AND ON THE REMOTE HISTORY OF THE EARTH. 
405 
Ma>(in°+hi ;) 
The p.e. of the system is 
Mm M get 2 
r v r 
Therefore the whole energy E of the system is 
and in gravitation units 
B=Mah ^-,--l 
l 9 r J 
Now since the earth is supposed to be plastic throughout all these changes, there¬ 
fore its ellipticity of figure 
.'ll? a 
e=i— 
9 
and 
If e, e + Ae and r, r+ Ar be the ellipticity of figure, and the moon’s distance at 
two epochs, if J be Joule’s equivalent, and cr the specific heat of the matter con¬ 
stituting the earth; then the loss of energy of the system between these two epochs 
is sufficient to heat unit mass of the matter constituting the earth 
Ma f , 1 «] , 
-ui* Ae -?, A d cle § rces ' 
and is therefore enough to heat the whole mass of the earth 
-fi{* Ae -s A i 1 } de « Tees - 
It must be observed that in this formula the whole loss of k.e. of the earth’s 
rotation, due both to solar and lunar tidal friction, is included, whilst only the gain of 
the moon’s p.e. is included, and the effect of the solar tidal reaction in giving the 
earth greater potential energy relatively to the sun is neglected. 
In the fifth and sixth columns of Table IV. of the last section the ellipticity of figure 
and the moon’s distance in earth’s radii are given; and these numbers were used in 
calculating the eighth column of the same table. 
I used British units, so that 772 foot-pounds being required to heat 1 lb. of water 
1 ° Fahr., J — 772; the specific heat of the earth was taken as -gth, which is about that of 
iron, many of the other metals having a still smaller specific heat; the earth’s radius was 
MDCCCLXXIX. 3 S 
