CHEMISTRY: W. D. HARKINS 
217 
helium and the Hthiimi series, if each series is named for its first mem- 
ber. However, it should be noted that while the formula for the helium 
series is wHe^ that for the lithium series is not nlA'. 
If the theory is correct it might be expected that some characteristic 
of the elements could be found, with respect to which there is a differ- 
ence from odd to even and from even to odd, or in other words the ele- 
ments should show variations in periods of 2 elements each. 
In order to have a basis for the comparison of the elements in the 
study of this problem there has been constructed in space a periodic 
model of which the accompanying figure is a drawing. In this model 
the elements are represented by balls strung on a spiral in the order 
of . their atomic numbers, which have recently been found to be much 
more characteristic of the elements than their atomic weights. The 
spiral is so arranged that the balls representing the elements belonging 
to one group and having the same maximum valence are strung on the 
same vertical rod. The balls are set at such heights that the vertical 
distance from the top down represents the atomic weight. This is 
essential, for otherwise the different kinds of atoms of one element, 
called by Soddy 'isotopes' cannot be represented. Thus in the lower 
right hand part of the table, on the lower part of Group 4B, the ele- 
ment lead is represented by 6 isotopes, with the atomic weights listed, 
as follows: lead from radium (uranio-Pb) 206.1; lead, 207.2; lead from 
thorium, 208.1; radium D, 210.1; thorium B, 212.1, and radium B, 
214.1. Thus the different kinds of lead, which seem identical chemi- 
cally and give the same spectrum, have atomic weights which differ 
by as much as 8 units, or by 4%. However, all of these isotopes have the 
same atomic number, 82, or according to the theory developed by various 
investigators, they have the same positive nuclear charge. 
When arranged in this form of periodic table the elements other than 
hydrogen and helium are found to arrange themselves in periods as 
follows : 
1. First short period Li — Ne: 8 = 2X2^ elements 1 „ , i _ J2 
2. Second short period 
3. First long period 
4. Second long period 
K 
Kr: 18 
2 X 32 elements! 
5. First very long period 
6. Second very long period 
It is thus seen that these periods and cycles make up a numerical sys- 
tem of a remarkably simple form, and it seems evident that this system 
