QUANTITATIVE ESTIMATES OF SENSORY EVENTS 279 



made by the present writer (49), who quotes references to fuller and more 

 technical accounts. 



The pioneer researches were marred both by imperfections and in- 

 adequacies of technique, and by theoretical misapprehensions. Of these 

 drawbacks, those of the second type apply more particularly to methods 

 based on the principle of falling bodies, those of the first both to these 

 methods and to those based on the validity of the inverse square law. 



The principle that the intensity of a stimulus which reaches the receptor 

 from a distant source varies inversely as the square of the distance of the 

 source from the receptor is still sometimes used, in the form of the ' watch 

 test,' by practising aurists in the determination of hearing loss. This 

 method, while suitable for rough estimates, is not to be recommended for 

 accurate measurement, since reflection of sound waves is inevitable, and 

 practically uncontrollable, even in the open air. 



The method of falling bodies rests on the principle that the energy of a 

 falling body is proportional to the weight of the body, and to the height 

 of fall. Gravity being constant, it may be said that the product of height 

 and weight gives a measure of the energy. Since, however, not all the 

 energy is effectively transformed into sound, the simple ht. X wt. formula 

 does not hold, and it was found by the early experimenters that in general 

 a fractional power of the height had to be taken in calculating sound in- 

 tensity. These conclusions were often reached as a result of equating for 

 loudness the sounds produced by balls of varying size and weight, and it 

 was usually noticed that differences of quality made such observations 

 extremely difficult. Actually apparent equality of loudness under these 

 conditions is no criterion of equality of intensity, and it is surprising how 

 completely this rather obvious point was overlooked. Studies of the 

 inter-relation of sensory attributes, which for sound may be said to date 

 from the discovery in 1897 of the Broca phenomenon (6), have now 

 established beyond dispute the fact that no point-to-point correspondence 

 can be claimed between the psychological qualities of sensation and their 

 physical correlates. Following Fletcher (13), we may say that while loud- 

 ness is the subjective characteristic that is recognised as the magnitude of 

 the sensation, and which changes most rapidly with changes in intensity, 

 each of the three main subjective characteristics of sound — loudness, pitch 

 and timbre — depend on all three of the physical characteristics — intensity, 

 frequency and overtone structure. 



Attempts to measure sound intensity were also made using such devices 

 as singing flames, percussion systems with or without tuning-forks, phono- 

 graph records, blowing pressure, and direct microscopic examination of the 

 amplitude of vibrations. 



Some of these instruments were used in investigations of Weber's law, 

 and apart from this approach little attempt was made to measure sensation 

 as such, i.e. to express sensation magnitudes in relative or absolute units. 

 At the time of the 191 3 symposium in the British Journal of Psychology (40), 

 the general consensus of opinion was that theoretically sensation was not 

 measurable, but that Weber's law might hold, at least over a limited range, 

 in most sense-departments. Fechner's ' fundamental assumptions,' first 

 stated in i860 in the Elemente (12), on which he based his mathematical 

 development of the aS (sensation) = k log R (stimulus) relation,^ were taken 



1 Sometimes stated S = k log RjR^, to indicate that the stimulus is measured 

 in terms of its absolute threshold (R^) as unit. This is the law quoted in Warren's 

 Dictionary of Psychology under the heading Fechner's Law. The definition adds : 

 ' Fechner's law is frequently incorrectly called Weber's Law, and is now often 

 referred to as the W eber-Fechner law.' 



