With regard to masses. We naturally must first know that of the earth; having its size, if we can determine its density, the rest follows.
The problem of determining the mean density of the earth occupied the minds of many workers during the nineteenth century. Newton (about 1728) pointed out how it could be deduced by observing the deviation from the vertical of a plumb-line suspended near a large mass of matter—a mountain, the volume and density of which could be previously determined. This method, which is very laborious and requires the greatest skill and most delicate instruments, has been employed several times, by Bouguer and Condamine, in 1738, at Chimborazo; Maskelyne, in 1774, at Schehallien in Scotland; and James, at Arthur’s Seat, near Edinburgh.
At the beginning of the century another method was introduced by Cavendish. This consists in measuring the attraction of two large spheres of known size and mass, such as two balls of lead on two very small and light spheres, by means of a torsion balance constructed by Mitchell for this purpose.
The most recent determination by this method, and one which is considered to give us perhaps the most accurate value, is that which is due to the skill and ingenuity of Professor Boys. His improvement consisted in constructing a most delicate torsion balance; the attracted spheres consisted of small gold balls suspended by a quartz fibre carrying a mirror to indicate the amount of twist. The whole instrument was quite small, and could easily be protected from air currents and changes of temperature, while the use of the quartz fibres reduced to a minimum one of the greatest difficulties of the Cavendish experiment. The value of the mean density of the earth is now considered to be 5.6, which means that if we have a globe of water exactly the same size as our own earth, the real earth would weigh just 5.6 times this globe of water. The earth’s weight, in tons, does not convey much idea, but that it is six thousand trillions may interest the curious. This determination has enabled the masses of the sun, moon, planets and satellites, and many sidereal systems to be accurately known in relation to the mass of the earth.
SOME ACHIEVEMENTS OF MATHEMATICAL ANALYSIS
Uranus, a planet unknown to the ancients, was discovered by its movement among the stars by William Herschel in 1781. It was not until 1846 that another major planet was added to the solar system, and this discovery was one of the sensations of the century.
The story of the independent discovery of Neptune by Adams and Le Verrier, who were both driven to the conclusion that certain apparent regularities in the motion of Uranus were due to the attraction of another body travelling on an orbit outside it, has been often told. The subsequent discovery of the external body not far from the place at which their mathematical analysis had led them to believe it would be seen, will forever be regarded as a fine triumph of the human intellect.
But the results of the inquiries which now concern us are generally of not so sensational a character, although they lie at the root of our knowledge of celestial motions. They more often take the shape of tables and discussions relating to the movements of the bodies which make up our solar system.
Gauss may be said to have led the way during the nineteenth century by his Theoria molus corporum coelestium solem ambientium. This was a worthy sequel to the Méchanique Céleste, in which work, towards the end of the eighteenth century, Laplace had enshrined all that was known on the planetary results of gravitation.
In later years Le Verrier and Newcomb have been among the chief workers on whom the mantle of such distinguished predecessors has fallen. From them the planet and satellite tables now in use have been derived.