266 



ELEMENTARY BIOLOGY 



sufficient to excrete the waste matters for a larger quantity of 

 protoplasm than the cell contains at that moment. Beyond 

 this point, growth is manifestly impossible, although at this 

 point the protoplasm may be able to maintain indefinitely the 

 balance of income and outgo that is, to " live." 



We must not suppose that 

 the ratio of volume to super- 

 ficial area is the only factor 

 that stops the growth of cells, 

 or that it necessarily has any- 

 thing to do with it. This is 

 simply a possible reason why 

 the growth of cells cannot go 

 on indefinitely. There may 

 be other factors, chemical or 

 mechanical or electrical per- 

 haps, that play important 

 roles in this matter. We may 

 say that the growth and mul- 

 tiplication of cells go on as 

 though the ratio of volume 

 to area had something to do 

 with it. 



FIG. 104. The ratio of volume to diameter 

 and area 



The cube a has six surfaces, each a square and 

 all the same size. The larger cube, /5, of twice 

 the diameter, has eight times the volume and 

 four times the surface that a has. As a body in- 

 creases in size the surface increases in the same 

 proportion as the square of the diameter, whereas 

 the volume increases as the cube of the diameter. 

 A growing plant or animal may thus reach a size 

 at which the surface is insufficient for the ex- 

 change of materials necessary to maintain the 

 inclosed protoplasm 



In a thread-shaped alga 

 like Spirogyra the thread 

 of cells may grow indefi- 

 nitely, because the receiv- 

 ing and excreting surface 



of the cell is not much reduced by contact with neighboring 

 cells (see Fig. 105). The thread-shaped cells of many fungi 

 get to be several inches in length without dividing ; this sup- 

 ports the idea that the ratio of surface to volume has something 

 to do with the amount of growth possible. 



320. Healing and resumption of growth. When a full-grown 

 man cuts his hand, the cut will heal up by the formation of 

 new cells in the neighborhood of the injured surface. These 



