444 
Proceedings of the Royal Society 
If each hemisphere were collected at its centre of inertia the attrac- 
tion would he times as great. The centrifugal force tending 
to split the planet across a diametral plane through the axis (it is 
easily shown to be greater per unit of area on a diametral than on 
any other plane) is 
where <o is the angular velocity of rotation. The ratio of these is 
4 
CIO) 2 
or the ratio of gravity to centrifugal force at any point on the 
equator. Hence, so far as gravity is concerned, the earth would 
split across a meridian if it were to revolve more than seventeen 
times faster than it does. 
It is known that, if the earth revolved seventeen times faster 
than it does, centrifugal force would just balance gravity at the 
equator. The relation of this fact to the above statement depends 
upon the geometrical proposition that the volume of a very small 
slice from the surface of a sphere is half the product of its thick- 
ness by the area of its base. 
And cohesion would not sensibly alter this state of things ; for, 
assuming the earth’s diameter to be 8000 miles, its mean density 
5*5, and the weight of a cubic foot of water at the surface 63 lbs., 
while the average tensile strength of its materials is taken as 500 
lbs. weight per square inch, the cohesion between two hemispheres 
is shown to be only 
1 
25,410 
th part of their gravitation attraction. 
Even if we made the extreme assumption that the tensile 
strength is (throughout) that of steel, cohesion would in the case 
of the earth be only about -i_th of gravitation attraction, between 
hemispheres. 
