348 GENERAL DISCUSSION 



given doses. For it can be assumed that (other things being reasonably equal) two groups 

 of individuals that show an equal frequency of survival from irradiation have had the 

 same proportions of cells killed witliin the individuals. Thus when the induced mortahty 

 of two chromosomally different groups, such as males and females, is studied in relation 

 to radiation dosage, it will become evident what dose when applied to, say, the females, 

 causes the same amount of damage as a given dose, d, applied to males. Suppose, for 

 instance, that this dose for females is 2d. These actual doses can then be substituted for 

 the term d in the two respective expressions for the frequency of cell survival in females 

 and males. Then when these two expressions are equated to one another they can be 

 solved for a. In other words, the frequency of cell death is thus discovered, if the formulae 

 are correct. 



Now a check on the correctness of the formulae may be obtained by testmg whether 

 with the value for a thus deduced, there is the expected correspondence at other points 

 along the two empirically determined dosage-mortahty curves. That is, when some other 

 dose, such as l-5d, is applied to males, does one now find that the dose which, appUed to 

 females, gives the same mortality as l-5d does for males, bears the same relations to l-5c^, 

 as would be found by these formulae (using the a already determined)? 



Dr. Ostertag, who is wTittng up these methods, calculations, and results in detail, has 

 made some tests of this land, using Ms Drosophila results, and has found that the formulae 

 check as closely as could be expected, that is, they give results consistent with the data 

 derived from different doses applied to the two sexes or to groups with a deficient 

 cliromosome. As for the actual values indicated, the example may be given that the dose 

 of 3,500 r applied to third-instar male larvae, wliich results in some 50% of them failing 

 to reach "viable maturity" (m wliich life has persisted till eclosion and for at least 5 

 additional days), can be reckoned to have caused about 84% of the cells to have effective 

 breaks m their X-chromosome, and that about a tliird this dose, which keeps 12% of the 

 males from maturity, causes effective breaks in about half their X-chromosomes. This 

 very liigh proportion of cell deaths must of course be understood to be concentrated in 

 certain critical tissues and cell stages. 



Once results like these have been obtained, estimates can be made of the amount of 

 mortality of mdividuals to be expected for some other structural constitution of the 

 genotype, such as one having a deficiency in a given major autosome. For the latter 

 case may be treated as if the individual were haploid for that autosome, and one would 

 reckon with the autosome as one does for the single X-cliromosome of a male, except 

 that the effective length, L, would be correspondmgly greater. Another method of check- 

 ing that Ostertag is applying, is the cytological study of the chromosomes as observed at 

 the first mitoses that foUow irradiation. In these ways the general theory can be tested 

 and can be tried out in diverse organisms. 

 rotblat: Is the constant a the same for both sexes? 



mtjller: Yes, it is based on the effective breakabiUty for unit length, 8, with IiijS' = — a, 

 but the choice as to what constitutes a unit of length is arbitrar}^ The results do not 

 indicate a difference in a for the two sexes. L of course represents the number of the 

 units present in a cliromosome. If one wished to do so one could dispense with the 

 constant a by incorporating it along with L into a variable that one might term B (for 

 effective breakabHity), but one would still have to deal with the ratios between different 

 £'s, preferably in terms of a standard B, so that we would return to a term equivalent to 

 a after all. 



ALEXANDER: If cliromosome damage were a major or predominant cause of cell death in 

 mammalian cells, would you not expect the bone-marrow of a male mouse to be more 

 sensitive than that of a female mouse? We beUeve that the LD^q for an acute dose is 



