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



ommatidium in an interacting set will be described by an equation of the 

 form of equation (1) expressing its response /• in terms of its excitation e and 

 an / which is a function of the r's of all the other ommatidia in the set. The 

 resulting set of equations, one for each receptor, must be solved simultane- 

 ously to determine the values of any of the r\ in terms of the e\ (that is, in 

 terms of a distribution of light over the retinal mosaic). It is the "recurrent" 

 mutual interaction of the receptor units in the eye of Linmlus that requires 

 description by such sets of simultaneous equations. 



Before we can give explicit form to the equations we have proposed, two 

 pieces of information are required: we must know the form of the functions 

 describing the partial inhibitory terms and we must know how these partial 

 terms are to be combined to make up the function describing the total in- 

 hibition on a given receptor unit. Experiments provide the empirical answers 

 to these two questions. 



The form of the function that may be taken to describe the relation between 

 the frequency of a given receptor and the amount of inhibitory influence it 

 exerts on a particular neighbor is suggested by the graphs of Fig. 12. It is 

 evident that, above a certain threshold, a linear relation describes the data 

 satisfactorily. For example, the inhibitory action (/i, 2) exerted by ommati- 

 dium 2 on ommatidium 1 is proportional to the amount by which 2's fre- 

 quency of discharge (r-z) exceeds the threshold r^i, 2 for its action on 1 : 



/i. 2 = Ki, 2{ro - r\ 2). (2) 



A similar expression holds, of course, for I's action on 2: 



k, 1 = K2, i(ri - r% 1). (2a) 



These statements are true for any arbitrarily selected pair of ommatidia in 

 a set of interacting receptor units — an inference from the fact that we have 

 always observed this relationship in every experiment we have performed. 

 Thus the partial inhibitory terms making up / in equation (1) are each of the 

 form given by equation (2) with appropriate subscript labels to identify the 

 pair of elements involved and the direction of the action that is being con- 

 sidered. 



The law of combination of inhibitory influences also turns out to be a 

 simple one ; the partial inhibitory terms are merely added to express the total 

 inhibition exerted on a given receptor. Thus for ommatidium 1 the total in- 

 hibition exerted by all of its neighbors (all of the other ommatidia in a group 

 of n interacting units) is expressed by: 



h = h, 2 + /'i, 3 + ... h, n (3) 



This law of "spatial summation" of inhibitory influences is not an a priori 

 assumption; it has been derived from experimental findings. Two patches of 

 light were projected on to regions on either side of a test receptor, close 



