DYNAMICS OF MORPHOGENESIS 71 



of the wound. Under given external conditions, it probably 

 does not differ very greatly in pieces of different length and from 

 different regions. The rate in the region y (rate y), on the other 

 hand, varies, as we have seen, with size and level of body. When 

 rate y is sufficiently high in relation to rate x, the cells at x are 

 prevented from beginning independent development and produc- 

 ing a new head. On the other hand, the lower the rate of y in 

 relation to the rate of x, the more independent are the cells at 

 X and the more likely to produce a head. 



The fact that head-determination in pieces occurs almost 

 immediately after section, shows that the critical period is at the 

 very beginning of the division and growth in the region x. Evi- 

 dently, the determination whether a head shall arise or not is 

 essentially simply a question whether the region x shall develop 

 with at least a certain degree of independence of the region y, 

 in which case it produces a head, or whether its development 

 shall be inhibited by y. 



If this conception of the process of head-determination is 

 correct, then we arrive at a very simple expression for the head- 

 frequency in pieces of different size and from different regions, 



rate x 

 VIZ., head-frequency = — ; — . 



rate y 



We do not know positively whether rate y must actually be 

 higher than rate x in order to inhibit head-formation, but there 

 is no reason to believe that such a difference is necessary. It 

 has been pointed out in earlier papers (Child '11 d, '12, '13 c) 

 that in the intact animal the rate of metabolism decreases from 

 the head region posteriorly. If this is the case and if the effects 

 of section and the local effect of the wound could be eliminated, 

 rate x in a piece should always be higher than rate y. But the 

 region ?/ is a system of correlated parts with conducting paths 

 and metabolic mechanisms fully developed and capable of a 

 relatively high degree of stimulation. The region x, on the other 

 hand, during the first few hours after section (i.e., the period when 

 its fate is determined) is merely a group of cells without definite 

 mechanism of correlation corresponding to a head. It is possible 

 that the fully developed region y may overbalance and inhibit 



