XIV. 



X RAYS AND X IRRADIATION 485 



small X-ray exposure, and finally results in an S-shaped inactivation 

 curve, the single hit or absorption event concept will no longer hold. 

 This means that it takes more than one absorption event in the vital 

 volume of each organism to produce the results. A Poisson equation 

 of moiT terms will be needed to fit such results, depending on the 

 specific iiumbor of absorption events that must occur in the vital 

 volume before the observed effect is produced. Biologically, the 

 niunber of X-ray absorption events necessary for different materials 

 have been observed to range all the way from one to forty or fifty. 

 The general e(}uation is of the form: 



n 



= no e-<^ fl + arf + ^ {aciy + ... ]_ ^^, (aJ)^-iJ 



The first term in this equation determines the number of organisms 

 that have not received an absorption event in the vital volume ; the 

 second term, those receiving just one; the third term, those receiv- 

 ing just two, and so on to those receiving exactly r absorptions. The 

 biological interpretation of a multiple hit curve is not so satisfactory 

 from a philosophical standpoint as that when only one radiation ab- 

 sorption is sufficient to produce the biological effects. 



The Poisson equation has other uses in X-ray research. For cer- 

 tain materials it is impossible to count by customary plating methods 

 the particles affected by the X rays as against those which are not. 

 Dilution methods offer the only easily available means of estimating 

 the number of organisms surviving the different treatments. The 

 radiation experiments yield untreated control and irradiated sus- 

 pensions of the organisms. The problem is to estimate the number of 

 organisms for each of these treatments. The solution under test 

 is diluted in geometrical series, fre(|ucntly by multiples of ten, but 

 possibly better for some materials by multiples of five, three, or two. 

 Tests on these diluted samples are run. The place where the most 

 dilute sample shows no lesions represents the case where no self-repro- 

 ducing virus particles were included in the test solution. The next 

 higher dilution may show positive takes. This represents the case 

 in which one or more virus particles survive in the test solution. By 

 repeated tests the percentage of sterile cultures out of the total 

 number tested is established. The percentage of sterile samples, p, 

 is related to the average number of living organisms as p = e~'", 

 where m is the average number of living organisms in the sampling 



