90 PROC. ENT. SOC. WASH., VOL. 24, NO. 4, APR., 1922 



by this insect. Now let us suppose that one of the other races 

 of senilis here described was found to parasitize abundantly 

 some other European insect already existing in the infested 

 areas: and that this race had been assumed on the report of a 

 reputable specialist to whom the adult parasites had been sub- 

 mitted to be identical with the form attacking the Borer. In 

 such a case the collection and shipment of parasitized caterpil- 

 lars of the other insect would naturally appear to be a legitimate 

 and desirable proceeding: and unless a subsequent study of the 

 larval forms disclosed the differences between the two parasites, 

 the total failure of an experiment which perhaps entailed a con- 

 siderable expenditure of time and money would come as a dis- 

 agreeable surprise and the reasons for this failure would, remain 

 quite obscure. 



The question is, however, whether the phenomenon of poecil- 

 ogony really exists: or in other words whether it might really 

 be impossible for the trained specialist, even when fully awake 

 to the difficulties presented by a particular case, to discover 

 definite characters for the separation of the races in the adult 

 stage. 



At first sight it would seem that such differences must of 

 necessity exist: for if two individuals produce offspring mor- 

 phologically different at birth it would seem to follow logically 

 that the differences in these offspring must have their origin in 

 differences in the adults which it ought to be possible for the 

 trained eye of the specialist to detect. Viewed from this 

 stand-point which I have found in practice to be that of a 

 representative and reliable specialist the phenomenon of 

 poecilogony appears to be an impossibility. Nevertheless it 

 can be shown to be practically if not theoretically possible: 

 and to demonstrate this it is only necessary to reduce the 

 phenomenon to its simplest expression and study it in its simplest 

 form. 



Reduced to its most general form the question of the existence 

 of poecilogony may be expressed somewhat as follows: 



Whether two continuous series expressed by different formulae 

 and consequently fundamentally different when taken as a whole 

 are nevertheless under certain circumstances practically indis- 

 tinguishable in certain homologous portions of their trajectories. 



So expressed, the question can for practical purposes be solved 

 by the use of elementary mathematical methods: bearing in 

 mind the fact that the mathematical study of plane curved and 

 straight lines is simply a morphological study of a type much 

 simpler than that with which the biologist has usually to deal 

 a morphology in which the laws of form are both clearly and 

 simply expressed. 



In figures 19 A and 19 B I have plotted the corresponding 



