746 PATTERNS AND PROBLEMS OF DEVELOPMENT 



in which //5-;/i are the numbers or percentages of the different head forms (7/5, 

 normal, to «,, acephahc) and N is the total number of pieces in the lot or of living 

 pieces, or, in percentages, 100. Since it is not certain that the different groups of 

 head forms represent corresponding amounts of physiological difference or change, 

 the values assigned are arbitrary, except that they indicate the order of degree of differ- 

 ential inhibition. The value, /, therefore is not a true mean head frequency but merely 

 an index. 



The recent application by W. A. Castle (1940, "Methods for evaluation of head 

 types in planarians," Physiol. ZooL, 13) is of particular interest as providing a basis for 

 more accurate general expression of head frequency data. However, the head fre- 

 quency curves obtained in this way differ little in most cases from those graphed 

 from the "head frequency indices" obtained by the method described above. The 

 following quotation from Castle's paper summarizes the situation: 



It is not to be inferred that the originators and users of the old scale of indices intended it 

 to be more than an approximation for convenience. Indeed, Buchanan has stated 11923a, 

 p. 410] that "no claim is made that the values 5, 4, 3, 2, i, represent any exact mathematical 

 valuation of regenerated tissue; this is simply a convenient and consistent way of showing the 

 effects of the agent on head frequency." For the purpose designed, the old scale of equal in- 

 tervals appears in most cases to have been entirely adequate for outlining major differences 

 in head frequency along the axis of the planarian body or for distinguishing between the 

 head frequencies of experimental and control groups where the differences are not obscure. 

 Where such differences are slight, however, the use of a scale in which the indices or class 

 ranges do closely approach the values based on observed frequencies of occurrence of the re- 

 generated structures probably comes closer to revealing the real relationships between control 

 and experimental groups. 



