CHEMISTRY: HARKINS AND WILSON 
279 
which is obtained by making use of the symmetry of the equa- 
tion. The evaluation of this integral gives the value l/2a so G = 
^uK^e^ /{'\:Trac^) . The mass represented by this value of G is Aw = 
±eV(47rac2) where Aw is the change of mass due to the overlapping of 
the fields of the electrons. Now the longitudinal mass is mi = e^/ {6irc^R) 
where J? = radius of the electron. By division Am/wi = 3i?/2a, where 
a equals one-half the distance apart of the electrons. 
Taking R as the radius of the positive electron, and — 0.77% as the 
packing effect, it is seen that in this simple case the distaxice apart of 
the positive and the negative electrons would be 400 times the radius 
of the positive electron. However, the system used for the calculation 
does not correspond to any actual atom, but if it is considered that the 
gold nucleus is smaller than corresponds to a radius of 3.4 X 10~^2 ^j^^ 
as Rutherford calculates, then when it is considered that the large 
number of positive and negative electrons contained in this space must 
make up a very complex system, undoubtedly with a special structure, 
it is evident that the distances of the electrons as calculated to give 
the observed packing effect, is of the right order of magnitude to give a 
gold nucleus of the kind supposed by Rutherford's theory. 
The Hydrogen-Helium System. Fajans,^ Soddy,^ Russell,^ von 
Hevesy,^ and Fleck, ^ have proved that when a radioactive element 
ejects an alpha particle, found by Rutherford to have a mass of 4 units, 
and to give ordinary helium gas, the new substance produced has 
different properties and a different valence from the parent material. 
The change is such that the new element lies two groups to the left in 
the periodic table and therefore has an atomic number and a valence 
with values two less than before. Now that this relation has been 
found to apply to elements of high atomic weights, the question arises 
as to whether the same relations hold for the lighter atoms which have 
not been found to give an appreciable alpha disintegration. If they 
do, then the atomic weights of the elements of even atomic number 
could best be found by beginning with helium, and adding a weight of 
4 for each step of two atomic numbers, and by proceeding in the same 
way beginning with lithium for the odd numbered elements. This gives: 
Atomic number even = 4 8 12 16 20 24 28 32 
Atomic number odd = 7 11 15 19 23 27 31 35 
which are on the whole the correct atomic weights. The system ob- 
tained in this way may be best represented in the form of a periodic 
table as in the table. 
When given in this way it is seen that the atomic weights not only 
follow the helium system derived from the behavior of the radioactive 
