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The observations detailed in this paper are comprised in two se­ ries. By the result of the first, the pendulum of experiment, which was constructed upon the same principles as that used by 'Captain Kater, and described in the Philosophical Transactions for 1819, was found to make 86166,108 vibrations in twenty-four hours, and by the result of the second series, 86166,048, the mean being 86166,078; so that the result of each series differs from the mean only-Hhlhrth of a beat in twenty-four hours. The length of the seconds pendulum at Madras, deduced as the mean of these two series of observations, is 39*026302 inches of Sir George Shuckburgh’s scale, at the temperature of 70° in vacuo, and at the level of the sea. By comparing this with the length of the pendulum vibrating se­ conds in London, we obtain itvt-as the ellipticity of the earth, which is very nearly the mean deduced from the observations of Cap­ tain Kater in England, and those of the French mathematicians.

Observations for ascertaining the length of the pendulum at Madras in the East Indies, latitude 13° 4' 9''·1 with the conclusions drawn from the same