Ill 
100 , 101 ] Inadequacy of Terrestrial Sources 
Radium, the most energetic of the radioactive elements, generates about 
1,600,000 ergs of radiation per gramme per second, so that the sun’s present 
radiation could be accounted for by supposing one part in 800,000 of its mass 
to be radium. But as the average life of radium is only about 2800 years, 
such a sun would be extinguished after a few thousand years. During its 
whole life a gramme of radium emits about 14 x 10 17 ergs of radiation, so that 
a sun which consisted initially of pure radium would have sufficient capacity 
for generating energy to maintain the sun’s radiation at its present rate for 
about 5000 million years. For uranium the corresponding figures are 2'2x 10 17 
ergs of radiation per gramme and 8000 million years. 
These figures shew that, contrary to a prevalent impression, radioactivity 
is capable of providing for the total amount of energy radiated by the sun 
since the earth solidified. On the other hand, no known combination of 
radioactive elements is capable of forming a sun which would radiate at the 
required rate for the required time—in brief, uranium is too slow, radium is 
too rapid, and all the other radioactive transformations have too little energy. 
Moreover we shall find evidence later that the ages of the stars are incom 
parably greater than the 1500 million years which we have taken to be the 
age of the solid earth, and radioactive substances of the kinds known on earth 
are found to be utterly inadequate to provide stellar radiation throughout 
the whole lives of the stars. 
Sub-atomic Sources of Energy. 
101. Thus we have to conclude that no source of energy known to us on 
earth is anything like adequate to account for the radiation of the sun and stars* 
We can make progress only by striking the problem from an entirely new 
angle. Instead of surveying the sources of energy known to us on earth, we 
survey the general laws of physics which we believe to hold sway in the sun 
and stars as well as on earth, and examine whether any energy-transformation 
known to them, but not to us, is capable of providing adequate energy for the 
radiation of the sun and stars. In approaching this question it must be 
emphasised that the energy which is radiated away must have resided some 
where before it was radiated; it cannot have been created, as needed, out of 
nothing. Its total amount is so great that if it resided in the star, it must 
have resided in a very concentrated form indeed. Now the only places known 
to physics in which energy can reside in a concentrated form are the nuclei 
and electrons of which matter is formed, and the electromagnetic fields in 
their immediate neighbourhood. 
It is well known that a moving electron has a greater mass than a stationary 
electron; more force is required to deflect it from its path or to produce a 
specified acceleration. If m 0 is its mass when at rest, its mass m when moving 
with a velocity v is given by 
v 2 \ ~i 
07 
m 
= m 0 
( 1011 ),