THE CRITERIA OF LIVINGNESS 93 



regular shape increases in volume, it does not proportionately 

 increase in surface. If it be a sphere, the volume of material 

 to be kept alive increases as the cube of the radius, while 

 the surface, through which the keeping alive is effected, in- 

 creases only as the square. Thus there tends to be a hazard- 

 ous disproportion between volume and surface, which may 

 set up instability. The disturbed balance may be restored 

 by the emission of processes from the surface of the cell, 

 making it like a country with a big coast-line, as in Rhizopod 

 Protozoa or in the amoeboid cells found in most multicellular 

 animals. But the disturbed balance is normally restored 

 by the cell dividing into two cells. This view indicates the 

 advantage of cell-division, but beyond the hint that a dis- 

 proportion between volume and surface may induce physio- 

 logical instability, perhaps a cell-solution or cytolysis, it 

 does not tell us what brings the process about. 



It is an interesting fact that if a non-nucleated fragment 

 of cell-substance be cut off from a large Protozoon, it can 

 move about for a time, but it cannot feed or grow, and 

 sooner or later it dies. But a nucleated fragment does not 

 'die. There are other facts which point to the same conclu- 

 sion that the nucleus is a sort of dynamic centre to the cell 

 (especially a trophic centre), and that stability depends on 

 keeping up a certain proportion or relation between the 

 nucleoplasm and the cytoplasm. It follows, therefore, that 

 if growth imply an increase of cell-substance out of pro- 

 portion to nuclear substance, a state of physiological in- 

 stability may set in, which cell-division may counteract. 

 In many large Protozoa there are numerous nuclei. 



It has also been suggested that a period of growth is auto- 

 matically followed by a process of " autokatalysis ", or self- 

 fermentation, but precise data are awanting. What we wish 



