copal Church, in the Diocess of Pennsylvania; a Sermon preached on the Evening of Sunday, the 8th May, in St. Stephen's Church, Philadelphia. By William H. De Lancey, an assistant minister of Christ's Church, St. Peter's, and St. James, Philadelphia.

An Outline of Bible History; with Notes and Observations, adapted to the minds of youth, and designed for Sabbath and other schools; with engravings. By Rev. Charles A. Goodrich. One vol. 18mo. S G. Goodrich, Hartford.

Remarks on the Rise, Use, and Unlawfulness of Creeds and Confessions of Faith, in the Church of God. In two parts. By John M. Duncan, Pastor of the Presbyterian Church, Tammany-street, Baltimore. One vol. 12mo. Cushing & Jewitt, Baltimore.

The design and the Importance of the Education Society of the Protestant Episcopal Church in the Diocese of Pennsylvania. A sermon preached on the evening of Sunday the 8th of May, in St. Stephen's church, Philadelphia. By William H. De Lancey. 8vo. Printed by Staveley & Bringhurst.

The Christian Spectator. Vol. VII. No. VI. June, 1825. NewHaven.

Discourses on the Offices and Character of Jesus Christ. By Henry Ware, jun. Minister of the Second Church in Boston. 12mo. pp. 217. Boston.

A Sermon on the Art of Preaching, delivered before the Pastoral Association of Massachusetts, in Boston, May 25, 1825. By Edward D. Griffin, D. D. President of Williams College. 8vo. pp. 35. Boston. The Gospel Advocate, No. LIV. for June, 1825.

The Claims of Past and Future Generations on Civil Rulers. A Sermon preached at the annual Election, May 25, 1825, before His Honor [!!!] Marcus Morton, Esq. Lieut. Governor, the Honorable [!!!] Council, and the Legislature of Massachusetts. By William B. Sprague, Pastor of the First Church in West Springfield. 8vo. pp. 36. Boston. True & Greene.

A Collection of Essays and Tracts in Theology. By Jared Sparks. No. X.

Boston.

The Duties of an American Citizen. Two Discourses delivered in the First Baptist Meeting House in Boston, on Thursday, April 7th, 1825, the Day of Public Fast. By Francis Wayland, jun. 8vo. pp. 52. Boston. James Loring.

The Christian Spectator, conducted by an Association of Gentle men. Vol. VII. No. V for May, 1825

Redeeming the Time; a Sermon by the Rev Samuel M. Emerson, pastor of a church in Manchester.

The American Baptist Magazine Vol. V. No 5, for May, 1825. Discussion of Universalism; or, a Defence of Orthodoxv against the Heresy of Universalism, as advocated by Mr. Abner Kneeland, in the Debate in the Universalist Church, Lombard-street, July, 1824, and in his various publications, as also in those of Mr. Ballou and others. By W. L. McCalla. Philadelphia.

The Christian Journal and Literary Register, for May, 1825. NewYork. T. & J. Swords.

The Christian Examiner and Theological Review, No. VIII. for March and April. Boston. Cummings, Hilliard & Co.

THE

NEW-YORK REVIEW.

SEPTEMBER, 1825.

ART. XXIV.-Account of Experiments to ascertain the length of the Seconds Pendulum at Columbia College, New-York, by Captain EDWARD SABINE, of the Royal (British) Artillery, F.R. S. and Honorary Member of the Historical, and of the Literary and Philosophical Society of New-York; being the second paper in the Transactions of the Literary and Philosophical Society of New-York, Vol. II. Part I. New-York. E. Bliss & E. White. 1825.

THE pendulum is, for many reasons, among the most valuable of the instruments employed in the researches and experiments of physical science. It furnishes by far the most accurate mode of dividing time; it enables us to ascertain the force of gravity at each different point on the surface of the earth, and the relation of the intensities of this force at different places; and it has been proposed as a standard of universal

measure.

The isochronism of the vibrations of pendulous bodies was first observed experimentally by the celebrated Galileo; and they were shortly afterwards applied by Sanctorius to the regulation of time-keepers. But it is to the celebrated Huygens that we are indebted for a more full exhibition of the principle of their action.

If a gravitating body of very small dimensions were suspended by an inflexible rod entirely devoid of weight, it would constitute what is called a simple pendulum. Such a one, it is obvious, cannot in reality exist, but the mathematical properties of the instrument may be deduced from the consideration of this hypothetical form, and then extended to the seve ral cases of pendulums of determinate figures and magnitudes, suspended by rods of weights and dimensions too great to be neglected. If such a pendulum as we have imagined were withdrawn from the vertical position in which it would naturally hang under the action of gravity, and then left to itself, it VOL. I.

