68 MATHEMATICAL BIOPHYSICS OF THE CENTRAL NERVOUS SYSTEM 



j(S) = X f h *<r(S,h) dh 



Jht 



so that, as in chapter iii, 



X f^e(S f h) dh 



1+X(K-K) 



(21) 



(22) 



Thus from e(S,M = e(S,h 2 ) = j(S), we may determine h^S) and 



MS). 



Define a Weber ratio S(S) by the equation 



MS) =MS + S<$). 



(23) 



The definition implies that when the intensity S is changed to S + Sd , 

 a completely different set of neurons is activated, so that we may ex- 

 pect a response to S + Sd which is distinct from the response to S . 



In order to proceed we must prescribe the function f(h). The 

 simplest assumption is that f(h) is proportional to h over a sufficient- 

 ly wide range, which amounts to setting f(h) = In if any constant 



X White 



Brodhun 



Konlg 



O 670 \X (Jl 



A White 



a 670 a U 



5 



10 



log 



10 



Figure 6. — Comparison of theory with experiment: intensity-discrimination 

 at varying intensity-levels for visual, auditory, and tactile sensations. Solid 

 curves, theoretical prediction by equations (25) -(28) ; points and dotted curve, 

 experimental. Visual data from Konig and Brodhun, 1888 and 1889. Abscissa, 

 intensity (on logarithmic scale) of stimulus; ordinate, ratio of just-discriminable 

 difference to total intensity. 



