PSYCHOPHYSICAL DISCRIMINATION 



69 



multiplier is absorbed in the constant X . The graph of e(S,h) is an 

 inverted parabola with a maximum at 5/2 , and thus th and h* are 

 equidistant from S/2 . Define the "relative interval," x , by 



Then 



Sx = S-2h 1 = 2h a -S. 

 e(S,h 1 )=e{S,h 2 ) =SH1 - x 2 )/4 = j(S) 



(24) 

 (25) 



Introducing s = h(S—h) in equation (22) and the result into equa- 

 tion (25), we obtain 



where u is defined by 



ux 3 + x 2 — 1 = 



u = 2XS/Z 



(26) 



(27) 



and is thus proportional to the intensity. The value of x for S + Sd 

 is given by 



x(S + Sd) = [6- x(S)]/(d + 1), (28) 



7 J 



Auditory data; Rlesz 



1000 cycles per sec. 



70 " " " 



h 

 5 



2 • 



1 - 



Figure 7. — Comparison of theory with experiment: intensity-discrimination 

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

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

 experimental. Auditory data from Reisz, 1938. Abscissa, intensity ( on logarith- 

 mic scale) of stimulus; ordinate, ratio of just-discriminable difference to total 

 intensity. 



