INHIBITORY INTERACTION IN THE RETINA 257 



fixed inhibitory influence from neighboring receptors. This, too, is not the 

 consequence of any a priori speculation. It could well be imagined that, for 

 example, the relative decrease (percentage reduction in frequency) might have 

 turned out to provide a more useful theoretical structure. For the Limulus 

 eye, however, it is the fact that no matter what the level of activity of a parti- 

 cular ommatidium whose nerve fiber is on the recording electrodes, the 

 absolute decrease in frequency produced by a fixed inhibitory influence from 

 neighboring elements is always the same. 



We can express this experimental fact in the equation: 



r = e-i (1) 



In this equation the term r stands for the response of the ommatidium under 

 observation, measured by the steady frequency of its discharge of nerve 

 impulses while it is being subjected to inhibition from its steadily illuminated 

 neighbors. The term e represents the magnitude of the external excitation 

 supplied by the stimulating fight of given intensity. It is to be measured by 

 the frequency of discharge that the receptor would have in the absence of 

 any inhibitory illumination, that is, when that ommatidium alone is illu- 

 minated at the given intensity. The term / represents the inhibitory influence 

 exerted on the ommatidium by its neighbors; it is some function, as yet to be 

 specified, of the activity of those elements. 



Implicit in our use of this notation is the understanding of several restric- 

 tions: /• and e, being frequencies cannot be negative; the quantity / likewise 

 is to be restricted to positive values, since we are dealing with a purely in- 

 hibitory interaction. In defining a notation for some other system, however, 

 one might not wish to be bound by these particular restrictions. For example, 

 the mechanoreceptors of lateral line organs and of vestibular ampullae dis- 

 charge impulses "spontaneously" and one might wish to consider levels of 

 activity both above and below the resting discharge. For the Limulus eye, 

 however, these restrictions apply. For the present, moreover, we will restrict 

 our consideration to the steady conditions of response, after all of the transi- 

 ents have subsided that are associated with turning on the stimulating light 

 and establishing the inhibitory interactions. Later in this paper we will de- 

 scribe briefly some preliminary experiments on transient effects. 



In the equation (1) the term /, representing the total inhibitory influence 

 exerted by the combined action of all the neighboring elements that are 

 activated by a given pattern of retinal iUumination, is to be expressed as a set 

 of "partial" terms, each representing the action of some one neighbor on the 

 ommatidium under consideration, all combined in an appropriate manner as 

 yet to be specified. Each partial inhibitory term is to be written as a function 

 of the response r of the particular neighbor whose action it represents; this 

 expresses the experimentally established principle of mutual interdependence 

 of receptor responses, discussed above. As a consequence, the activity of each 



