Experiments of the first class in which the pull of a known mass is compared with the pull of the earth maybe termed experiments on the mean density of the earth, while experiments of the second class in which the pull between two known masses is directly measured may be termed experiments on the gravitation constant.
We shall, however, adopt a slightly different classification for the purpose of describing methods of experiment, viz:—
1. Comparison of the earth pull on a body with the pull of a natural mass as in the Schiehallion experiment.
2. Determination of the attraction between two artificial masses as in Cavendish’s experiment.
3. Comparison of the earth pull on a body with the pull of an artificial mass as in experiments with the common balance.
It is interesting to note that the possibility of gravitation experiments of this kind was first considered by Newton, and in both of the forms (1) and (2). In the System of the World (3rd ed., 1737, p. 40) he calculates that the deviation by a hemispherical mountain, of the earth’s density and with radius 3 m., on a plumb-line at its side will be less than 2 minutes. He also calculates (though with an error in his arithmetic) the acceleration towards each other of two spheres each a foot in diameter and of the earth’s density, and comes to the conclusion that in either case the effect is too small for measurement. In the Principia, bk. iii., prop. x., he makes a celebrated estimate that the earth’s mean density is five or six times that of water. Adopting this estimate, the deviation by an actual mountain or the attraction of two terrestrial spheres would be of the orders calculated, and regarded by Newton as immeasurably small.
Whatever method is adopted the force to be measured is very minute. This may be realized if we here anticipate the results of the experiments, which show that in round numbers Δ = 5.5 and G = 1/15,000,000 when the masses are in grammes and the distances in centimetres.
Newton’s mountain, which would probably have density about Δ/2 would deviate the plumb-line not much more than half a minute. Two spheres 30 cm. in diameter (about 1 ft.) and of density 11 (about that of lead) just not touching would pull each other with a force rather less than 2 dynes, and their acceleration would be such that they would move into contact if starting 1 cm. apart in rather over 400 seconds.
From these examples it will be realized that in gravitation experiments extraordinary precautions must be adopted to eliminate disturbing forces which may easily rise to be comparable with the forces to be measured. We shall not attempt to give an account of these precautions, but only seek to set forth the general principles of the different experiments which have been made.
I. Comparison of the Earth Pull with that of a Natural Mass.