Page:ComstockInertia.djvu/13

case of the powerful reaction between hydrogen and oxygen forming water, the change of mass would only he of the order $10^{-13}$ gram. In the case of radioactivity, however, the energy change is very much greater and an appreciable effect is to be expected. Thus if a radium atom gives off an $\alpha$-particle of mass ($m$) with velocity ($\mu$), then there should be a diminution in the sum of the masses of the \alpha -particle and the remaining atom equal to

${\frac {4}{3}}{\frac {1}{V^{2}}}\left({\frac {1}{2}}m\mu ^{2}\right)$,

since ${\tfrac {1}{2}}m\mu ^{2}$ represents the energy lost, and this, calling $m=4$ (using gram-atomic weight) and $\mu =2.5\cdot 10^{9}$, gives

$\Delta (\mathrm {Mass} )=-1.7\cdot 10^{-2}\mathrm {gram}$;

an amount large enough to cause discrepancies in calculating the atomic weights of radioactive substances from the number of $\alpha$-particles lost. Since $\Delta$(Mass) is proportional to the square of the velocity of the $\alpha$-particle, its value would be greatly increased by a slight error in the determination of ($\mu$) and the effect could easily be much larger.

12. A consideration of some interest is the following. If we adopt the disintegration theory, we are obliged to think of the various atoms as combinations or groups, more or less modified, of the lighter atoms. If there were perfect conservation of mass this would introduce a certain uniformity in the relations between the atomic weights, a uniformity which apparently does not exist. On the other hand, if we take into consideration the inevitable change of mass when the electromagnetic energy of the system is modified, the atomic weights will involve a correction term depending upon the change in this energy, and hence they will no longer bear simple, exact relations to each other. In a highly important paper (Zeitschrift fur Anorg. Chemie, xiv. p. 66, 1897) Rydberg has shown that the atomic weights of the first twenty -seven elements of the periodic system approximate to whole numbers very much more closely than chance could bring about. He has also shown that the atomic weights of these elements are best considered as the sum of two parts ($N+D$) where $N$ is an integer and $D$ is a fraction, in general positive and smaller than unity. If $M$ is the number of the element in the system (called by Rydberg the "Ordnungszahl"), then $N$ is equal to $2M$ for the elements of even valence and $2M+1$ for the elements of odd valence. Below is given a table showing the various quantities. I have used,