1919-20.] 
The Absorption of X-Rays. 
35 
47 tk _ _ 87 rNe 2 # f T sin (gtf — tan -1 hgl(f- mg 2 )) 
T “ T» X cos gt ((/-mj^ + lV)! dt 
0 _^ir u a 
J *" c - r jo cos gt (f-mg”-f + hY dt 
47rT$e 2 hg 
(/— m/) 2 + ft 2 / 
(3) 
if t is very large compared with the period. (3) is the ordinary expression 
used to represent the variation of the coefficient of absorption through an 
absorption band. The advantage of the above method of deriving it over 
the conventional method, which is given in the same notation in chapter 
xxiv of my book on Light, is that the conventional proof requires that 
there should be many electrons to the wave-length, and consequently is not 
suitable for wave-lengths as short as those of X-rays. The above proof is 
free from this restriction. 
Let us assume now that v differs very slightly from unity, and that k is 
plotted as a function of g ; g is, of course, 2ttc/\. It will be found that 
the second term in the denominator affects the shape of the curve very 
slightly ; we may consequently write instead of (3) 
2 tt Ne 2 hg 
K ~ (/- mg 2 ) 2 + h 2 gj 
(I) 
where g m is the value of g corresponding to the maximum value of k. g m is 
given by /— rngj 2 = 0 . The curve falls away to zero on both sides of this 
maximum. The area of the curve is given by 
27 rNe 2 hgdg 7rNe 2 /7r _ 1 / \ 7 r 2 Ne 2 
Jo (f-mg*y + hSjjJ = ^\2 + tan " 
since / is large compared with hg m . Now e and m are constants of nature, 
and g m can be determined from the curve ; hence if an absorption band has 
the shape required by theory, and we graph k as a function of g, the 
number of electrons per unit volume concerned in its production is 
m 9ml( 7 r 2 e 2 ) times the area of the curve. But, what is more, any 
irregularly shaped band can be regarded as due to the superposition of 
a number of component bands, each of which has the theoretical shape, and 
for which the value of g m does not vary much. The number of electrons 
concerned in the production of the resultant band is equal to the sum of 
the numbers of electrons concerned in the production of each of the 
component bands. Thus the above rule holds for an absorption band of 
any shape whatever. 
§ 2 . Professor Barkla has discovered absorption bands or “ fluorescent 
absorption ” in the X-ray region. These possess certain similarities to 
