Relation of Mass to Energy. 13 
case of the powerful reaction between hydrogen and oxygen 
forming water, the change of mass would only be of the order 
10~ 10 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 a-particle of mass {in) with velocity (fi) t then there should 
be a diminution in the sum of the masses of the a-partiele 
and the remaining atom equal to 
4 1 
since i>»^ 2 represents the energy lost, and this, calling 
m = ± (using gram-atomic weight) and /*=2\5 . 10°, gives 
A (Mass) = -1-7 . 10~ 2 gram; 
an amount large enough to cause discrepancies in calculating 
the atomic weights of radioactive substances from the number 
of a-particles lost. Since A (Mass) is proportional to the 
square of the velocity of the a-particle, its value would be 
greatly increased by a slight error in the determination of 
(fju) 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 con- 
servation 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 thev will no longer 
bear simple, exact relations to each other. In a highly im- 
portant paper (Zeitschrift fin 1 Anorg. Cliemie, xiv. p. 66, 1897) 
ftydberg 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 " Ordnungs- 
zahl"), 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. 
