20 COLOUR VISION 



which is independent of the absolute magnitudes of the stimuh. For 

 white hght Fechner could distinguish a difference of jljy, v. Helmholtz 

 y^y, of the light intensity. 



Fechner went further and attempted to express sensations in terms 

 of quantitative units. His most important assumption was that all 

 just noticeable differences of sensation contain an equal number of 

 sensation-units. 



Fechner's law states that the sensation varies as the logarithm of the 

 stimulus ; i.e. the sensation changes in arithmetical proportion as the 

 stimulus increases in geometrical proportion. 



Stated algebraically, if E is the measure of a sensation and hE the 

 just appreciable difference, S the measure of the stimulus and hS a small 

 increment, then 



8^=0^ (Weber's Law) 



where C is a constant : therefore, on the questionable assumption that 

 it is permissible to integrate BiwaW finite quantities {hE, etc.) 



= C log S + C (Fechner's Law) 



where C" is another constant. 



Weber's law does not hold good for very low or very high intensities 

 of stimuli, and is only approximate at the best. An immense super- 

 structure has been built up upon these psycho-physical foundations^. 

 The bases are insecure on mathematical as well as on physiological 

 grounds. So far as the latter are concerned we have no unit of sensation 

 (cf. p. 61), and the variations, though quantitative, are only relative. 

 The chief difficulty, however, is to be found in the ever-changing 

 condition of the sensory apparatus. The deductions are not without 

 value, for some quantitative relationship certainly exists, even if it be 

 not so simple as Fechner's law implies. 



The problem is still more complicated when we come to comparison 

 of specific qualities in sensations. Thus we recognise brightness as a 

 quality of coloured lights and we may say with some degree of certainty 

 that a given red light has the same brightness or luminosity as a given 

 blue light. We can thus estimate qualitatively equivalent stimuli and it 

 is also true that we can attempt to estimate qualitatively equivalent 



^ Lipps, Grundriss d. Psychophysik, Leipzig, 1903 ; G. E. Miiller, Ergeb. d. Physiol. 

 II. 2, 267, 1903 ; v. Kries„ in Nagel's Ha7idb. d. Physiol d. Menschen, m. 16, 1904. 



