MERISTIC PHENOMENA 35 



passed on from germ to germ, yet the power of increase which 

 must be attributed to it remains so incomprehensible that the 

 mystery is hardly at all illuminated. 



When however we pass from the substantive to the meristic 

 characters, the conception that the character depends on the 

 possession by the germ of a particle of a specific material becomes 

 even less plausible. Hardly by any effort of imagination can we 

 see any way by which the division of the vertebral column into x 

 segments or into y segments, or of a Medusa into 4 segments or 

 into 6, can be determined by the possession or by the want of a 

 material particle. The distinction must surely be of a different 

 order. If we are to look for a physical analogy at all we should 

 rather be led to suppose that these differences in segmental 

 numbers corresponded with changes in the amplitude or number 

 of dividing waves than with any change in the substance or 

 material divided. 



PHENOMENA OF DIVISION 



I have said that in the division of a cell we seem to see the 

 problem in its simplest form, but it is important to observe that 

 the problem of division may be presented by the bodies of animals 

 and plants in forms which are independent of the divisions be- 

 tween cells. The existence of pattern implies a repetition of 

 parts, and repetition of parts when developed in a material 

 originally homogeneous can only be created by division. Cell- 

 division is probably only a special case of a process similar to 

 that by which the pattern of the skeleton is laid down in a uni- 

 cellular body such as that of a Radiolarian or Foraminiferan. 

 Attempts have lately been made to apply mathematical treat- 

 ment to problems of biology. It has sometimes seemed to 

 me that it is in the geometrical phenomena of life that the most 

 hopeful field for the introduction of mathematics will be found. 

 If anyone will compare one of our animal patterns, say hat of a 

 zebra's hide, with patterns known to be of purely mechanical 

 production, he will need no argument to convince him that there 

 must be an essential similarity between the processes by which 

 the two kinds of patterns were made and that parts at least of 



