Some experiments on the proportionality of mass and weight

The earliest experiments on this subject were carried out by Newton, who came to the conclusion that the gravitational accelerations of gold, silver, lead, glass, sand, common salt, wood, water and wheat were equal to within one part in a thousand. In 1827, similar experiments were carried out by Bessel. His method was to suspend his pendulum bob from two threads of different length and to measure the period in each case by comparison with a standard clock. The difference in length of the two threads being known, Bessel was able to calculate the length of the “ simple pendulum which beats a second.” His experiments were carried out with great care, and Bessel came to the conclusion that, with one possible exception—the case of water—the gravitational acceleration was the same for all substances which he tried to one part in 60,000. Bessel endeavoured to explain the difference which he had found in the case of water by assuming that the water acquired a velocity relative to the containing vessel, on account of the difference of the centrifugal force at various points in the liquid. M. Lubeck has shown that Bessel’s explanation is not the correct one, and himself offers an explanation which is hardly satisfactory.