Child, Driesch's harmonic equipotential systems in form-regulation. 585 



p. 413) he such as this, and this is by no means an isolated case, 

 make Driesch's frequent imputations to others of carelessness 



tatively in the posterior than in the anterior regions. Moreover, Dries ch has not 

 yet stated at all the rather important result that regeneration in the anterior 

 direction is always not merely quantitatively, but qualitatively incomplete at all 

 levels posterior to the cephalic ganglia, whether food is present or not. Repeated 

 incorrect statements, says: „Wo also in aller Welt habe ich von mathematisch- 

 strikter Proportionalität geredet? Das wüsste ich wahrlich gern. Und ferner wäre 

 mir lieb zu wissen, wo bei seinen Proportionalitätsmessungen an Hydrantanlagen 

 von Stammstücken verschiedener Größe oder verschiedener regionaler Herkunft oder 

 verschiedener Polarität denn Child auch nur irgend etwas gefunden hat, was von 

 meinen wahren Befunden und Aussagen, wie sie vorliegen, abweicht?" The answers 

 to these questions are to be found in the above quotations from Driesch's „wahren 

 Befunden und Aussagen, wie sie vorliegen", and my remarks concerning them. 

 Driesch's formula x = gA for „das eigentlich Lebensautonome — am Geschehen" 

 is impossible without the assumption of strict mathematical proportionality. Moreover, 

 he has nowhere stated that the lengths of the primordia decrease less rapidly than 

 the lengths of the pieces. What he did state was „es ist hier (i. e., for Tubularia) 

 konstatiert, dass von einer bestimmten Stammlänge an abwärts, die Längen der Ge- 

 samtanlageareale verschiedener Objekte sich annähernd verhalten wie ihre Stamm- 

 längen" (D riesch, 1901, p. 174). I must still believe that this statement does 

 not express my own results, for I found that under certain conditions the length 

 of the piece might decrease more than twice as rapidly as the length of the jm- 

 mordium. 



Driesch has also accused me (Driesch, 1908, pp. 412 — 413) of imputing 

 to him the belief that a mathematically exact proportionality exists in Tubularia. 

 This I have never done, I have maintained and must still do so on the basis of 

 the above quotations, that Driesch's conception of the harmonic equipotential 

 system is based on the assumption of mathematically exact proportionality. The 

 formula x = gA has been discussed above: in the definitions quoted we find the 

 expressions „ganz festen relativen Lageverhältnis" and ,,ganz bestimmte Beziehungen". 

 If words possess any definite meaning, it seems to me that we are forced to inter- 

 pret these various expressions as signifying exact proportionality. I was familiar 

 with Driesch's various statements to the effect that only approximate proportionality 

 existed in Tubularia, but I cannot find that he has ever stated that there are 

 characteristic regional, polar and dimensional differences in the proportions of the 

 primordia. 



But Driesch (1908, p. 413) still asserts, in spite of my data, that approxi- 

 mate proportionality exists in Tubularia. Final decision upon this point is impos- 

 sible until Driesch defines approximate proportionality. But a brief reference to 

 some of my data will show the basis for my conclusions. In my measurements 

 (Child, 19071, p. 289, Table III), where pieces of given lengths compared, I found 

 that in pieces of 4 mm and 2 mm respectively the difference in the lengths of the 

 primordia was in one series about 9°/o, in another 21°/o, i. e., the length of the 

 pieces hat decreased 50 "/o and the length of the primordia, in one case 9''/o, in the 

 other 21 «/o. 



In pieces of 6 mm and 4 mm respectively, a decrease in length of the pieces, 

 of 33,3 "/o, the decrease in length of the primordia was ö^/o and in p)ieces of 6 and 

 2 mm respectively, a decrease in length of the pieces of 66,7 °/o, the decrease in 

 length of the primordia was 25 "/q. Is this approximate proportionality between the 

 length of the primordium and the length of the piece? 



Driesch, in his measurements (Driesch, 1899 b, Table VIII, p. 119), grouped 

 pieces of three different lengths in eech class, e. g., he compared pieces, 3, 4, and 



