260 



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



Fig. 15. The summation of inhibitory influences exerted by two widely separated 

 groups of receptors and by two groups of receptors close together. Each panel in 

 the figure is a map of the same small portion of the eye. The test receptor, location 

 indicated by the symbol X, was illuminated steadily by a small spot of light 

 confined to its facet. Larger spots of light were placed singly in one of three 

 locations, as shown in the three panels on the left side of the figure, and in pairs, 

 as shown in the three panels on the right. The filled circles indicate the spots 

 illuminated in each case; the other locations (not illuminated) are indicated in 

 dotted outline merely for purposes of orientation. The number of impulses dis- 

 charged from the test receptor in a period of 8 sec was decreased upon illumina- 

 tion of the neighbouring spot or spots by the amount shown at the right in each 

 panel. (From Hartline and Ratliff", 1958.) 



Still to be combined by simple addition to describe quantitatively the net 

 inhibitory effect. An experiment served to establish the law of summation for 

 a special case (no interaction); the assumption serves to extend it to the 

 general case. The vahdity of this assumption will be demonstrated below, 

 where we will present experimental evidence based on measurements of the 

 simultaneous activity of three interacting ommatidia. 



We can now write explicitly the set of n simultaneous linear equations 

 describing the interaction of a set of n interacting receptor units : 



r„ = e„ 



S K (r— rO •) 



{n equations) 



P=\n, ... n (4) 



Restrictions : 

 all r, 6-, ^ < 



all rj < r%j 



These equations can be solved by conventional methods, expressing all the 

 r's as functions of the e's (distribution of light on the retinal mosaic), and of 

 the K's and r^'s (parameters of the inhibitory interaction). All of these, in 

 principle at least, can be measured by direct experiment. 



