REPRODUCTION 103 



grows, obviously the surface will increase synchro- 

 nously with the volume, but not in the same ratio, 

 for mathematicians tell us that, in a sphere, while the 

 mass increases as the cube of the radius, the surface 

 increases only as the square. Under these circum- 

 stances there will come a time when the mass must 

 attain a size just such as may be adequately nourished 

 by the possibilities of the surface as a means of 

 entrance of food, and adequately purified by the 

 possibility of getting rid of waste. A further increase 

 in the volume is obviously impossible, since not only 

 is there no surface available for the entrance of suffi- 

 cient food, but the surface is 

 also inadequate for the ex- 

 cretion of the waste. The 

 cell must then either die or 

 readjust the relation between 

 surface and volume. If it 

 divides into equal parts, its 

 volume is at once halved and F IG . 49. 



the surface area of each half is 



increased by the whole circular face exposed by the 

 division (Fig. 49). For instance, in the spherical cells A 

 and B, let us assume that the radii are two and three 

 millimetres respectively. The volumes of these 

 spheres may be calculated from the formula i TT r s , 

 where r = radius and ?r = a number approximately 

 estimated at 3i. The volume of A will thus be 33^ 

 cubic millimetres. The surface of a sphere may be 

 determined from the formula, 4 TT r 2 , so that the extent 

 of the surface of cell A amounts to 50S- square milli- 

 metres. Similarly, the volume of cell B will be 113-1 

 cubic millimetres, and its area will be 113^ square 

 millimetres. Assuming for the sake of argument that 

 an area of 1 square millimetre is sufficient for the 



