ULTRAVIOLET RADIATION AND CANCER 545 



day to day. This is illustrated in Fig. 14-5, where the growth rate is 

 shown as rising abruptly to a new level with each dose, the new rate being 

 maintained until the next dose is received. Without assuming that this 

 diagram pictures the exact happenings in a tumor, it may be accepted as 

 an approximation which may be put to test. 



The dotted line in the figure represents a smooth acceleration, which 

 for a long series of doses would very closely approximate the stepwise 

 curve we have drawn. This line is described by 



dV kDt 



V dt i 

 which, when D and i are constant, may be integrated to 



(14-10) 



where Fo and V are the volumes of the tumor at the beginning and end of 

 the time t, D is the dose of ultraviolet radiation, i is the interval between 

 successive doses, and /c is a proportionality constant.^'' The rate of 

 growth is assumed to be negligible at the time of the first dose. 



The development time td has already been defined as the time from the 

 first exposure until the tumor reaches a given volume designated as Vd. 

 For this case, Eq. (14-11) may be rewritten as 



If, in addition, the assumption is made that Fo is the same in all cases, this 

 is equivalent to saying that Vd/Vo is a constant at the time td.^^ For any 

 series of experiments in which the interval i is maintained constant, td 

 should therefore vary inversely as the square root of the dose D, since by 

 rearrangement we obtain 



td = 



2i , 1 d 



¥^"ro 



D-y^ (14-13) 



and all the values within the brackets are constants. Figure 14-C illus- 

 trates what happens when this relation is applied to the data. In this 

 figure values of td are plotted against D, on log-log coordinates. The 

 values of td plotted are based on the time to 50 per cent incidence of 

 tumors within groups of identically treated mice. Examination of the 



" The equation may be used to describe tumor growth when t has high values, but 

 does not hold exactly for short periods. A treatment applicable to the latter which 

 has to be used in interpreting some of the data is developed more completely in the 

 original paper, but Eq. (14-11) serves the present purpose. 



^' This is a tentative assumption. The data are better fitted if Fo is considered 

 to vary (unpublished analysis). 



