36 
Proceedings of the Royal Society of Edinburgh. [Sess. 
absorption bands in the visible spectrum, such as those of the aniline 
colouring matters. They also possess certain well-marked differences. So 
doubt might be expressed as to whether the application of the above rule 
to them is justifiable. However, I have applied it to them with striking 
numerical results. 
The absorption bands in the X-ray region are divided into four classes, 
J, K, L, and M bands, in the order of increasing wave-length. They shift 
progressively along the spectrum in the direction of decreasing wave- 
lengths, as the atomic number of the element increases. The data on K 
and L bands are reproduced in Kaye’s X-Rays ; the data on J bands 
are given in a paper by Barkla and White.* The tops of the M bands 
have not been reached yet ; we have only measurements of the slope on the 
side of decreasing wave-length. X-ray absorption spectra are characteristic 
of the atom, and strictly additive; there is no disturbing “ constitutive 
influence.” 
The absorption in the X-ray region is measured by the mass absorption 
coefficient fj.jp, where p is the density of the substance, p, is connected with 
k, the coefficient of absorption in optics, by the equation 
4-7T/C 
fX = ~\T‘ 
If we take our rule and translate it into terms of jul and X, it runs : if ptX 
be graphed as a function of 1/X, and the area of the absorption band 
measured, then the number of electrons per unit volume concerned in its 
production is (mc 2 )/(X m ire 2 ) times the area of the band, where X m is the 
wave-length of the maximum of the band. The number of atoms per unit 
volume is p/{wm n ), where w is the atomic weight and m H is the mass of 
the hydrogen atom. Consequently the number of electrons per atom is 
me 2 
X m 7re 2 
wm n 
x area 
P 
or 
w 
pX m 7T 
x area 
( 5 ) 
if e be changed to electromagnetic units. On substituting the numerical 
values (5) becomes 
1 iv 
f area 
( 6 ) 
If we are dealing with a single absorption band, another formula may 
be used instead of the above. For, starting from (4), we find that the 
maximum value of k is given by 
2 Ne 2 
hc/m ’ 
* Phil. Mag., xxxiv, p. 270, 1917. 
