60 INVERTEBRATE PHYSIOLOGY 



tion, we assume that there is a constant hnear proportionahty between <f> 

 and ^c and between <^c and /x, respectively, and if we define the propor- 

 tionality factors as A (opt) and A(neck) respectively, then 



ii^ = A(opt) X A,„eck) X <^ or 



~ ^ A, opt) X -'^(neck) 



9 



The ratio ix/(f> will be named Ac (total) , the total interior amplification of 

 the control circuit. You may note that this is a pure number without any 

 dimension. It may be worth while to give an example of how that works. 

 Assume the system has an Ac (total) of 4, and a fly comes into sight at 

 cr = -(- 20°, that is 20° to the right. Then the fixation process will come to 

 rest exactly at a head deviation /a of -|- 16°, ^ thus being +4°. For only 

 with that optic input can the neck motor output be + 16°, if we have 4 times 

 total amplification. Thus in general : 



o- 1 + Ac(total) 



and the prey will be better centered as Ac (total) increases. The ratio 



^— will be named the "fixation-deficit." 

 a 



Now we are able to formulate the hypothesis, namely as follows : It is 

 assumed that fi is converted by the hair-plate system into a message 8c, and 

 that the neck muscles are steered by the difiference between the optic center 

 message 4>c and the proprioceptor center message 8c- Thus there are two 

 circuits working together (see Fig. 6b). 



In order to understand the operation of these circuits, let us watch the 

 proprioceptive subcircuit acting in isolation. Suppose the head to be thrown 

 out of its median position by some extraneous influence, say 20° to the 

 right. Then the hair plates will transmit a message causing a head move- 

 ment to the left. The system will come to rest at the smallest value of /a 

 allowed for by the amount of the extraneous influence and the total amplifi- 

 cation of the proprioceptive circuit. Therefore we may say that this circuit 

 tends to minimize /x against all extraneous influences. Because the optic 

 circuit — as we have just learned — tends to minimize (j>, it can easily be seen 

 that there must be a rivalry between the two systems, except only in the 

 case that o- = 0, the prey being straight ahead of the prothorax — then 

 cj} and IX should be zero. In all other prey deviations neither the one nor the 

 other circuit wifl reach its target. Thus under the conditions adopted the 

 fixation-deficit must have a finite value, and hence, at equilibrium, there 

 will be a constant correlation between the proprioceptive input, the optic 

 input, and the deviation of the prey from the body axis. Consequently the 

 optic and the proprioceptive center messages (4>c, 8c) must also have a 



