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In this communication Captain Kater, having noticed the circumstances to which his researches owe their origin, proceeds to detail his investigations, and to describe the implements and apparatus employed in his various inquiries; the construction of the pendulum and its appendages is minutely explained, as also the rate of its expansion for each thermometric degree, whence is deduced the corresponding correction to be applied to the number of its vibrations. The operations at each station, with their results, are enumerated at length, and illustrated by numerous tables. The length of the seconds pendulum for the latitude of London is 39·13722 inches in parts of the scale which forms the basis of the trigonometrical survey; for the latitude of Unst 39·16939 inches, of Portsay 39·15952, of Leith Fort 39·15347, of Clifton 39·14393, of Arbury Hill 39·14043, and of Shanklin Farm 39·13407 inches. The calculation of the latitude of each of these stations is given at length, to afford the opportunity of any further examination desirable on that subject; but these and the other details relating to calculation do not admit of abridgement. Captain Kater concludes this paper with some observations respecting the figure of the earth. It having been shown by Clairaut that the sum of the two fractions, expressing the ellipticity and the diminution of gravity, from the pole to the equator, is always a constant quantity, and equal to 5/2 of the fraction, expressing the ratio of centrifugal force, find that of gravity at the equator, it follows that if the decrease of gravity from the pole to the equator be subtracted from this constant quantity, the remaining fraction will express the ellipticity of the spheroid. The diminution of gravity may be known by finding the difference of the length of two pendulums, vibrating in equal times at the equator and pole, which are to each other directly as gravitation; but as such experiments cannot be made at the pole, Captain Kater proceeds to describe the means of obtaining the desired result by observations at intermediate stations; whence it appears that the length of the seconds pendulum at the equator, deduced from the observations at Unst and Dunnose, is 39·00527 inches, and gravitation at the equator 16·040 feet; hence the centrifugal force at the equator is 1/288 of gravitation, or 1/282 of gravity, which last being multiplied by 5/2 gives ·0086505 for the sum of the fractions, expressing the ellipticity of the earth and diminution of gravity from the pole to the equator.

abstracts of the papers printed in the philosophical transactions of the royal society of london

An account of experiments for determining the variation in the length of the pendulum vibrating seconds, at the principal stations of the trigonometrical survey of Great Britain