From this equation \(K\) can be determined, if \(S_{1}\) and \(S_{2}\)
are known.
An uncertainty however arises in estimating \(S_{1}\) and \(S_{2}\)
for the rate of leak in \(A\) and \(B\) is made up of the current due
to emanation alone and the current produced in the gas by the excited
radioactivity on the electrodes. As the amount of excited radioactivity
increases with the time, the ratio of the current due to the emanation
and to the excited radiation varies with the time allowed for
diffusion. The ratio of the current due to the excited radiation can be
determined by removing the central electrode and finding the amount of
current immediately after the introduction of a new electrode.
When the emanation is allowed to diffuse for half an hour, the current
due to excited radioactivity was about \(\cdot 4\) of the whole.
The calculated value of \(K\) was found to be about 20 per cent greater
when the correction for the amount of excited radioactivity was applied.
The value of \(K\) deduced from the experiments was found to be between
\(\cdot 08\) and \(\cdot 15\). All the later observations gave a value
about \(\cdot 08\).
This variation in the value of \(K\) deduced from the experiments is
not altogether due to errors of experiment, the values obtained at
first with a new specimen of radium were in all cases higher than when
it had been laid by for several months. It appears as if the emanation
were not simple in character, and that part of the emanation first
given off was of lower molecular weight than that emitted after several
months exposure to the air. Further experiments are now being carried
out to see if the radium emanation undergoes a progressive change with
time. For the purpose of comparison, we will now give a few of the
coefficients of inter-diffusion of gases, compiled from Landölt and
Bernstein's tables.
\begin{array}{|l|l|l|}
\hline Gas or vapour & Coefficient of diffusion into air. & Molecular weight \\
\hline Water vapour & \(0 \cdot 198\) & 18 \\
\hline Carbonic acid gas & \(0 \cdot 142\) & 44 \\
\hline Alcohol & \(0 \cdot 101\) & 46 \\
\hline Ether & \(0 \cdot 077\) & 74 \\
\hline
\end{array}
In the above table we see that the coefficient of inter-diffusion
follows the inverse order of the molecular weights. In cases of the
simpler gases it has been shown experimentally that the coefficient
of inter-diffusion is approximately inversely proportional to the
square root of the product of the molecular weight. If we apply these
considerations to the emanations \((K= \cdot 08\, \text{to}\, \cdot
15)\) we see that it is a gas or a vapour of molecular weight (allowing
a wide margin) probably lying between 40 and 100. These numbers exclude
the possibility of the substance being a vapour of radium, for it has
already been shown by M. and Mme. Curie that the atomic weight of
radium is greater than that of barium. We must therefore conclude that
the emanation is in reality a heavy radioactive vapour or gas.
On account of the rapid decay of the radiating power of thorium
emanations, it is not possible to determine its coefficients of
diffusion in the same way; but special experiments show that it
diffuses rapidly, and is also probably gaseous in character. T he
physical properties of these emanations or gases are most remarkable.
The radium emanation not only continues for long inter vals to be a
source of radiation which is apparently similar in character to easily
absorbed Röntgen rays, but in some way manufactures from itself a
positively charged substance, which travels to the negative electrode
and becomes a source of secondary radioactivity.
[Footnote 1: Wiener Akad., 1871.]