The law of gravitation states that two masses M1 and M2, distant d from
each other, are pulled together each with a force G. M1M2/d^2, where G
is a constant for all kinds of matter--the _gravitation constant_. The
acceleration of M2 towards M1 or the force exerted on it by M1 per unit
of its mass is therefore GM1/d^2. Astronomical observations of the
accelerations of different planets towards the sun, or of different
satellites towards the same primary, give us the most accurate
confirmation of the distance part of the law. By comparing accelerations
towards different bodies we obtain the ratios of the masses of those
different bodies and, in so far as the ratios are consistent, we obtain
confirmation of the mass part. But we only obtain the ratios of the
masses to the mass of some one member of the system, say the earth. We
do not find the mass in terms of grammes or pounds. In fact, astronomy
gives us the product GM, but neither G nor M. For example, the
acceleration of the earth towards the sun is about 0.6 cm/sec.^2 at a
distance from it about 15 X 10^12 cm. The acceleration of the moon
towards the earth is about 0.27 cm/sec.^2 at a distance from it about 4
X 10^10 cm. If S is the mass of the sun and E the mass of the earth we
have 0.6 = GS/(15 X 10^12)^2 and 0.27 = GE/(4 X 10^10)^2 giving us GS
and GE, and the ratio S/E = 300,000 roughly; but we do not obtain either
S or E in grammes, and we do not find G.
The aim of the experiments to be described here may be regarded either
as the determination of the mass of the earth in grammes, most
conveniently expressed by its mass / its volume, that is by its "mean
density" [Delta], or the determination of the "gravitation constant" G.
Corresponding to these two aspects of the problem there are two modes of
attack. Suppose that a body of mass m is suspended at the earth's
surface where it is pulled with a force w vertically downwards by the
earth--its weight. At the same time let it be pulled with a force p by a
measurable mass M which may be a mountain, or some measurable part of
the earth's surface layers, or an artificially prepared mass brought
near m, and let the pull of M be the same as if it were concentrated at
a distance d. The earth pull may be regarded as the same as if the earth
were all concentrated at its centre, distant R.