ULTRAVIOLET RADIATION AND CANCER 541 



a just observable volume, 1 mm^ is assumed at the beginning of tj. The 

 rates of growth are, of course, quite different for the three curves. That 

 for curve I {G = 0.127) is close to the average estimate for experimental 

 tumors after they were large enough to be measured. 



It seems hardly necessary to point out that the idea of growth of the 

 tumor at a constant rate is incompatible with the experimental finding 

 that tumors appear only if repeated doses are given during the time td, so 

 the simple equation we have used cannot be applicable to our experi- 

 mental data. It has been used only to illustrate the inherent weakness of 

 the assumption, implicit in many theories of carcinogenesis, that separate 

 induc^tion and growth periods can be supported by purely qualitative 

 observations. There are further objections in the present instance. 



Hypotheses based on the idea of separate induction and growth periods 

 usually contain the tacit assumption that the tumor cells proliferate in a 

 more or less unrestricted fashion once they are formed. The tumor is 

 often said to grow "autonomously," which seems to mean that the rate of 

 proliferation of the tumor cells is inherent in these cells themselves. If 

 this were so there should be no direct relation between their proliferation 

 rate and the time required for tumor induction. To see how the present 

 data bear on this point let us assume for purposes of argument that the 

 development time may be separated into two distinct periods of induction 

 and growth, which may be represented by the equation 



td = ti + tg (14-6) 



where ti represents an induction period during which the tumor cells are 

 formed and t,; represents the growth period during which these tumor cells 

 proliferate. Using the symbols from Eqs. (14-4) and (14-5) with similar 

 meaning, we may write 



t, = f{N,G', . . . ) (14-7) 



to indicate that the growth period is a function of the number of cells N, 

 and of the rate of their proliferation which is related to G'. The function 

 is indicated as incomplete because other unspecified factors may enter; 

 thus we are not restricted to accepting the relative growth equation in its 

 simple form. Combining the last two equations, we obtain 



td = /, -{-f{N,G', . . . ). (14-8) 



Now we are confronted with a serious obstacle. Examination of Figs. 

 14-1 and 2 shows that the tumor incidence curves for a constant schedule 

 of doses always have the same shape and slope when plotted against the 

 logarithm of id. This can mean only that the shape and slope of the 

 curves are continuously determined by some basic relation. To ration- 

 alize such a relation with Eqs. (14-6 to 14-8), the induction period ti and 

 the growth period t„ would always have to be proportional. It follows 



