THEORY OF RELATIVITY 
275 
?.trictly speaking of ‘inertia mass/ has lost its meaning and is 
merged, as was indicated in the introduction, with the principle 
of the conservation of energy. 
We have already treated of the change of mass of electrons by 
virtue of their motion and indicated there that the same was 
true of any mass. This comes about in the following way. The 
inertia mass changes if it takes up energy of radiation from 
without. The kinetic energy of a point mass in the pre-relativity 
mechanics is expressed by : 
mv“ 
. 
according to relativity by : 
mc- 
V 1— 
c- 
This expression becomes infinite as v approaches c, showing in 
the first place that it can not become equal to c, involving as this 
would an infinite amount of kinetic energy possessed by a point 
mass. 
If the expression above is expanded in series we have : 
V“ 3 
mc'+m — 1 m — / . . . . 
2 8 c^ 
The second term is the one standing for the kinetic energy in 
the old mechanics, the third term is very small if is small 
in comparison with unity, and the first term does not con- 
tain v; its meaning will come out in the subsequent discussion. 
If a moving body according to electrodynamics takes up the en- 
ergy E in form of radiation, the increase of energy becomes : 
Vi— ^ 
c- 
and the energy of the body becomes : 
(m-j- ^ )c- 
This body has therefor the same energy as a body of mass : 
Fo 
m-^ 
c- 
