QUANTITATIVE ESTIMATES OF SENSORY EVENTS 325 



As the phenomenal relation involved in the grading is sameness of the 

 relation between adjacent members of the series, it is independent of the 

 size of the intervals, and the same criterion should be operative even if the 

 intervals are made so small that we are just able to distinguish between the 

 members of adjacent pairs. If the intervals are less than this, the perception 

 of pairs, and therefore of any relation at all between pairs, is impossible. 

 Thus so long as the members of a mean-gradation series are distinguishable 

 from each other they are related by our criterion of sameness of interval. 

 But we have now reached what is, in effect, a j.n.d. series, from which we 

 see that the successive stimuli in such a series must be graded in intensity 

 by the same law as the members of a mean-gradation series, i.e. in accord- 

 ance with the apparent ratio of their intensities. Apart from adventitious 

 causes due to difference in the experimental conditions in which the two 

 types of experiment are carried out, the departures from a true grading in 

 terms of objective stimulus ratios should depend on the same physiological 

 (or other) systematic causes, and should be of a similar character. 



The results of actual experiments of these two types are, in general, as 

 predicted by the foregoing considerations. In the case of vision, both 

 equal-appearing-interval series and j.n.d. series grade stimuli very nearly 

 correctly in accordance with relative intensity over the very large range of 

 intensity associated with normally comfortable seeing, departures from the 

 true grading only becoming serious at low and excessive intensities. The 

 results for sound are less definite, as a perusal of the section of this Report 

 prepared by Dr. Semeonoff will show. This is also to be expected. Owing 

 to the very indefinite clue to direction given by our auditory apparatus, we 

 do not hear a ' picture ' of our environment in which the constituent sound 

 waves reaching us are definitely associated with the sources or reflecting 

 objects from which they come. Hearing is rather like seeing in a thick mist, 

 in which we may perceive the general direction from which light is coming 

 but see no objects. With sound therefore we are usually unaware of the 

 exact origin of the stimulus and feel that we are simply immersed in a 

 nebulous ' cloud ' of sound surrounding our heads. But this nebulous 

 cloud is not the sensation ; it is the objective environment which, in virtue 

 of the sensation it evokes, we ' hear,' just as when immersed in a translucent 

 mist the nebulous cloud of luminescence we see is not our sensation, but 

 constitutes the objective environment of whose presence we are made aware 

 by our sensations. What we hear is outside us in exactly the same sense 

 that what we see is outside us, a point that seems to be entirely overlooked 

 by many writers on audition. However, owing to the nebulous nature of 

 the objective world, as perceivable by hearing, it is relatively rare for us to 

 make a definite association between any sound pattern and a unique source. 

 It is only on the occasions when we know, for other reasons, that some 

 object is the origin of the sound, as when we simultaneously see and hear a 

 person speaking or an orchestra playing, and so on, that we make such an 

 association at all. The associative bonds between any psychological relation 

 and a corresponding phenomenal relation are likely, on this account, to be 

 much less strongly developed for audition than for vision, where the bonds 

 are reinforced by almost every experience. Nevertheless, such uniqueness 

 for recognitive purposes as any auditory relation can have must be derived 

 from that fraction of our experience in which associations are established ; 

 and must, for the reasons we have discussed, correspond to sameness of 

 relation-shape depending in audition, as in vision, on the apparent relative 

 intensities of stimuli and not on their absolute magnitudes, and must tend, 

 as in vision, to approximate to a recognition of the true relative intensities 

 within a reasonably wide range of intensity. 



