248 



BIOLOGICAL EFFECTS OF RADIATION 



increase or decrease. This equation may be written in a variety of 

 forms, among them being 



where e" = 10" = .4 = the value of y when x = 



and e^ = 10* — B — the ratio of the y vahie at any x position to the 



y value at the position, x — 1. Since the equation may also 



be written in the form 



log y = a -\- bx 



we see that the logarithm of y is related to x in linear fashion and the 

 constants a and b may be derived by using the logarithms of the y values 

 with the corresponding x values and following the procedure just outlined 

 for the straight line. To facilitate the treatment of such relationships, 

 arithlog plotting paper has been developed having an arithmetic scale 

 on one axis and a logarithmic scale on the other. On such paper we may 

 plot our X values arithmetically and our y values logarithmically, and if 

 the observed material is following an exponential relationship, the points 

 obtained will fall on a straight line except for experimental variations. 



This exponential equation might be appropriately applied to the 

 observations taken by Henshaw (1) in his study of the effect of roentgen 

 rays on the time of the first cleavage of marine invertebrate eggs. Differ- 

 ent lots of the eggs were irradiated for different lengths of time and 

 inseminated at varying times after the beginning of irradiation, the delay 



Table 9. — Effect of Roentgen Rays on the Retardation in Onset of First 

 Cleavage in Arbacia Eggs According to Duration of Exposure and Time 



of Insemination 



Exposure, min. 



10 



20 



40 



60 



Interval, 



Retar- 

 dation, 

 min. 



5 

 15 

 25 

 45 

 65 

 85 

 125 

 165 



55 8 

 44 5 

 38.2 

 35.5 

 28.8 

 20.2 



Note: Interval, min = Interval from start of irradiation to insemination, minutes. 

 Retardation, min, = Retardation in cleavage, minutes. 



