RELATION OF SENSATION TO STIMULUS 485 



vary with each sense-organ, and it does not hold either for very weak or for 

 very strong stimuli. Within these limits the ratio which an increase of 

 stimulus must bear to the whole stimulus to produce an increase of sensation 

 may be given approximately as follows for the different sense-organs : 



When weights are placed on corresponding points of two sides of the 

 body, e.g. on the two hands, we can appreciate differences of about one-third ; 

 if the contrast be successive, i.e. if the weights be placed on the same spot 

 in succession, we can appreciate differences between one-fourteenth and 

 one-thirtieth. The range over which this amount of accuracy is attained ex- 

 tends 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, B is the stimulus, and AR is the minimal increase of stimulus. 



If the same relation may be allowed to hold for infinitesimally small differences 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 unprovable and unjustifiable assi mp- 

 tion 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 assumption 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. 



