PSYCHOPHYSICAL DISCRIMINATION 65 



one stimulus with the other's response may occur even though the 

 first stimulus would be inadequate, if presented alone, to produce its 

 own response. Thus if the application were made to the interaction 

 of auditory with visual perception, the mechanism provides that even 

 a subliminal auditory stimulus would raise the absolute threshold for 

 visual stimulation. With appropriate modifications — crossing excita- 

 tion instead of crossing inhibition — the possibility of a mutual lower- 

 ing of threshold could be similarly treated. 



To link the mechanism with crossing inhibition more substan- 

 tially with possible experimental results, we consider the effect of 

 threshold-fluctuations, or, what is more convenient and mathemati- 

 cally equivalent, random variations in the o-'s at s x and s 2 . Since 

 a^j?we cannot, as before, represent the combined effect by varia- 

 tions at only one synapse, but any variations occurring also at Si 

 and s 2 could be formally accounted for by suitably modifying the 

 distribution-functions at the first two synapses alone and we suppose, 

 for simplicity, that with this modification the resulting distributions 

 are identical at the two synapses. Denote these functions by p(C), 

 C being the random addition to either synapse and having zero as its 

 mean. 



The mutual influence of the stimuli upon absolute thresholds can 

 be determined from an investigation of near-threshold stimulation 

 where the functions <f> and xp can be represented linearly: 



<j>(S) =aS-a',y>(S) =ps-p, a > p . (9) 



Corresponding to equations (1), chapter iii, we have 



a 1 = a(S 1 + Cx) -a'-/?(S 2 + C 2 ) + /J', 



(10) 



<r 2 = a(S 2 + k) - a' - fiiSi + d) + fi' . 



Then the respective conditions for the responses R 1 and R 2 are, 



aS 1 -pS 2 + at 1 -pz 2 -h>0, (11) 



aS 2 - pS 1 + a^~ PCi~h>0, (12) 



where 



h = a'- p + h' , (13) 



and each efferent from s x ' and s 2 has the threshold h' . Let (RR), 

 (RO) , (OR) and (00) denote the occurrence of both responses, the 

 first only, the second only, and no response, respectively. The prob- 

 abilities of these events, where Si and S 2 have given values, are 



P(RR)= f p(Ci) J f»(f.)<Zf»<Zti f (14) 



