ULTRAVIOLET RADIATION AND CANCER 539 



Cancers grow as the result of the proliferation of cells ; at least, this is 

 what happens after they first appear. And so it must be assumed that 

 the rate of tumor growth is always some function of the number of existing 

 actively dividing cells. In general, the individual cancer cell does not 

 enlarge beyond a certain quickly attained volume, and the rate of growth 

 of a tumor is also a function of its volume. Hence the growth may be 

 described by giving its volume T', or, alternatively, the number of cells 

 composing it, N, as a function /, of the time t, 



V = m 



Nv = m (14-1) 



where v is the average volume of the individual tumor cell, assumed to be 

 constant. An exact understanding of the process of tumor development 

 requires knowing how this function depends on the conditions under 

 which the tumor grows. Since the character of this function during the 

 earlier stages of tumor development is not determinable at present, 

 any hypothesis regarding carcinogenesis is in a quantitative sense an 

 extrapolation. 



For purely formal illustrative purposes let us begin by considering 

 growth at a constant rate — the simplest possible type of growth. We 

 assume that after somehow having reached a volume Fo, the tumor grows 

 at a constant relative rate. We may think of Fo as the initial volume, 

 i.e., the volume at zero time. The constant growth rate is expressed by 



dV 



% = GV (14-2) 



where G is a constant. Integrating, we obtain 



\n^ ^ Gt (14-3) 



y 



in which F is the volume at the end of time t. Similarly, if it is assumed 

 that a tumor is composed of a large number of cells and these are dividing 

 at random with respect to each other but at a constant rate, the growth 

 of the tumor is described by 



dN 



and 



In ^ = G't. (14-5) 



iVo 



In the present case G' may be treated as equal to G. 



Assuming such constancy of relative rate of tumor growth, we may 

 examine the consequences. In the experiments described above the 

 tumor has at time ta a volume Va of approximately 100 mm''. For pur- 



