest single study of the effects of subjective condi- 

 tions on loudness judgments is that of Steinberg and Munson (53), whose 

 general conclusion was that ' when sounds of different tonal character are 

 compared by small groups of observers, we must expect appreciable 

 differences of judgment to occur.' 



Stevens (54) states the same point in still more general terms when he 

 says that ' we do not measure the magnitude of a sensation, but only of a 

 particular dimension or aspect of sensation within a single sensory modality.' 

 Any auditory attribute is a function of both dimensions of the stimulus 

 (frequency and intensity), and ' loudness is a name which we give to a class 

 of discriminatory responses on the part of an organism under certain 

 conditions of "set" and stimulation.' Stevens goes on to propose a new 

 unit of loudness, the sone — the loudness of a 1,000-cycle tone listened to 

 with both ears at an intensity level of 40 db. This corresponds closely to 

 Churcher's (8) value i, and is also said to be of the order of magnitude of 

 just noticeable differences of moderately intense tones of the musical scale. 



The sone has not as yet been at all widely accepted, but it must be 

 recognised as the first real unit of psychological magnitude. The phott 



