296 H. K. SCHACHMAN AND R. C. WILLIAMS 



(a) The survival curve of irradiated viruses is exponential with dose of 

 radiation (a single-hit curve). 



(6) The effect of a given dose is independent of the intensity at which the 

 dose is given. 



(c) The same degree of effect is produced by increasing radiation doses as 

 one proceeds from y-rays, through soft X-rays, to a-particles. 



In general, the cross section or the volume of the target within a virus 

 can be calculated on the target theory by making observations as to the 

 inactivation effects of various doses of differing types of radiation. When 

 the inactivation is of the single-hit type a plot of the logarithm of the sur- 

 viving virus activity against dose is linear, demonstrating an equation 

 that can be written: 



n=Woe-^/^» (39) 



where Wq = initial infective titer, n = infective titer of survivors, D = dose, 

 and Dq = dose required to score an average of one hit per target. When 

 njriQ = 0.368, then D = Dq, and this value of D is called the "37 % dose." 

 Its evaluation is the first step in establishing the target size. 



The experimental data on radiation inactivation may be initially handled 

 in forms depending upon the type of radiation employed. If high-energy 

 electrons or X-rays are used, the ionizations produced are sparse and at 

 random, and they are unlikely to produce more than one hit per target. The 

 chances of a given target being hit then depend simply upon its volume and 

 upon the number of ionizations per unit volume produced by the radiation 

 dose. If the dose given equals Dq (for n/wp = 0.37), and if such a dose 

 produced L ionizations per cm.^, then the target volume is IjL cm.^. 



If efficiently ionizing a-particles are used, only the cross-sectional area of 

 the target can be calculated, since it is now anticipated that every ionizing 

 particle going through a target will create an ionization within it. If, then, 

 the dose equals D^, and if such a dose amounts to M a-particles per cm.^, 

 then the target area is IJM cm.^. It is to be noted that if the target is large, 

 the volume calculated as IjL will be an underestimation, while if the target 

 is small, the calculation of its cross-sectional area as 1/M will also be an 

 underestimation. As the targets become smaller the calculation of a target 

 volume should become more nearly correct, and similarly with the area 

 calculations as the target becomes larger. Lea (1947) has developed a method 

 of calculation, called the "associated volume" method, that is applicable in 

 the intermediate case where the target is neither large nor small compared 

 to the separation of ionizing events along the particle track. 



It is seen that in principle it is possible to obtain a unique type of infor- 

 mation about viruses from radiation experiments: a size (the target) that 

 refers to the infective activity of the virus, on the assumption that only 

 direct hits are responsible for loss of activity. Information about the size of 



