220 



THE EVOLUTION OF SEX. 



actual necessities require. There is a surplus for further up- 

 building after mere reparation has been made. This surplus 

 is the condition of growth. Popularly, but yet accurately, it 

 may be said that growth or addition to the capital of the 

 organism occurs when income 15 in excess of expenditure, when 

 construction preponderates over disruption. 



But beside this familiar fact, it is necessary to place another 

 certainty, that of the limit of growth. We may fairly call giants 

 a few of the Protozoa, such as the large amoeboid Pelomyxa, 

 some of the gregarines, and even more markedly the extinct 

 nummulites, which were sometimes as large as half-crowns. So 

 an occasional alga, like Botrydium, may swell out into a large 

 single cell, and the ova of animals, e.g:, birds, are often greatly 

 expanded by the accummulation of yolk. Yet the unit masses 

 generally remain very small. They have their maximum size. 



Cell-division at the limit of growth. 



approximately constant for each species. Up to this point they 

 grow, but no further. The same, as every one know^s, is true 

 of multicellular animals. The size fluctuates slightly according 

 to the conditions of individual life, but the average is strikingly 

 constant. 



§ 2. Spencer's Theory of Growth. — The first adequate dis- 

 cussion of growth is due to Spencer. He pointed out, that in 

 the growth of similarly shaped bodies the increase of volume 

 continually tends to outrun that of the surface. The mass of 

 living matter must grow more rapidly than the surface through 

 which it is kept alive. In spherical and all other regular units 

 the mass increases as the cube of the diameter, the surface only 

 as the square. Thus the cell, as it grows, must get into physio- 

 logical difiiculties, for the nutritive necessities of the increasing 

 mass are ever less adequately supplied by the less rapidly 

 increasing absorbent surface. The early excess of repair over 



