INHIBITORY INTERACTION IN THE RETINA 261 



The restrictions require comment. We have explained why only positive 

 values of r, e and K are considered in this particular formalism. The second 

 restriction, that no partial inhibitory term may be admitted for which the r 

 is less than the r° with which it appears in that term, reflects experimental 

 fact. Without exception, a receptor that aff"ects a neighboring receptor has 

 been found to do so only if its frequency of discharge exceeds a certain 

 threshold value characteristic of the pair and of the direction of the action. 

 No "subliminal" inhibitory effects have ever been observed: if an omma- 

 tidium is caused to discharge at a frequency below the threshold of its action 

 on another ommatidium, it does not add anything to the inhibition exerted 

 on that second one by other ommatidia in the neighborhood. (The absence 

 of any subliminal effects that might sum to produce appreciable inhibition 

 from large dimly hghted regions has an important practical bearing on this 

 experimental work. It assures us that the halo of scattered light, so difficult 

 to avoid entirely in any experiment, contributes notliing to the interaction, 

 at least for moderate levels of "focal" illumination.) The restriction of equa- 

 tions (4) to r*s that are suprathreshold for all partial inhibitory terms implies 

 that the equations as written hold only for those values of the e's for which 

 solutions meet this requirement. In any other case, the equations may be 

 solved tentatively, the solutions inspected, and those partial terms for which 

 /• < rO set equal to zero. The resulting set of equations may then be solved, 

 and the process repeated as often as necessary, until solutions have been 

 found that meet the requirement for all terms. 



The requirement j ^ p \x\ any of the summations is meant to express an 

 unwiUingness to consider the possibility of "self-inhibition" in this formal 

 treatment (cf. equation 3). Now, there is no a priori reason to deny the exist- 

 ence of "self-inhibition" — it may well occur in the eye of Liniulus, where the 

 ommatidia are themselves complex cellular entities, or in other interacting 

 systems that we might wish to consider. "Self-inhibition" might conceivably 

 be demonstrated by the use of some pharmacological agent, for example, 

 which could abolish all inhibition without otherwise affecting the neural 

 elements. But "self-inhibition" really concerns the intimate mechanism of the 

 ommatidium itself as a functional unit and therefore is properly excluded from 

 a theory of m/eraction. 



We choose to avoid the entire question of self-inhibition for the present by the 

 following treatment. Suppose the receptor units did inhibit themselves by the same 

 mechanism by which they inhibit each other; call the frequency with which a unit 

 responds in the absence of all inhibitory influences e'; call its inhibitory coefficients 

 A". K'p, j will be the "actual" coefficient representing the inhibitory action of the 

 yth receptor on the plh and, by admitting 7 = p, K'p, p appears as the "coefficient of 

 self-inhibition" (with r%, p the threshold of the "self-inhibition"). Then in a set of 

 equations (4') (not written here) where the primed letters replace the unprimed in (4), 

 collect terms and divide by 1 +K'p, p in each equation. This yields a set of equations 

 of the same form as (4), in which the quantity (e'p + K'p, p r° p, p)/(l + K'p, p) appears 

 in place of ep (unprimed) and K'p, y/(l + K'p, p) appears in place of Kp, j, and in 



