Absorption and Scattering of X- Rays. 281 



Absorption Formulae. 



Various attempts have been made to express the absorption 

 simply in terms of X, but without mentioning these in par- 

 ticular it may be said that for the most part they give only 

 rough averages over very limited regions ; they are respon- 

 sible for many inaccuracies. 



As we have indicated, 



Total absorption = scattering absorption + fluorescence absorption 



(1) ' £ = + * 



P P P 



(2) =s ; + r..5 + 5 + 5 + ..i 



P L p p p J 



But ajp is a function both of the atomic weight (<w) of the 

 absorbing substance and of the wave-length (X) of the 

 radiation. 

 Thus 



(3) £ = F(», x) + [• . -jfifrM + */k(x/x k ) + z/l(x/x L- ) + . . .] 



p 



As the relative values of the constants j, k, I, &c, seem to 

 be the same for different substances, a single constant n 

 depending on the particular atomic weight or atomic number 

 may be placed outside the bracket, giving, within probable 

 limits, 



(4) £ = F(a>,X) +n[. . ./j'(\/Xj) +/ k ' (X/Xk) +/l'(X/X l ) + . . .] 



F(a>, X), however, varies little with the particular absorbing 

 substance except when X is great. It is also approximately 

 independent of X over a certain range of wave-lengths. The 

 general form has already been indicated. 



Consequently within certain limits equation (4) may be 

 written simply 



(5) ^- = C + A/(X), where k only depends on the particular 

 p element*. 



Hull and Rice, from the experiments on the penetrating- 

 radiations from a Coolidge tube, have recently pointed out 

 that except when X of the absorbed radiation is near the 



* This we have previously written in the form , ,' _r\\ =&, a constant 



for any two substances for any radiation of much more penetrating type 

 than any characteristic radiation excited in either substance. 



