484 JOHN W. GOWEN 



tract, i.e., the eye of Drosophila was shown to be laid down as early 

 as twelve hours after development started. The uses of such methods 

 are yet in their infancy. 



X-ray effects on regenerating tissues have quite similar uses. 

 Regeneration studies have one advantage in that if one limb is left 

 intact it acts as a control on the irradiated tissue (2, Chapter 12). 



G. STATISTICAL TREATMENT OF RADIATION DATA 



The statistical methods required in evaluating irradiation data 

 include most of the kno^\Ti methods in the field (49). Three quanti- 

 tative expressions for the effects of X rays have been adopted. 

 Where the X-ray effect is measured by survival of the organisms, the 

 doses of X rays that cause 50 or 63% of the organisms to die have 

 proved convenient measures. Where the effects are measured as 

 gene mutations or chromosome rearrangements, a popular means of 

 expressing X-ray action is the percentage of these mutations or 

 chromosome rearrangements per chromosome for a dose of 1000 r. 

 units. The curves expressing the full range of X-ray effects are of 

 several different shapes depending upon the material irradiated (see 

 Fig. 7). From an interpretative standpoint one class of these curves 

 is outstanding. This curve occurs when the relation between X-ray 

 dosage and biological effect follows a Poisson distribution in which a 

 single absorption act is sufficient to produce an observed change (see 

 Fig. 6). When such data are plotted on the grid, logarithms of the 

 numbers of organisms showing no effect plotted against the increasing 

 X-ray doses, this curve takes the form of a straight line. Data on in- 

 activation of viruses or bacteria and on gene mutations or certain 

 chromosome rearrangements frequently take this form of curve. 

 The equation representing these results is: 



n = no e""" 



where a is the probability that some specific energy absorption event 

 occur per unit dose in the vital volume, and d is the dose or the num- 

 ber of such energy units to which the biological material is exposed. 

 The survivors are represented by n, the original number by no, and 

 e is the natural logarithm. The mean lethal dose, the dose that will 

 inactivate all but 37% of the material, may be determined directly 

 from the graph. If a semilogarithmic plot of the X-ray data does not 

 turn out to be a straight line but is a curve showing no changes for a 



