QUANTUM THEORY OF RADIATION ABSORPTIONS IN TISSUES 1313 



n{n- l)(n-2) • • • (n - r + 1) 

 r a^(l - a)"-' 



These considerations and the fact that the number of electrons is large 

 compared with the number required to kill, r, lead to Poisson's law 

 as the general theorem to describe these results 



Or for the case when one electron absorption will suffice to produce the 

 observed result, the number of experimental objects escaping the electrons 

 will be 



This curve plots as a straight line on the semilogarithmic grid. When 

 two absorptions are necessary, the ratio of those showing no effect 

 to the original number is A2/A0 and equals e~""(l + an). This curve 

 plots as a convex curve on the semilogarithmic grid. Or where r absorp- 

 tions are necessary, the ratio is 



Ar/Ao = e-«"[l + an + Hian^ + • • • l/ |r - I jany-'] 



Values of r as high as 50 have been noted in data taken from different 

 experimental objects, depending sometimes on the material and at others 

 on the technique. The simplest type of curve where but one absorption 

 is necessary for death is seen for certain bacteria, Drosophila sperm, and 

 possibly Antirrhinum pollen, when exposed to X-ray. Figure 1 shows 

 data taken from Wyckoff (93, 93a, 94, 96) which demonstrate the linear 

 nature of the death rates (on the semilogarithmic grid) of B. coli when 

 they are exposed to electrons of the cathode-ray tube or irradiation from 



o 



X-rays of 0.564- to 3.98-A wave-lengths or ultra-violet radiation in the 

 range 2536 to 3132 A. In all cases the curves pass through the point of 

 treatment at the 100-per-cent survival, there being no lagging of the 

 deaths in the range of the lower doses. 



More complex types of survival curves have been noted for many 

 experimental objects. These types may arise from several causes, one of 

 the most prevalent of which is the many-celled character of the material. 

 Wyckoff and Rivers (96) have shown that if the cells of B. coli — which 

 give the simple straight-line curves of Fig. 1 when they are distributed as 

 single cells over the culture plate at irradiation — are incubated a short 

 time so that each cell becomes a tiny colony of two or more cells, the 

 survival curve of such a population on irradiation with cathode rays is no 

 longer a straight line on the arithlog grid but a convex curve having a low 

 initial death rate with a subsequent rapid increase after the short lag 

 period. The two or more cells in each colony which must be killed before 

 that individual may be recorded as dead by the X-ray obviously require 



