The mean density of the earth is a constant of high importance, because it is necessary for the determination of the masses of all the other heavenly bodies. Astronomers and physicists accordingly have bestowed a great deal of labour upon the exact estimation of this constant. The method of procedure consists in comparing the gravitation of the globe with that of some body of matter of which the mass is known in terms of the assumed unit of mass. This body of matter, serving as an intermediate term of comparison, may be variously chosen; it may consist of a mountain, or a portion of the earth’s crust, or a heavy ball of metal. The method of experiment varies so much according as we select one body or the other, that we may be said to have three independent modes of arriving at the desired result.
The mutual gravitation of two balls is so exceedingly small compared with their gravitation towards the immense mass of the earth, that it is usually quite imperceptible, and although asserted by Newton to exist, on the ground of theory, was never observed until the end of the 18th century. Michell attached two small balls to the extremities of a delicately suspended torsion balance, and then bringing heavy balls of lead alternately to either side of these small balls was able to detect a slight deflection of the torsion balance. He thus furnished a new verification of the theory of gravitation. Cavendish carried out the experiment with more care, and estimated the gravitation of the balls by treating the torsion balance as a pendulum; then taking into account the respective distances of the balls from each other and from the centre of the earth, he was able to assign 5·48 (or as re-computed by Baily, 5·448) as the probable mean density of the earth. Newton’s sagacious guess to the effect that the density of the earth was between five and six times that of water, was thus remarkably confirmed. The same kind of experiment repeated by Reich gave 5·438. Baily having again performed the experiment with every possible refinement obtained a slightly higher number, 5·660.
A different method of procedure consisted in ascertaining the effect of a mountain mass in deflecting the plumb-line; for, assuming that we can determine the dimensions and mean density of the mountain, the plumb-line enables us to compare its mass with that of the whole earth. The mountain Schehallien was selected for the experiment, and observations and calculations performed by Maskelyne, Hutton, and Playfair, gave as the most probable result 4·713. The difference from the experimental results already mentioned is considerable and is important, because the instrumental operations are of an entirely different character from those of Cavendish and Baily’s experiments. Sir Henry James’ similar determination from the attraction of Arthur’s Seat gave 5·14.
A third distinct method consists in determining the force of gravity at points elevated above the surface of the earth on mountain ranges, or sunk below it in mines. Carlini experimented with a pendulum at the hospice of Mont Cenis, 6,375 feet above the sea, and by comparing the attractive forces of the earth and the Alps, found the density to be still smaller, namely, 4·39, or as corrected by Giulio, 4·950. Lastly, the Astronomer Royal has on two occasions adopted the opposite method of observing a pendulum at the bottom of a deep mine, so as to compare the density of the strata penetrated with the density of the whole earth. On the second occasion he carried his method into effect at the Harton Colliery, 1,260 feet deep; all that could be done by skill in measurement and careful consideration of all the causes of error, was accomplished in this elaborate series of observations5 (p. 291). No doubt Sir George Airy was much perplexed when he found that his new result considerably exceeded that obtained by any other method, being no less than 6·566, or 6·623 as finally corrected. In this case we learn an impressive lesson concerning the value of repeated determinations by distinct methods in disabusing our minds of the reliance which we are only too apt to place in results which show a certain degree of coincidence.