44 CHEMICAL AGENTS AND PROTOPLASM [Cn. I 



tions may be shown by the following table, following one given 

 by PFEFFER ('84, p. 401) : 



s corresponds to r'. 



s-f- 30s = 31s corresponds to r'+r. 



31s-f 30x31s= 31 x 31 s corresponds to r'+r +r. 



31 x 31 s+30 x 31 x 31 s = 31 x 31 x 31 s corresponds to r'+r+r+r. 



That is to say, while the stimulation increases geometrically, 

 the reaction increases arithmetically. In the preceding table 

 the second term of the left-hand member of the equation is 

 always the differential threshold stimulation. 



The most important objection that can be urged against this 

 formula of FECHNEB is that there is not sufficient reason for 

 believing that the various reactions (r) to the differential 

 threshold stimulations of various strengths are equal, nor that 

 the stronger reaction to the strong stimulus is composed of 

 many weak reactions. If these assumptions were true, it would 

 follow that when the successively higher stimuli increase as a 

 series of numbers the reactions increase as the logarithms of 

 these numbers. If now we adopt as a unit in this phenomenon 

 the quantity of the threshold stimulation (estimated in units of 

 concentration of solution, of mass, light intensity, heat inten- 

 sity, etc.), which we may call s, the strength of any stimulus 

 ($) may be estimated in those units, and the strength of the 

 corresponding reaction (.72) will be indicated by the equation 

 R = c log S, in which c is a constant to be determined empiri- 

 cally, and S the strength of the stimulus expressed in units of 

 the threshold stimulation.* 



While we are not yet in a position to understand the signifi- 

 cance of WEBER'S law, we cannot fail to be struck with the 

 resemblance of the phenomena with which it concerns itself to 

 those of acclimatization referred to in the second section of 

 this chapter. We there showed that organisms subjected for a 

 while to a chemical agent no longer reacted as at first to that 

 reagent. We have here shown that organisms subjected for 



* Since the German word for stimulus is Heiz (initial .R), and since the re- 

 action is usually indicated by the initial letter in Empfindung, in German text- 

 books this formula usually runs E = c log 7?, which differs from the above 

 equation only in the symbols employed. 



