January 1899] ANIMAL SYMMETRY 51 



defining the mathematical forms they sought not by the surfaces but 

 by axes and their poles." 



By certain French and English botanists the terms " symmetry," 

 "symmetrical," and "asymmetrical" have been employed in a very 

 different connection, namely, to express the numerical correspondence 

 or otherwise between the constituent elements of concentric whorls. 



A definition which would include all these ideas would have to 

 express merely a vague order of some kind, involving repetition, as 

 existing between the parts of an organ or organism. 



The term is used commonly amongst zoologists in a sense resembling 

 the wider usage amongst botanists. Thus the acknowledged distinction 

 of radially and bilaterally symmetrical organisms rests upon this inter- 

 pretation of the term symmetry. But the so-called " zonal symmetry " 

 instituted a fresh conception of the term " symmetry," which, if accepted, 

 would again require a vague definition. In the former case we deal 

 with the definite arrangement of the parts of an organism about a 

 median geometrical centre; in the latter is introduced the idea of 

 a serial repetition of certain parts along an axis, thus leading to 

 a confusion between the terms " segmentation " and " symmetry." 

 Haeckel 1 has recognised this distinction by applying the term " antimere " 

 to the unit of so-called " radial " symmetry, and " metamere " to the 

 segment or " zoonite." 



Gedcles 2 clearly shows how the study of symmetry implies the 

 attempt to force mathematical or mechanical conceptions upon the 

 organic world, and indicates that the attempts of Moseley and Goodsir in 

 this direction were based upon many analogies which, " savouring more 

 of the IVatwyhilosophie than of sober mathematics, could only serve to 

 discourage further inquiry and interest." 



The analogy drawn from time to time between the organism and 

 a crystal and the parallel between Haeckel's " promorphology " and 

 crystallography have an underlying basis of truth, but they are liable 

 to be misconstrued if carried too far. The material basis of vital 

 phenomena, namely protoplasm, is essentially amorphous (or truly 

 asymmetric, see later) as regards any properties inherent in itself; and 

 the form assumed by any mass of it, constituting for the time being an 

 individual, must depend entirely upon the particular environment at 

 that time. In highly differentiated individuals the exact extent of the 

 direct effect of environmental changes is a disputed question, but by 

 whatever particular path the process may be effected it may be taken 

 as a truism that an organism tends to change its form in relation to 

 changes of environment, and that while in the lower types the change 

 is effected many times in the history of the individual, in the higher 

 types it is with equal certainty effected in the history of the species. 

 These considerations do not apply to the crystal. 



On the other hand, the crystal and the organism are each isolated 



1 Haeckel, " Generelle Morphologie, " Berlin, 1866. 2 Loc. cit. 



