58 ON MAGNITUDE [ch. 



the final configuration of the whole material structure. But it is 

 by no means true that form and growth are in this direct and simple 

 fashion correlative or complementary in the case of minute portions 

 of living matter. For in the smaller organisms, and in the indi- 

 vidual cells of the larger, we have reached an order of magnitude 

 in which the intermolecular forces strive under favourable conditions 

 with, and at length altogether outweigh, the force of gravity, and 

 also those other forces leading to movements of convection which 

 are the prevailing factors in the larger material aggregate. 



However, we shall require to deal more fully with this matter in 

 our discussion of the rate of growth, and we may leave it mean- 

 while, in order to deal with other matters more or less directly 

 concerned with the magnitude of the cell. 



The hving cell is a very complex field of energy, and of energy 

 of many kinds, of which surface-energy is not the least. Now the 

 whole surface-energy of the cell is by no means restricted to its 

 outer surface; for the cell is a very heterogeneous structure, and all 

 its protoplasmic alveoli and other visible (as well as invisible) hetero- 

 geneities make up a great system of internal surfaces, at every part 

 of which one "phase" comes in contact with another "phase," and 

 surface-energy is manifested accordingly. But still, the external 

 surface is a definite portion of the system, with a definite "phase" 

 of its own, and however little we may know of the distribution of 

 the total energy of the system, it is at least plain that the conditions 

 which favour equihbrium will be greatly altered by the changed 

 ratio of external surface to mass which a mere change of magnitude 

 produces in the cell. In short, the phenomenon of division of the 

 growing cell, however it be brought about, will be precisely what 

 is wanted to keep fairly constant the ratio between surface and 

 mass, and to retain or restore the balance between surface-energy 

 and the other forces of the system*. But when a germ-cell divides 

 or "segments" into two, it does not increase in mass; at least if 

 there be some shght alleged tendency for the egg to increase in 



* Certain cells of the cucumber were found to divide when they had grown to 

 a volume half as large again as that of the "resting cells." Thus the volumes 

 of resting, dividing and daughter cells were as 1:1-5: 0-75; and their surfaces, 

 being as the power 2/3 of these figures, were, roughly, as 1:1-3: 0-8. The ratio 

 of SjV was then as 1 : 0-9 : 1-1, or much nearer equality. Cf. F. T. Lewis, Anat. 

 Record, xlvii, pp. 59-99, 1930. 



