CONDITIONING 83 



of proportionality. The theory could be developed formally regard- 

 ing- Aa as a purely empirical constant with no definite physiological 

 significance. But the model enables us to relate this constant to such 

 variables as the strengths of the conditioned and the unconditioned 

 stimuli, temporal factors, and the like, and so provides the possibility 

 of relating a larger group of variables in a single formulation. 



For interpreting some experimental results in these terms, we 

 consider the net shown in Figure 2 (Landahl, 1941). Let a stimulus 

 S c normally produce a response R c , and let a pleasant response R 1 

 always follow R c in the experimental situation. Let S w normally pro- 

 duce R w , which, in the experimental situation, leads to an unpleas- 

 ant stimulus, less pleasant stimulus or to an equally pleasant stimulus 

 but after a longer time. Let the circuits M and C each represent a 

 large group of circuits of different thresholds. Let the part of the 

 structure composed of neurons III, III', IV, IV be equivalent to the 

 corresponding part of Figure 1 of chapter ix. We shall consider only 

 simultaneous presentation of S K and S c . On the first trial, neither 

 C nor C can become active, and thus we have acting at s c a quantity 

 e, oc ; and similarly at s lc a quantity e, ow . Then, if one of the two re- 

 sponses must be made, the probability P c of the response S c may be 

 given by the approximate equation (8) of chapter ix, with £! — e 2 

 replaced by £ oc — £ow • 



After S c and S w have been presented together n times, the re- 

 sponse R c will have been made, say, c times and the response R w , w 

 times. We shall refer to n as the number of trials, c as the number 

 of correct responses, and w as the number of wrong responses. Then 

 P c , the probabilty of a correct response, may be identified with the 

 proportion of correct responses, so that approximately 



P c = dc/dn; (5) 



and similarly 



P w = dw/dn , (6) 



Thus 



P c + Pw = l, c + w = n. (7) 



When a stimulus S c is presented, a certain group of the circuits 

 M are brought into activity. Then, each time there is a response R t , 

 conditioning may take place in some circuits of C and the amount, 

 as measured by the increase in the excitatory factor Ae c at s c , will not 

 be dependent upon the time t c between the presentation of S c and 

 response Ri . But, if the circuits M are acted upon by inhibitory neu- 

 rons from various external sources, or if the circuits are replaced by 

 single neurons, the activity will decay with the time, t c , roughly ex- 

 ponentially. Thus, we may obtain an expression for Ae c similar to 



