about thirty million years. 
APRIL 22, 1915] 
NATURE 
203 

and I can only wonder that it has not had a more 
marked effect in popularising the general principle. 
Prof. Thompson’s illustrations from biology (attri- 
buted in-part to Spencer) are, of course, of first-rate 
importance, RayLeIGu. 

The Age of the Earth. 
Some fifty years ago Kelvin announced that the 
temperature of the earth could not have been anything 
like its present value for more than some 20-30 
million years. This estimate was based upon three 
independent considerations, namely, the temperature 
gradient inside the earth’s crust, the amount of tidal 
friction, and the total amount of energy radiated by 
the sun. 
The first of these arguments has been invalidated 
completely -by the discovery of the radio-active ele- 
ments. The other two arguments are scarcely 
affected by this event. 
The geologists always found some difficulty in com- 
pressing the history of the earth, more especially of 
the sedimentary strata, into the period allowed them 
by Kelvin. Prof.- Harker’s presidential address be- 
fore the Yorkshire Geological Society, reprinted in 
your issue of March 25, seems to show that there 
is a general impression abroad that Kelvin’s esti- 
mates have been superseded, and that the discoveries 
in radio-activity allow one to assume a period of the 
order of thousands of millions of years since the 
earth has reached a constant state as regards climate. 
I should like to be allowed to ‘state as succinctly as 
possible what difficulties this view entails. 
The mean temperature of the earth is about 280° 
absolute. It therefore radiates about I-7x 1074 ergs 
per second into space. 
cal 
cm.” min. 
constant, the earth receives 1-72 x 1074 ergs per second 
from the sun. Therefore the radiation from the sun 
just compensates the amount lost by the earth; in 
other words, the temperature of the earth is deter- 
mined by the temperature of the sun. The possibility 
that the earth’s temperature might have been main- 
tained by radio-active processes before the sun was 
incandescent, and that the radio-active substances have 
died off since then need scarcely be discussed seriously. 
For quite apart from the well-known sterilising effects 
of the rays, any radio-active substances with a suffi- 
ciently long life to keep up the temperature of the 
earth for any considerable length of time would not 
disappear quickly. Uranium, for instance, only 
diminishes at the rate of about I’5 per cent. in 100 
million years. 
One may conclude, therefore, that the time during 
which the earth can have existed in its present state 
cannot be greater than the time since which the 
effective temperature of the sun has been about 
000°, its present value. This time cannot exceed 
For the sun loses energy 
Assuming the latest value 1:92 for the solar 
: , ergs 
at the rate of about 3°8 x 10% ae » and the total energy 
to be gained by a mass of 1-97 x 1038 gm., contracting 
to a radius 6'96x 10! cm., is 2-2 x 1048 ergs, assum- 
ing approximate homogeneity. (Talking the increase 
in density towards the centre into account does not alter 
these figures much.) Now even if one assumes that 
the whole of this energy was radiated at a rate of 
Oe. . . 
about 3°8x108"S 76, at the present rate, it will only 
sec. 
last 18-3 million years. But any other supposition, 
namely, that the sun at one time emitted more or less 
NO. 2373, VOL. 95] 

energy per second, leads to a shorter period for the 
earth in its present state. 
To explain a greater age it was necessary to find 
other sources of energy, and since neither the heat 
of chemical combination nor any possible increase in 
the specific heat was anything like large enough, the 
heat of radio-active transformations was invoked. 
This was perhaps excusable in the early days before 
very much was known about the laws governing these 
processes, but it seems quite inadmissible to-day. 
It has been suggested that at the enormous pressure 
and temperature inside the sun radio-active processes 
might be modified, and even that ordinary elements 
might break up. A consideration of the quantita- 
tive relations involved shows that this is most un- 
likely. Though one can_ scarcely apply ordinary 
thermodynamics to radio-active processes one can cer- 
tainly apply the general rule, which may also be de- 
veloped from the quantum theory if desired, namely, 
that a reaction the energy of which is A ergs per mole- 
cule is affected chiefly by the collisions of atoms of 
energy of the order A. Now A is of the order 10-5 
ergs in radio-active processes, and one can therefore 
only expect the temperature to affect those if an appre- 
ciable number of atoms have an amount of energy 
of this order. The average energy of an atom would 
be 10-° ergs at about 5-10!° degrees. Therefore even 
at. 500 million degrees only one atom amongst 10%? 
would be moving fast enough to influence a reaction 
which liberates 10-* ergs. Obviously 500 million 
degrees is quite beyond the bounds of possibility in 
any part of the sun. One must conclude, therefore, 
that any process which liberates anything like the 
requisite energy is unaffected by solar conditions, 
and takes place at the same rate on the sun as on 
the earth. Thus one must fall back upon the 
ordinary radio-active materials, and as Sir Ernest 
Rutherford has pointed out, one would only gain a 
paltry five million years even if the whole sun were 
composed of uranium. The only way out would seem 
to be to suppose that the sun was created some 10° 
or 101° years ago out of special radio-active material 
which produces an enormous amount of energy, and 
that it has been breaking up ever since. This 
material does not exist on the earth though, so the 
earth would have to*be the object of a special creation. 
Such an assumption, of course, can neither be contro- 
verted nor even discussed. But unless some such 
hypothesis is introduced, i.e., unless the presumably 
radio-active solar material which liberates a quantity 
of energy sufficient to keep up the sun’s heat for the 
desired 10° or 101° years, is supposed to have been 
created by some inconceivable force at the epoch at 
which the sun is supposed to have begun to radiate, 
this material would have disintegrated long ago. 
It might be objected that the same holds good of 
uranium, that the fact that uranium exists in measur- 
able quantities proves that it has not existed for a 
time great in comparison to 5-10° years. 
This is doubtless true, but there is no real difficulty 
about assuming uranium or. other radio-active sub- 
stances to have been produced if one supposes the 
solar system to have been formed by the collision of 
two stars. 
At the moment of collision the velocity of two stars 
Bees eee 7 being 
Jy Sec. 
the distance between the centres of gravity. Suppose 
they both contained some lead, this would reach a 
‘ Teexano2! 
temperature of the order —— 
half the mass of the sun would be 
, 2.e., of the order 2*10° 

degrees at the moment of collision. As has been 
shown above, an appreciable quantity of radio-active 
