320 
Trmisoictions of the Royal Society of South Africa. 
From Table III the change in proportionality between absorption per atom 
and (see fig. (i) at B) is of the order 7*5 for elements whose atomic 
numbers are in the region of 46, and therefore, according to the theory 
outlined, 
+ 71^ + . . . 
Now Table III does not tell us anything directly about the M spectrum. If 
it did, the last result could be tested at once with Moseley's formula. 
Cabrera, however,* claims that the M spectrum is given by 
* Nature, October 7th, 1915, p. 144. 
(r^ - i) 21-^)' 
and therefore for an element of atomic number N. 
Accepting this tentatively we obtain for an element whose atomic number 
is of the order 46. 
= 53 
and putting this relationship into (iii) derived in this paper we obtain 
y^K 4- ^^i. + + • • • H r 
."^^=7-4, 
whilst Moseley's formula gives for an element 46. 
which is in close agreement with the result obtained from the present 
theory. 
In applying these results we are very much limited. In Barkla's original 
work on selective absorption there were large gaps in the sequence of 
absorbers used, and it is impossible to locate exactly the element at which 
the transition takes place in the region of the L absorption " band." We 
do know, however, that if radiation from an element R was being absorbed, 
the transition from the K to the L radiation must have occurred in an 
absorber lower in atomic number than E. The transition between the L and 
M radiation is given by Chapman's formula 
2Nk = Ni. - 24. 
Taking as a typical case for the calculation from (iii) of — the results 
given by Barkla and Sadler,* we obtain the following from the mass absorp- 
tion co-efficients of absorbers ranging from carbon (6) to gold (80) for nickel 
* Phil. Mag. (6), xvii, p. 749. 
