60 PHYSIOLOGICAL GENETIC8 



to the end. If the size of the Anlage at each moment of normal 

 development is given by the normal growth curve on top, the 

 ordinates of the other curves ought to indicate also the size of the 

 degenerating Anlage at different times, in fractions of the normal 

 size at the same time. The curves for the different alleles have 

 really been drawn according to the values of these fractions, 

 actually found and noted in the diagram. The resulting pheno- 

 type is marked on the right side. The diagram, then, represents 

 all the facts mentioned in terms of rates of production of some- 

 thing and apparently this general form, which might be varied 

 considerably in details, is the only consistent method of repre- 

 senting all the facts. (According to Kirchhoff's classic definition, 

 an explanation is the shortest description of all the facts.) As 

 mentioned before, the same facts may just as well be presented in 

 terms of production of something that destroys wing tissue. If 

 we accept this reciprocal type of representation, the curve (Fig. 

 20) means, besides the growth curve, the curve of production 

 of the substance in question which from a certain moment on 

 destroys tissue. This representation seems at first sight less 

 probable. But a most remarkable parallel is available, which 

 makes it worth while to investigate whether there is not some- 

 thing more than a superficial resemblance behind the two 

 phenomena. In a series of papers on the kinetics of bacteri- 

 ophage, Krueger (see 1936) found the following facts: 



If a mixture of phage and growing bacteria is kept, the increase 

 of phage depends upon the bacterial growth in so far as it does 

 not occur without the latter. But the rate of increase of phage 

 is considerably greater than the rate of bacterial reproduction, 

 and therefore the ratio of phage to bacteria is constantly increas- 

 ing. When a certain ratio in favor of phage is reached — the 

 lytic threshold — lytic destruction of bacteria begins and proceeds 

 rapidly to completion. The time of onset of this destruction is 

 proportional to the initial concentration of phage in the mixture. 

 Phage may be inactivated and reactivated by differentiations. 

 In addition, in the presence of manganese, the lytic action begins 

 earlier; this is solely an effect upon the threshold, i.e., the quantity 

 of phage /bacterium requisite for lysis. Figure 21 represents 

 Krueger's graph for these experiments, which shows a perfect 

 model of the vestigial case. The growth curve of bacteria 

 corresponds to the normal wing growth in Drosophila. The same 



