270 H. K. HARTLINE, F. RATLIFF AND W. H. MILLER 



interpretation was readily shown by enlarging the spot of light illuminating 

 the test receptor so as to include several of its neighbors. Then the combined 

 effect of A and B together was clearly greater than the sum of their separate 

 effects (Fig. 4 in Harthne and Ratliff, 1958). Of course, the interaction of the 

 group X, even when it consisted of the test ommatidium only, was of neces- 

 sity present in all of the other experiments we have described. It is never 

 possible in these simple experiments to provide an entirely unambiguous 

 evaluation of the various inhibitory effects. The formulas for the combined 

 and separate effects involve combinations of the inhibitory parameters of the 

 several groups, and measurement of the activity in just one receptor does not 

 provide enough information to calculate the parameters individually. Never- 

 theless, the theoretical formulas are useful in providing insight into the pro- 

 perties of the interacting system which can sometimes be unexpectedly 

 complex even for relatively simple configurations of retinal illumination. 



We need not reproduce here the analytic expressions derived theoretically 

 to describe these experiments, but will show instead theoretical solutions 

 plotted by an analog computer (Fig. 20). The examples chosen show all of 

 the features found in actual experiments, and a few others not yet observed. 



We will now turn to an aspect of the inhibitory interaction that has a special 

 significance in visual physiology. In the foregoing analysis, we have treated 

 the inhibitory interaction as determined by parameters r^ and K whose 

 numerical values were specified without inquiring how different values could 

 arise. We will now discuss the principal factor that determines the values of 

 these parameters. This is the distance separating any two ommatidia in the 

 retinal mosaic (Ratliff and Harthne, 1959). Inhibitory influences are exerted 

 more strongly, on the average, between near neighbors in the mosaic of retinal 

 receptors than between widely separated ones. For example. Fig. 21 shows an 

 instance in which the action of a group of receptors (A) on a nearby receptor 

 (B) had a low threshold (r%A = 5 impulses/sec) and a high coefficient of in- 

 hibition (A'ba = 0T7); on a more distant ommatidium (C) the threshold of 

 A's inhibitory action was higher {r^cA = 18 impulses/sec) and its coefficient 

 lower (K^x = 0-07). C was approximately 3 mm from A; ommatidia separa- 

 ted by more than 5 mm rarely exert any observable influence on one another. 

 The explanation of this dependence of inhibitory interaction on retinal separa- 

 tion is unknown. Perhaps inhibitory influences are conducted decrementally 

 over the fine nerve branches of the plexus; perhaps there are merely less 

 profuse connections between ommatidia that are widely separated than there 

 are between near neighbors. More complete knowledge of the inhibitory 

 mechanism and of the histology of the plexus is required. 



The rule we stated above for the diminution of the inhibitory influence 

 with distance, while true on the average, often fails in specific instances when 

 apphed to the interaction of individual ommatidia. The interaction of pairs 

 of ommatidia of equal separation may vary considerably even in the same 



