416 Proceedings of Royal Society of Edinburgh. [sess. 
came together as loose nebulous matter before any considerable 
condensation took place — which seems probable — this matter must 
have had a motion of rotation about its centre of inertia, the 
various parts circulating in every conceivable direction, hut the 
balance of the whole in the plane and direction in which the earth 
and moon are now rotating. Collisions of small masses would, in 
this case, be comparatively frequent, and would tend to bring the 
colliding parts more and more nearly towards the centre of inertia, 
but the aggregation of the mass would be so slow that the heat 
caused by these collisions would be readily dissipated by radiation, 
and not until the central mass began to approximate the size of the 
moon would it have power to produce such velocities of impact as 
would liquefy the body striking and the part struck, and such 
heating would always be superficial, would come to a maximum at 
once, and would soon be lost by radiation on that account. 
On the above views as to the formation of the earth there is no 
need to suppose that the central parts were originally different, either 
in kind or density, from the other parts. Now, as the average 
density of the earth is known to be 5*527 times the density of 
water, and as the density of the rocks on the surface does not 
average more than half of this, it is obvious that much energy 
must have been spent in compressing, and therefore in heating, the 
mass. Assuming, then, that the matter of which the earth’s 
substance is composed had originally an average density of 2*76,* 
let us consider what it is likely to be at the different depths now. 
If the radius be divided into ten equal parts, and the average 
densities of the corresponding spherical shells be taken successively 
at 3*3, 4*4, 5*5, 6*6, 7*7, 8*8, 9*9, 11, 12*1, and lastly 13*2 for the 
central sphere, we shall find that this gives the average density of 
the whole mass correctly, and we may consider the amount of 
energy required to compress a cubic foot of matter of density 2*76 
to density 13*2 under a final force equal to the pressure to be 
found at the centre from the foregoing data. 
The writer has attempted this by means of a graphic process, 
and has deduced from the above data a curve showing the intensity 
of gravity at all points of the earth’s radius, and also a curve 
whose ordinates are proportional to the pressure at each point 
* This is about the density of granite. 
