590 WHEELER P. DAVEY 



Due to a breakdown of the transformer, the data to date at 

 any other voltage than 50 KV. are fragmentary. Figure 5 shows 

 the data obtained at 68 KV rms just before the transformer broke 

 down. The beetles were gathered at the same time as those of 

 figure 3 and the raying was done within 3 days of that of figure 3. 

 The two graphs may therefore be compared for what they are 

 worth. It is hoped later to determine more accurately the 

 effect of voltage. 



THEORETICAL 



It has been shown above that if the dosage of X-rays is 

 sufficiently large, the experimental relation between length of 

 life (Y) and X-ray dosage (X) is of the form 



Y = A - B log. X 



This formula may be easily derived from an extension of the 

 Psycho-physic law which states that a change in response to an 

 external stimulus is directly proportional to the change in the 

 stimulus, but inversely proportional to the amount of the stimu- 

 lus. (Thus, the flicker-sensation caused by suddenly dimming 

 a light is directly proportional to the amount of dimming, but 

 inversely proportional to the total intensity of the light.) Now 

 let us suppose that the same principle applies to the action of 

 X-rays on living cells. 



Let Y = the number of days a beetle will live after being 

 X-rayed. 



Let X = the amount of the X-ray dose. 



Then d Y is directly proportional to d X and inversely pro- 

 portional to X. Moreover, an increase in X produces a decrease 

 in Y. 



Therefore, d Y = - B ^ 



X 



Integrating — Y = A — B (log. X) 

 which is the same as the equation of the experimental graph. 



The constant of integration A has at present only a theoreti- 

 cal meaning, for it represents the number of days a beetle would 



live if it were X-rayed only 1 ^^^ at 50 KV. and if no proc- 



