472 



Mr. C. Lloyd Morgan. 



cent. A disc with 49 per cent, was constructed and shaded quite 

 satisfactorily. At the same time all I venture to claim is that the 

 general principle is correct. For other eyes the mid-point of the 

 black-white scale may differ somewhat from the 12 per cent, which 

 for me gives the best results. For them the luminosities of the colours 

 may be slightly or even markedly different. But I believe that if the 

 luminosities be determined on their scale it will be found that for them, 

 too, equal increments of sensation are due to increments of stimulus 

 in geometrical progression. 



I have not so far adequately correlated my own results with those 

 obtained by previous observers. I regard the investigation as still 

 incomplete, and think that this important part of the work should be 

 reserved as an appendix to follow the presentation of independent 

 observations. A few words may be added in conclusion, however, on 

 the relation which the empirical scale of sensation may hold to an 

 absolute scale based on certain assumptions. 



It will be remembered that for purposes of comparison with the 

 black- white curve colour luminosities were determined and recorded in 

 terms of the arbitrary scales. Sir Win. Abney's determinations are 

 in reference to an absolute zero, his black having a value of about 3- 3. 

 Let us assume that the absolute zero of stimulation lies a little less 

 than 2 per cent., or more exactly 1 -87474, below the arbitrary zero of 

 my curve, and let this amount be added to the stimuli throughout the 

 scale, so that the white becomes 101*87474, the mid-point 13*87474, 

 and so on. On this assumption the arbitrary scale becomes, so far as 

 stimulus is concerned, an absolute scale. And on this absolute scale 

 of stimulus, the sensations, + some undetermined constant, form an 

 arithmetical series, while the stimuli which are in relation to them 

 form a geometrical series. In other words, the addition of this 

 constant] to the summed increments of stimulus at any stage of the 

 scale causes these summed increments to fall into line as the terms of 

 a geometrical progression. The stimulus value of our mid-point on 

 the absolute scale is the geometrical mean between the values of our 

 extremes on the same scale. On this assumption, therefore, and 

 between these limits, Weber's Law and Fechner's expression of it hold 

 good. 



Fechner's logarithmic law, however, involves other assumptions. It 

 involves the assumption that some unit of stimulus 1, gives sensation 0, 

 <ind that below this threshold of sensation there range an indefinite 

 series of sensations or quasi-sensations of negative sign. And, pushed 

 to its logical conclusion, it further assumes that the logarithmic law 

 holds good throughout this negative series. 



Now it is clear that no studies in sensation can throw light on what 

 lies below the threshold of sensation. But physiological research may 

 afford data for the continuation of the curve into the subliminal region. 



