54 A. T. MASTERMAN [january 



predominant number will be six, corresponding to twice the number 

 of dimensions. The geometrical representatives of these two conditions 

 are the tetrahedron and the octahedron respec- 

 tively, and the other possible numbers are re- 

 presented by the cube, dodecahedron, and the 

 ..--'' icosahedron. An absence of secondary centres 



I ■-- x. results in the sphere, hence the term " spherical 



symmetry," as used by Spencer. All truly centro- 

 symmetric organisms should conform to the types 

 of the regular polyhedron or the sphere, but are 

 not necessarily confined to the latter. This type 



Fig. 1.— Cento-symmetry. agreeg a l so w j t j 1 t ] ie ce ntrO-Stigma Or sphaero- 



typic group of Haeckel. 



The organisms exhibiting this form of symmetry consist of a great 

 number of Protozoa, such as the Heliozoa, and a large proportion of 

 the Eadiolaria and Eeticularia. In addition to these, we may include 

 certain of the Flagellata, as Uroglena, Syncrypta and Pandorina, and 

 Acinetaria. A great number of the Protozoa also assume this form of 

 symmetry as a transitory phase in their life -history (encystment). 

 Apart from adult organisms, the great majority of the eggs of higher 

 types conform more or less closely to this type, as also do the so-called 

 blastula larva of the Metazoa, and the gemmules of Porifera, e.g. 

 Spongilla. 



We thus notice that the animal organisms which exhibit centro- 

 symmetry are confined to the adult phases of the Protozoa and to 

 the early ontogenetic phases of many higher Metazoa. It is evident 

 that, with the form and constitution of the earth as it is at present, 

 it is impossible to conceive of an environment in itself which is 

 centro-symmetric, that is, symmetrical round a point. The fact that 

 organisms dwell upon the surface of a sphere (oblate spheroid, to 

 be more accurate), causes a constant heterogeneity in one dimension 

 which, through the physical factors of gravity, and in most cases light, 

 will be a constant factor in the induction of a certain amount of 

 heterogeneity in organisms. Hence, in the attempt to correlate structure 

 and environment, the existence of centro-symmetric organisms would 

 appear to be a difficulty. This, however, is only apparent, for the 

 effect of environment upon the organism is dependent not only upon 

 the environment, but upon the manner in which the organism, so to 

 speak, allows itself to be subjected to it. Thus Spencer points 

 out that centro-symmetric organisms are usually free to rotate 

 about their centre, either actively or passively, thus eliminating the 

 effect of axo-symmetry in the environment. 



Again, if the organism be for a time removed from the influence of 

 its environment by the formation of a coat, a cyst, or a shell, the influ- 

 ence being reduced to zero in all directions, the centro-symmetric form 

 will be assumed. 



