1322 BIOLOGICAL EFFECTS OF RADIATION 



copper radiation 148.7 electrostatic units were given per sec. /cm. ^ in 

 1 cm. of air. 



The number of ion pairs per sec./cc. at the position of the irradiated 

 sex chromosome is consequently 148.7 X electrons in one electrostatic 

 unit, or 0.21 X lO^" ion pairs /sec. = 3.12 X 10^^ ion pairs/sec./cc. 



For material composed of atoms of low atomic weight these absorption 

 coefficients vary directly with the density of the substance. If this 

 conclusion is applied to chromatin, the amount of absorption per sex 

 chromosome is 



3.12 X 10^^ X 1.70 X IQ-^'^ X 1.00 _ 

 1.00 X 1.165 X 10-3 



45.5 ion pairs/sec. per sex chromosome. 



Since direct measurement of the dimensions of the sex chromosome are 

 1.56 X 10"* cm. long and 0.33 X 10"^ cm. wide, hence — considering the 

 sex chromosome a rectangular block of chromatin — the volume is 

 1.70 X 10~^3 cc. The density of chromatin is assumed to be 1.00 and 

 the density of the air at the temperature used is 1.165 X 10-^. 



In order to obtain the number of X-ray quanta absorbed per second 

 it is necessary to know how many ions are liberated by one quantum 

 absorbed in air. The best available measurements (Kulenkampff, 51) 

 show that X-rays of the quality used require about 35 volts for each 

 electron pair. The voltage equivalent of the K — a lines of copper fol- 

 lows from the quantum relation: Voltage (in kv.) = 12.34/wave-length 

 of copper X-rays (1.537) = 8.029 kv. 



The number of ion pairs arising through the absorption of one quantum 

 of Cu K — a X-rays is 8,029/35 = 229. The average number of quan- 

 tum absorptions per second is 45.5/229 = 0.199. 



The average number of absorptions which actually produced mutation 

 was determined from the experimental data by fitting the curve pre- 

 viously derived, survival = e~"'\ to the actual data by the method of 

 least squares. The resulting curve was Y = e-°°' ^^^'. 



If the sex chromosome was entirely composed of vital recessive genes 

 then every hit would be expected to kill, or the rate of killing with time 

 should be 0.199 per second. The exponent 0.00165 per second for the 

 actual data shows that this is not the case. The chance of hitting the 

 vital volume within the sex chromosome clearly decreases as its volume 

 relative to the whole sex chromosome becomes less. The theoretical 

 absorption 0.199 per second represents the whole volume. The effective 

 absorption 0.00165 represents the vital volume. Their ratio, 1.0: 0.00829, 

 represents the whole volume compared with this vital volume. In other 

 words, the sex-chromosome volume has 829 hundred-thousandths of its 

 volume composed of vital dominant genes. Since there are 1280 of these 

 genes, the average size of one of them would be 



