THE CELL AND CELL DIVISION 77 



extent of the surface of these parts of the cells in relation to the two 

 masses. 



Immediately after mitosis is completed the nucleus grows very rapidly 

 for a brief period, and then much more slowly or not at all. The cyto- 

 plasm, however, does not show this rapid initial growth, but maintains 

 a fairly uniform and continuous growth rate. As a result, in a newly 

 formed cell the ratio of nuclear mass to cytoplasmic mass becomes quite 

 high, but soon diminishes, and in an older cell diminishes rapidly, since 

 the cytoplasm continues to grow after the nucleus nearly ceases. Con- 

 sidering first the relation of the surface to the mass, and assuming for 

 illustration that the cell and nucleus are both spherical, we can see how 

 this increase in size alters the relation of mass to path of interchange, 

 since the area of the surface of an enlarging sphere increases relatively 

 slower than the volume. Should the cell double its diameter through 

 growth, it increases its volume eight times and its surface only four times. 

 A cubical cell doubling the length of its sides reduces its ratio of area to 

 volume as 2 : 1. Or expressing a similar relation somewhat differently, 

 a spherical cell doubling its volume, lessens its ratio of surface to volume 

 approximately as 5 : 4, while a cubical cell doubling its volume reduces 

 the same relation approximately as 6 : 4.75. 



These relations are probably important for both of the chief interac- 

 tions of cell life, those between nucleus and cytoplasm, and between 

 cytoplasm and surrounding medium. The only pathway between cyto- 

 plasm and nucleus is the nuclear membrane, while the surface of the 

 cytoplasm or cell wall forms the pathway between cell and medium. 

 There is of course a limit to the capacity, so to speak, of these surfaces, 

 and as the cell increases in volume this limit tends to be reached. The 

 ratios of these surfaces to the masses are raised by the division of the 

 cell, which reduces volume more than surface, and thus restores the 

 efficiency of the surfaces as pathways of interaction. The tendency for 

 the cytoplasmic mass to increase more rapidly than the mass of the 

 nucleus in older cells seems to be of even greater importance than these 

 surface to mass relations. There seems to be a fairly definite specific 

 limit to the ratio of nuclear mass to cytoplasmic mass, although it is 

 difficult to say whether after all the nuclear surface relation is not even 

 here an equally important factor. This mass relation is called the 

 "kern-plasma" or nucleo- cytoplasmic relation, the importance of which 

 is emphasized particularly by Richard Hertwig. There is a definite 

 average cell size in a given tissue and species ; a large or a small organ 

 or organism does not possess respectively larger or smaller cells, but 

 larger or smaller numbers of cells of the same average dimensions. 

 The limiting factor, however, seems to be not the actual bulk of the cell, 

 but the proportion between the volume of the nucleus and that of the 



