INHIBITORY INTERACTION IN THE RETINA 263 



experiments furnish a variety of combinations of interaction effects, all in- 

 structive but not all equally crucial as a test of the theory. The more inter- 

 esting ones are those in which the interactions are strong between all three 

 units in all directions but preferably unequal, to display instructive asym- 

 metries in the actions. The satisfactory agreement between calculated values 

 and observed measurements suggests that the theory has been properly con- 

 structed and the assumption extending the law of spatial summation to the 

 general case of interacting receptors is valid under the conditions of our 

 experiments. 



It would be possible in principle to extend these experiments to larger 

 numbers of interacting elements measured individually. However, this would 

 be difficult in the Linnilus preparation; the three fiber experiments are diffi- 

 cult enough and it is doubtful whether much more would be learned. It is 

 instructive, however, to consider the interactions of groups of ommatidia. 



By illuminating large enough regions of the eye (spots of light 1-2 mm in 

 diameter) to include a moderate number of ommatidia (from 10 to 40) strong 

 inhibitory effects can be elicited. A test receptor in the neighborhood of such 

 groups can be used to analyze the properties of the inhibitory interaction as 

 we have done in experiments on disinhibition and spatial summation. Effects 

 of large groups on a test receptor are large; effects of a single test receptor, 

 exerted back on to large groups are relatively small (though often recogniz- 

 able) and the analysis is simplified. A more detailed analysis is provided by 

 choosing one of the receptors within a group as a representative of the 

 group. This is useful but not without its drawbacks, for individual receptor 

 units differ appreciably in their individual properties and in their interactions 

 with others. 



The theoretical treatment of group interaction may be approached by con- 

 sidering idealized situations. We will assume that within small compact groups 

 the receptor units have identical properties, that each receptor inhibits equally 

 all others in the group and that each one of the group inhibits and is in- 

 hibited by any one receptor unit outside the group to the same degree. We 

 know that actual receptor groups depart from these idealizations, often 

 considerably, but the theory may be developed for the simpler ideal case 

 and the results used to give understanding of the more complex actual ones. 



Starting with the consideration of a single group of n receptor units, our 

 assumptions state that all the e's, A"s and ^^''s are equal; the r's must then also 

 be equal. Just one of the set of n equations suffices and the subscripts may 

 be dropped: 



r = e-{n-\) K{r - /■») (5) 



or 



_ e + {n- \) KrO 



'~ 1 + (/t - 1) /: 



