Ionization of Gases and the Absorption of Bontgen Bays. 
317 
where A is constant and hni is a quantum of primary energy absorbed. 
This can be written 
AN^dmi;^^ + + + r • ) 
which can be written 
BW(hn^ + hn^ . . .) 
for the corpuscle cannot discriminate between a K ring of electrons or 
an L ring if the atom is neutral and also the number of K rings equals 
the number of L rings in a substance on the average. B is a constant, which 
is necessarily greater than A in fact 
B = A(l + x) 
where x is the number of K or L rings disturbed by the electron before 
its flight ceases. Suppose the absorber is so chosen that only the 
L electron is liberated. The atom which has lost this electron will radiate 
L and M, etc., radiations. As before the energy absorbed by these atoms 
can be written 
CNjAwi = Cl^Klmvl + hn^ +/in„ + . . . ) 
for the same primary radiation. is experimentally greater than N. 
Once again, if the energy ^mvl is distributed amongst x^, L rings, and x-^ 
M rings, etc., the absorption of energy from the primary radiation is 
DNi {Jin,^+ hn^ + . . .) where D = 0(1 -f- x^). 
This electron will not have sufficient energy to remove a K electron from 
the element since the whole quantum of primary radiation could not 
do so. 
The ratio of the energy absorbed in the first case to that absorbed in 
the second case is 
A(l + x)W{hn^ 4- hn,^ + . 
0(lT^i)N7(/mr+Ti?,« ' ' 
Bragg states* that when the logarithms of the co-efficients Ka» in 
(i) for any one wave length are plotted against the logarithms of the 
atomic numbers of the absorbers, a series of straight lines is obtained. 
The slope of the lines shows that the absorption varies as the fourth power 
of the atomic number, but the constant of proportion (Q) changes as one 
of the critical values (of the wave length or atomic number) is passed 
through. This is the well known effect of selective absorption or selective 
transmission that was originally investigated by Barkla. The absorption 
is not in the nature of an absorption band but it suffers a permanent and 
violent change at definite points in the atomic scale (fig. 1). 
The radiation is of sufficiently short wave length as to be able to excite 
the innermost K rings of the elements lying between A and B. Between 
the points B and 0 the second ring of electrons is excited, the innermost 
ring having a frequency too high to be in tune with the primary radiation^ 
* X-rays and Crystal Structure, p. 180. 
