46 Messrs. A. C. and A. E. Jessup on the 
The next term of a series of natural numbers arranged in 
this way which approximates most closely to the average 
number 46 is — 
(I + 2 + 3) + (l+2 + 3+4) + (1 + 2+3 + 4+5) 
+ (1+2 + 3 + 4 + 5 + 6) = 52. 
Now the average value of the differences is, as we have seen, 
approximately 46, a considerable diminution from the figure 
as given by the above series. In connexion with this, it is 
worthy of note that Runge and Precht * determined the 
atomic weight of radium spectroscopically, and found it to 
be 258, while the value found by chemical methods was 225. 
Rudorf f, in seeking to explain the discrepancy, made a 
series of observations upon the relation between the frequency 
differences of spectral lines of families of elements. He found 
that if d is the frequency difference of pairs of lines in the 
spectrum of an element atomic weight A, d/A 2 is approxi- 
mately constant for low values of A, but increases with A 
for higher values of A. This means that the elements 
towards the end of the series have a lower atomic weight 
than would be the case if the formula d/A 2 = constant were 
rigid. 
The phenomenon appeared in all the series of elements 
which were examined, and not only in group II. 
Thus we have another example of a formula yielding 
higher values for the atomic weights than those actually 
found. May it not be that these formulas give the atomic 
weights which the elements would naturally assume if not 
subject to some disturbing influence ? In other words, is it 
unreasonable to suppose that we are here face to face with 
the process of devolution ? 
We know that this process exists in a marked form in the 
later stages of each group, in the form of radioactivity. Is 
it illogical to postulate that its origin occurred at an earlier 
stage in the growth of the element ? 
If we may regard the formation of the elements as a com- 
bination of the processes of evolution and devolution, the 
former is most effective among the first elements of a group, 
and the latter among the last. 
Turning to devolution, and again examining the table of 
atomic weights, it is evident that there is no simple law 
connecting the various elements of high atomic weight, such 
as exists for the evolution. Moreover, since any term of the 
series of devolution is only obtainable when the difference of 
the atomic weights of two consecutive elements in any group 
* Phys. Zeitschr. vol. iv. p. 285 (1903). 
' + Zeit. Phys. Chem. vol. 50. p. 100(1904). 
