RELATION OF SENSATION TO STIMULUS 541 



of accuracy is attained extends from 50 to 1000 grammes. In judging 

 of weights with the help of movement (the method one ordinarily 

 adopts) the limit of accuracy is about one-twentieth ; for sounds 

 the appreciation of difference amounts to about one-ninth. The 

 organ which is most susceptible to slight changes of intensity is the 

 eye ; by this organ we can appreciate differences of one one-hundredth 

 to one one-hundred-and-twentieth in the total illumination. 



FECHNER'S LAW. Fechner has endeavoured to give a mathematical 

 expression to the facts described under Weber's law. According to Weber 

 the proportion between the increase of stimulus necessary to cause increase 

 of sensation and the whole stimulus is a constant for all intensities of excitation- 

 Thus if C is a constant 



where k represents the smallest appreciable increase of sensation evoked by 

 the minimal increase of stimulus, R is the stimulus, and AR is the minimal 

 increase of stimulus. 



If the same relation may be allowed to hold for infinitesimally small differ- 

 ences of sensation and infinitely small differences of stimulus, this formula 

 may be expressed by the equation : 



By integration we obtain the expression : 



E = C log. nat. R 



i.e. the sensation is proportional to the natural logarithm of the stimulus, which 

 is Fechner's psycho-physical law. 



In view of the fact, however, that Weber's law only holds good between 

 certain limits, not much practical value can be attached to such a mathematical 

 expression. Moreover Fechner's calculation is based on the improvable and 

 unjustifiable assumption that, within the limits of applicability of Weber's 

 law, the smallest appreciable increase in sensation is always the same, i.e. that 

 the increased sensation which is evoked by the addition of 6 grammes to a 

 weight of 100 grammes is identical with the increased sensation called forth 

 by adding 60 grammes to an initial weight of 1000 grammes. Such an assump- 

 tion does not, as a matter of fact, agree with our own experience ; and it is 

 probably premature here, as in many other departments of biology, to attempt 

 to include the complex of variable phenomena presented by animal functions 

 within the Procrustean bed of a mathematical formula. 



