414 C. M. CHILD 



the piece (fig. 3, y) is in a sense antagonistic, in that conditions 

 which stimulate or accelerate the physiological activity of x in 

 relation to y, or conversely, decrease the activity of y in relation 

 to X increase head-frequency, while conditions which increase the 

 activity of y in relation to x or decrease the activity of x in rela- 

 tion to y decrease head-frequency (Child, '14 d, '16). These re- 

 lations have been expressed in the formula head-frequency 



= — - — . This formula is merely a brief expression of relations 

 rate?/ - ^ 



indicated by the experimental data. The physiological situa- 

 tion is apparently as follows : In an isolated piece certain cells {x) 

 along the cut surface are isolated by the cut from all the correl- 

 ative factors that formerly reached them from parts anterior to 

 the cut and are also stimulated by the wound. These correl- 

 ative factors represented a large part of the factors which deter- 

 mined the differentiation and behavior of these cells as a part of 

 the body, and in their absence the cells tend to lose this differenti- 

 ation and to become physiologically younger. But the relation 

 of the cells x to the regions posterior to them {y) have not been 

 altered by the cut, and any correlative factors which reach x 

 from y must tend to prevent or retard its dedifferentiation and 

 independent development. Consequently, the result in any par- 

 ticular piece will vary as one or the other of these factors has the 

 ascendancy. For the present we may express this relation in 

 terms of the activity of the regions x and y. If the activity (and 

 probably the energy-liberating activity is primarily concerned) 

 of X is sufficiently intense as compared with that of y, the cells of 

 X will be in large measure independent of y and will dedifferentiate 

 and develop anew in spite of y, and the product of this develop- 

 ment will be a normal head; i.e., the primary developmental 

 reaction of planarian protoplasm will occur (Child, 'lie, '15 b, 

 pp. 96-102). If on the other hand, the activity of y in relation 

 to that of X is sufficiently intense to inhibit or retard these pro- 

 cesses to some extent, the development of the head will be retarded 

 and its structure will range from a slight degree of teratophthalmia 

 to extreme anophthalmia, or in the extreme case the development 

 of a head is completely inhibited and the piece remains acephalic. 



