113 
ioi-io3] The Annihilation of Matter 
consisted originally of pure hydrogen, the total transformation of this into 
heavier elements would involve a loss of mass equal to about (V0072 gramme 
per gramme of the star’s mass, so that the transformation would result in a 
total radiation of energy of amount 00072C 2 or 6‘5 x 10 18 ergs per gramme. 
This is ample to account for the sun’s radiation throughout the whole of the 
earth’s life and through epochs far beyond. But it is not adequate to account 
for the radiation of the stars through the lengths of life which, as we shall see 
later, are assigned to them by dynamical considerations, and this alone probably 
compels its abandonment. If the source of energy suggested by Perrin and 
Eddington were the true one, it would follow that young stars contained a 
larger proportion of hydrogen than old stars ; there is no evidence of this 
being the case, although this can hardly be regarded as a fatal objection. A 
more serious objection is that if stellar energy were produced by the trans 
formation of hydrogen into heavier elements, the rate of radiation of any 
particular star would be proportional to the frequency with which groups of 
hydrogen atoms got into the position appropriate for the formation of atoms 
of helium and heavier elements. A comparison of the rates of radiation of 
different stars does not suggest that they can be determined by any such law 
as this. Furthermore we shall see later that a star in which the energy was 
generated in the manner suggested by Perrin would be dynamically unstable, 
and this reason, apart from all others, would appear to compel the rejection 
of Perrin’s scheme. 
The Annihilation of Matter. 
103. Fifteen years before Perrin had suggested that stellar energy might 
originate in the formation of heavy atoms out of simpler ones, I had pointed 
out* that an enormous store of energy could be derived out of the total 
annihilation of matter, positive and negative charges rushing together and 
neutralising and so annihilating one another, the resulting energy being set 
free as radiation. In 1918 f I calculated the amount of energy which would 
thus be set free and the length of life which this source of energy allotted to 
the stars. 
The principle of this calculation is very simple. When a proton and an 
electron of masses m, M neutralise one another in the sun and disappear, the 
sun loses material massof amount m+M. A certain amount of radiation results ' 
and to satisfy the principle of conservation of mass, the mass of this radiation 
must be m + M. Hence, in accordance with Einstein’s principle already 
explained, the energy of the radiation must be (m + M) C 2 . In general the 
annihilation of a gramme of matter must set free C'\ or 9 x 10 20 , ergs of energy. 
The energy set free by the annihilation of matter is enormous compared 
with that which the same amount of matter can be made to yield in any 
* Nature, lxx. (1904), p. 101. 
t Problems of Cosmogony and Stellar Dynamics, p. 287.