60 



BIOLOGICAL EFFECTS OF RADIATION 



Rewriting (4), we have 



log. 



2.3 logio T 



1 



= —fJieX 



(5) 



which is the equation of a straight Hne of slope -/x. when log, I/h is 

 plotted against x. (Note that logarithms to the base 10 are used in 



Figs. 5 to 7; hence the slopes must be 

 multiplied by 2.3 in determining fXe.) 



Corresponding to He may be assigned 

 a so-called effective wave-length Xe. 

 From monochromatic X-ray absorption 

 data in copper or aluminum may be 

 found a wave-length X, for which the 

 monochromatic absorption coefficient fx 

 is numerically equal to /Xe- Then 

 X = X„ the true effective wave-length 

 (44). Thus we have the definition 

 that the effective wave-length of 

 Fig. 9. — Effective wave-length hetcrogeneous radiation is numerically 



(Duane) as a function of the percentage 



10 20 30 40 50 60 70 80 90 

 (EV(E) Par Cent 



transmission of given filters. 



equal to the wave-length of that 

 monochromatic radiation which has 



the same absorption coefficient as the heterogeneous radiation in question. 

 Where tables giving absorption data are not available, m may be 



calculated from Richtmyer's equations (34) 



(Copper) ^ = 153X^ + 0.2 

 P 



(Aluminum) ^ = 14.45X-^ + 0.15 

 P 



(6) 

 {6a) 



where /x is the absorption coefficient for wave-length X and p is the filter 

 density (pcu = 8.94 gm./cc. and pm = 2.70 gm./cc). These ^equations 

 apply closely for effective wave-lengths between 0.12 and 0.4 A. 



An approximation to the effective wave-length X^ described above 

 is obtained by a less laborious (and less accurate) procedure originally 

 proposed by Duane (19). From equations 5 and 6 he calculates (a) the 

 percentage by which the X-ray beam is reduced in passing through a given 

 fixed filter, and (6) the wave-length of the monochromatic beam which is 

 reduced by the same amount, the latter being defined by him as the 

 effective wave-length, X^„. Figure 9 gives a plot of the Duane effective 

 wave-length X^ff against the percentage transmission of the given filter. 

 The final result by this method is given through the slope of the cord to a 

 point on the complete absorption curve as against, more properly, the 



