ame everywhere; for at the equator a stone is further from
the average bulk of the earth (say the centre) than it is at the poles,
and owing to this fact a mass of 590 pounds at the pole; would suffice
to balance 591 pounds at the equator, if the two could be placed in the
pans of a gigantic balance whose beam straddled along an earth's
quadrant. This is a _true_ variation of gravity due to the shape of the
earth. But besides this there is a still larger _apparent_ variation due
to centrifugal force, which affects all bodies at the equator but not
those at the poles. From this cause, even if the earth were a true
sphere, yet if it were spinning at its actual pace, 288 pounds at the
pole could balance 289 pounds at the equator; because at the equator the
true weight of the mass would not be fully appreciated, centrifugal
force would virtually diminish it by 1/289th of its amount.

In actual fact both causes co-exist, and accordingly the total variation
of gravity observed is compounded of the real and the apparent effects;
the result is that 194 pounds at a pole weighs as much as 195 pounds at
the equator.

No. 13. A homogeneous sphere attracts as if its mass were concentrated
at its centre. For any other figure, such as an oblate spheroid, this is
not exactly true. A hollow concentric spherical shell exerts no force on
small bodies inside it.

A sphere composed of uniform material, or of materials arranged in
concentric strata, can be shown to attract external bodies as if its
mass were concentrated at its centre. A hollow sphere, similarly
composed, does the same, but on internal bodies it exerts no force at
all.

Hence, at all distances above the surface of the earth, gravity
decreases in inverse proportion as the square of the distance from the
centre of the earth increases; but, if you descend a mine, gravity
decreases in this case also as you leave the surface, though not at the
same rate as when you went up. For as you penetrate the crust you get
inside a concentric shell, which is thus powerless to act upon you, and
the earth you are now outside is a smaller one. At what rate the force
decreases depends on the distribution of density; if the density were
uniform all through, the law of variation would be the direct distance,
otherwise it would be more complicated. Anyhow, the intensity of gravity
is a maximum at the surface of the earth, and decreases as you travel
from the surface either up or down.

No. 1