CHEMISTRY: HARKINS AND WILSON 
277 
If the assumption is made that the other atoms are hydrogen com- 
plexes, then it is found that in the formation of the complex there must 
result a change of weight which is in general negative in sign. The 
percentage decrease in weight may be called the packing effect, and the 
average value of this effect for the 27 lighter elements in 0.77%. The 
magnitude of this effect is nearly constant, as is shown by the value 
0.77 for helium, while for the six elements from boron to sodium the 
packing effects are 0.77, 0.77, 0.70, 0.77, 0.77, and 0.77%. Since the 
value of the packing effect is — 0.77% for oxygen, and this is the aver- 
age packing effect of the 27 elements as well as the value of the effect 
for a considerable number of the different atoms, it is seen that the use 
of a whole number as the atomic weight of oxygen makes allowance 
for this effect and so gives to the other elements atomic weights which 
are whole numbers or very nearly whole numbers. 
In order to determine a cause for this decrease in weight which must 
result if the other atoms are built up from the nuclei of hydrogen atoms 
as units, it will be well to consider if this effect may not be due to the 
overlapping of the fields of the charged particles which unite to form the 
nucleus of the complex atom. Recent work shows that this nucleus is 
extremely small. Rutherford, from data on the scattering of alpha 
particles in passing through thin gold leaf, has calculated the upper 
limit of the nucleus of the gold atom as 3.4 XlO"^^ cm., and Darwin 
found the similar value for hydrogen to be about 0.8 X 10~^^ cm., which 
is of the order of size of the negative electron as usually considered. 
If the gold nucleus is built up of hydrogen nuclei this would mean that 
it would contain about 197 hydrogen nuclei and 118 negative electrons 
in its extremely minute volume, if the idea of van den Broek and 
Moseleyi that the positive charge on the nucleus is equal to the atomic 
number is used for the calculation. Thus over 300 particles would be 
contained in a volume which according to Rutherford's calculation 
has a radius of only 3.4 X lO"^^ ^j^^ j^s upper limit of value. It 
must be emphasized that in this paper only the electrons contained in 
the nucleus of the atom are the ones which are considered, and that 
the distance of the external electrons, sometimes considered as of the 
order of the assumed radius of the atom as about 10"^ cm., has absolutely 
nothing to do with the packing effect. 
The simplest case for an actual nucleus which could be calculated, 
is that of hehum, which may be assumed to contain four positive par- 
ticles and two negative electrons. However, the arrangement of these 
particles is not known, so the solution will be given for the case of a 
single positive and a single negative electron. That a change in mass 
