112 . The Source of Stellar Energy [ch. iv 
where G is the velocity of light. Its kinetic energy, when moving with velocity 
v, is 
m£' [(l - 4 - l] (101 ' 2) ' 
which, in virtue of the relation (101*1), can be written in the form 
(m — m 0 ) G 2 (101*3). 
Suppose that the electron, while moving with velocity v, is suddenly 
checked and brought to rest. Its kinetic energy (m — m 0 ) G 2 is transformed 
into radiation which travels off into space. At the same time the mass of the 
electron is reduced v by an amount m — m 0 . The conservation of mass, however, 
persists through this process, so that the mass m — m 0 is not lost, but must 
represent the mass of the radiation whose energy is (m — w 0 ) G 2 . In this 
special instance the energy of the radiation is seen to be G 2 times its mass, 
and the emission of radiation involves a loss of mass to the emitting system 
equal to l/(7 2 times the energy of the radiation. 
This is no isolated special instance. In 1905 Einstein shewed it to be a 
general consequence of the theory of relativity that a change of energy 8E in 
any system involved a change in its mass equal to 8E/G 2 . Thus the emission 
of radiation by a star or any other body at a rate E ergs per second necessarily 
involves a loss to the mass of the radiating body at the rate of E/C* grammes 
per second. The sun’s present radiation of 3*8 x 10 ss ergs per second involves 
a diminution of the sun’s mass at the rate of (3*8 x 10 s3 ) grammes a second. 
Putting (7=3 x 10 10 we find that the sun’s mass is diminishing at the 
rate of 4*2 x 10 12 grammes per second, or about four million tons a second. 
In the 1500 million years which have elapsed since the earth solidified, the 
sun’s mass must have diminished by 2 x 10 29 grammes, or one part in ten 
thousand. The question arises as to the form in which this additional 2X10 29 
grammes resided in the sun 1500 million years ago. 
102. It has long been known that the atomic weights of the elements 
cannot be expressed as exact whole numbers. If that of oxygen is taken to 
be 16, helium has atomic weight 4*00216, while that of hydrogen is 1*00778*. 
If four hydrogen atoms each of weight 1*00778 combine to form one helium 
atom, the system experiences a loss of mass 0*029 (the unit being a sixteenth 
of the mass of the oxygen atom), and this must be the mass of radiation 
discharged into space when, if ever, helium is built up out of hydrogen. In 
1919 Perrinf suggested that processes of the general type just described 
may be the origin of the radiation of the sun and stars, a suggestion which 
Eddington^; repeated in 1920 in a more precise form. If, for instance, a star 
* F. W. Aston, Proc. Roy. Soc. cxv. (1927), p. 510. 
t Annales de Physique, n. (1919), p. 89; and Revue du Mois, xxi. (1920), p. 113. 
X British Association Cardiff (1920) Address to Section A.