78 ERNEST POLLARD 



If the sensitive region which we are interested in has a volume V 

 cubic centimeters, then the average number of chisters of ionization 

 occurring within V is / V. We are interested in the probabihty of com- 

 plete escape. This can l^e estimated from the Poisson formula, from 

 which we deduce that if IV is the average number of "hits" then r(0) 

 the probability of no hit at all is 



P(0) = e-iv. 



If we state that the ratio of activity remaining, ii, to that initially 

 present, no, is a measure of P(0) we deduce that 



n 

 no 



- P{0) - e-^^ 



or 



(1) 



In many cases it is found that the activity remaining is related to the 



dose by the relation 



/n\ 

 In I — I = — (constant) (Dose) 



This can be converted into the same form as equation ( 1 ) by calculating 

 / from the dose. The constant is then immediately expressible as V. The 

 volume T^ is informative in regard to the nature of the biological unit 

 responsible for the activity which is lost because of radiation. 



STATISTICS OF HEAVY PARTICLE RADIATION 



If irradiation by heavy particles is used then the ionization cannot be 

 considered to be randomly distributed in volume, as the above reasoning 

 cannot be used. The heavy particles are much more nearly line probes 

 which are randomly distributed in area. Unfortunately this is only 

 approximately true, because the secondary electrons along the path of 

 the particle spread ionization away from the track. The amount of this 

 spread can be estimated and it is possible to use heavy particle radiation 

 to make estimates of the area of a molecule or molecular system, and 

 of its thickness. Neither are to be considered as precise, yet it is clearly 

 possible to tell whether an organelle is long and thin, or has one dimen- 

 sion small, or whether it is more nearly spherical, with no thin dimension. 



When such irradiations are performed, then, the dose is expressed as 

 particles per square centimetre, D, and if the effective cross-section is S 

 an area which is now the equivalent of the volume, V, used formerly, 



