290 



ESSENTIALS OF ZOOLOGY 



We have not been able to put our fingers on any one factor that 

 completely controls growth. We do know of certain relationships 

 that influence it. It will be recalled that all materials used by a 

 cell must pass through the cell membrane, and likewise all waste 

 substances must be discharged in a similar manner. Mathematics 

 states that the volume of a cell increases according to the cube of 

 its diameter; while its surface increases only according to the 

 square of its diameter. In other words, the amount of material in 



Nucleus 



Contractile 

 iracaole 



Fig. 96. — Binary fission in amoeba. A, Beginning of the process; B, nearing the 

 completion of two new cells. (Drawn by Joanne Moore.) 



New cells huclear fragment 



Fig. 97. — An amoeba encysted and undergoing the process of sporulation. (Drawn 



by Joanne Moore.) 



a growing cell increases approximately twice as fast as the plane 

 surface needed to surround it. It is logical, then, to assume that a 

 point may be reached when the surface area will not be sufficient 

 for the passage of necessary materials into and out of a cell. There 

 is, however, considerable variation in the size of cells; hence it 

 seems there must be other factors besides volume and surface rela- 

 tion in operation. Modified surface and difference in the rate of 

 metabolism certainly would be factors affecting the size of the 



