XV] Symmetry 277 



variations it may perhaps be found hereafter of use to bear 

 in mind that just as the divisions of germ-cells are of two 

 kinds, 



(i) Symmetrical, producing the resemblance called 

 Heredity, 



(2) Asym^netrical, producing the difference called 

 Variation, 



so are somatic cell-divisions recognizably of two kinds. For 

 there also we meet divisions by which similar parts are 

 divided from each other, and differentiating divisions by 

 which parts with distinct characters and properties are 

 separated. It is evident that when the conception of 

 symmetry is applied to such phenomena it must be under- 

 stood to include the case of production of like parts by 

 division which result in the formation of a successive series. 



In this connection reference should be made to a work 

 of more than ordinary suggestiveness lately published by 

 Jennings (163). Speaking of the fission of Paramoecium 

 which results in the formation of two individuals by a 

 transverse division, he truly says that *' it is evident that 

 even in Protozoa heredity is not a mere result of sub- 

 division," for in the new individuals the head-end produces 

 — regenerates, perhaps we might say — a tail, and the new 

 tail-end grows a head. 



That there must be a real difference between the 

 mechanical processes by which this repetition comes about, 

 and that in which two halves are formed as optical images 

 is clear. The latter is the obvious case of real geometrical 

 symmetry. But when two similar individuals are formed, 

 so that one is placed in succession to the other, this result 

 may be described as symmetrical in so far as the two pro- 

 ducts are similar, but the homologous parts instead of being 

 adjacent to each other, are arranged in alte^mating series. 



Jennings' observations relate to a remarkable case. He 

 found a Paramoecium with a monstrous outgrowth, or spine 

 of protoplasm, and as the animal successively divided, this 

 spine was handed on to one not both of the products of 

 division. Obviously there is here something which may be 

 interpreted as providing a rough model of the process of 



