HISTORY OF PHYSICAL ASTRONOMY.

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corresponding effect in the other half. It was generally considered, how-ever, that, when the oscillations are very small, the disturbance arisingfrom the resistance of the air was altogether insensible. We shall haveoccasion presently to mention a series of experiments which clearly esta-blished the fallacy of this opinion.

But the circumambient air exercises on bodies a statical effect, which istotally independent of the resistance it offers to their motion. Since abody immersed in a fluid suffers a diminution of w r eight equal to that ofthe fluid displaced by it, a pendulum will manifestly oscillate more quicklyin a vacuum than it will do in air. It is necessary, therefore, in all experi-ments to reduce the oscillations to those which would take place in avacuum, by computing the effect due to the -weight of the atmosphere asindicated by the barometer. This has been termed the correction for thebuoyancy of the atmosphere.

Numerous experiments were made with the pendulum in the course ofthe last century, for the purpose of ascertaining by means of them theellipticity of the earth ; but, as they were not conducted with due attentionto all those minute circumstances which affect such delicate operations,they cannot be considered as w-orthy of any reliance. We have alreadymentioned that experiments of this kind may be conducted by two distinctmethods. The length of a pendulum which performs a certain number ofoscillations in a given time (for example, the seconds’ pendulum) may bedetermined in different latitudes, and the results on being comparedtogether will indicate the variation of gravity, and hence, also, the ellipticityof the earth. The same object may also be effected by transporting aninvariable pendulum to different latitudes, and noting the number ofoscillations which it makes in a given time at each place. This is generallyconsidered to be the safest mode of experimenting, as it is independent ofthe absolute length of the pendulum, the ascertainment of which at anytime is an operation of extreme delicacy.

Borda, a French philosopher of great merit, was the first who deter-mined the length of the seconds’ pendulum with sufficient accuracy forscientific purposes. This step was suggested by the measurement of thegreat arc of the meridian of France , which took place towards the closeof the last century, and the operation was conducted by him with consum-mate skill in all its details. In 1807, Biot determined, by this method,the lengths of the seconds’ pendulum at various stations of the arc betweenDunkirk and Formentera , and the results obtained by him may be con-sidered as the earliest data of this kind which fully deserved the confidenceof astronomers. This distinguished philosopher afterwards made similarexperiments at various other places in the south of Europe , and also atLeith and Unst in the British Isles . Comparing together the lengths ofthe seconds’ pendulum at Unst and Formentera , he obtained ■Jot for thevalue of the earth’s ellipticity. This result agrees very well with thatderived from the comparison of geodetic measurements, and is doubtless avery near approximation to the truth. With respect to other stations,however, it must be acknowledged that the results were not in all casesequally satisfactory.

In 1818, fresh interest was awakened in experiments of this kind byCaptain Kater ’s invention of a new method of great ingenuity for deter-mining the length of the seconds’ pendulum. Huygens had already shewnthat, whatever be the form of an oscillating body, the centres of suspensionand oscillation are convertible. Availing himself of this beautiful property,Captain Kater attached two points of suspension to a pendulum, and then