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would descend in a circular arc to its pristine position, and passing that, would ascend in an equal and similar arc to a height on the opposite side nearly equal to that whence it fell. Were there no resistance from the medium in which the motion is performed, or from friction around the point of suspension, the pendulum would continue to perform vibrations or oscillations between these two extreme points. In consequence, however, of these retarding forces, the arc will gradually become less and less, until the pendulum is finally brought to rest. As the arc of vibration becomes less, the motion becomes slower, and the time in which the vibrations are performed varies. In order, then, that the vibrations may be perfectly isochronous, it becomes necessary that some mechanical contrivance be adopted, by which a quantity of motion, equal to that abstracted by the retarding forces, shall be restored at the commencement of each vibration. This purpose is in some measure answered by the works and moving power of a clock; a clock also serves to register the number of oscillations performed by the pendulum.

The proper adjustment of the moving power to the motion. lost at each vibration being a problem of great nicety, Huygens was led to seek for some other method of rendering the pendulum an exact measure of equal portions of time. In the course of his researches, he discovered that all the arcs of a cycloid whose axis is a normal to the horizontal plane, would be described by a gravitating body in equal times; and he was led to the theory of a mechanical contrivance, by which he conceived a pendulous body might be made to perform its vibrations in cycloidal arcs. Although this actually failed when it was attempted to apply it in practice, yet his discovery was not the less valuable; for we are now provided with means by which the vibrations of pendulums in circular arcs of known magnitudes may be reduced to those in a cycloid, whose axis is equal to half the length of the pendulum.

When pendulums are applied to clocks, it is unnecessary to determine their absolute length in any known measure. They are constructed of lengths not differing much from that which by experiment is known to perform vibrations in the space of time that they are to mark, and are afterwards experimentally adjusted. In clocks of the best construction, the arc of vibration is made very small; and thus any error that might arise from an inequality in the action of the maintaining power is rendered insensible.

The rods of pendulums are usually constructed of metallic substances; these are liable to be expanded by heat, and to

contract with cold. Hence the length of a pendulum, instead of being constant, is in fact continually varying with the evervarying temperature of the atmosphere. This defect has been obviated by a variety of ingenious contrivances called compensations. Of these there are a very great variety; their general principle, is however, the same, viz.: That the pendulum shall be suspended by two substances, in such a way that the expansion of the one upwards, shall exactly counteract the expansion of the other downwards. Such is the perfection attained in the construction of these compensations, that a clock belonging to Mr. Brown, of London, has never, during a long series of years, varied more than two tenths of a second from its established rate.

The application of the pendulum as a measure of time may therefore be conceived to have reached its ultimate point of perfection. The present paper has reference principally to its other uses, viz. that of ascertaining the relative intensity of gravity at different points upon the surface of the earth, and that of providing a universal standard of measure. We shall proceed briefly to explain some of the scientific principles connected with these objects.

When a body is made to revolve around a fixed axis, its several particles describe circles, whose planes are perpendicular to, and whose centres are in, the axis. In this way, all the particles, except those situated in the axis, become affected by a centrifugal force that would, did no other cause oppose its action, cause them to fly off in tangents to the centres in which they revolve, and the centrifugal force in each particle is proportioned to the radius of the circle it describes. In solid bodies revolving, the attraction of aggregation, generally speaking, possesses sufficient intensity to prevent any disintegration; and in larger masses of matter, whether solid or fluid, the attraction of gravitation performs a part similar to that which is filled by the attraction of aggregation in smaller solids. The earth is a body of a form not far from spherical, that is in a state of rapid rotary motion, performing a complete revolution around its axis in the space of a siderial day. Each point upon its surface is therefore acted upon by a centrifugal force; this is greatest at the equator, and becomes zero at the poles. And although the intensity of attraction of gravitation is such as to render this centrifugal force of no effect in throwing off any portion of the matter of which the earth or its surrounding atmosphere is composed; it is yet rendered manifest, by diminishing the intensity of that centripetal force. This diminution of the intensity of the gravitating force, will affect the rate at

which heavy bodies fall to the earth's surface, and the time of the oscillation of pendulums; it was first observed by Richter, a French astronomer, who visited Cayenne in 1672, for the purpose of making astronomical observations. He was furnished with a clock that marked mean solar time, in the latitude of Paris; to his surprise he found that in Cayenne, in lat. 5° north, its rate had become 2' 28" per day too slow. As this was a far greater change than could be accounted for by any alteration in the length of the pendulum, caused by difference of temperature, no explanation remained, except that furnished by the opposition of the centrifugal force to the attractive power of the earth. The centrifugal force, it has been already stated, is proportioned at any point of the earth's surface, to the radius of the circle described by that point in its diurnal revolution; but this is not the measure of the diminution it causes in the intensity of gravitation; for the latter acts in the direction of a radius of the terrestrial sphere, while the former is parallel to equatorial diameter. On account of this obliquity of action, the diminution in the force of gravity arising from the diurnal rotation of the earth, is every where proportioned not to the cosine of the latitude, but to its square.

By the investigations of Newton and Huygens into the laws of central forces, we have a method by which the relation between the whole gravitating force exerted by the earth, and the centrifugal force at the equator, may be determined; and this is found to be as 289: 1.

A great part of the surface of the earth is covered with water, and many of the theories of geologists conceive that the earth must have originally been in a liquid state. The general figure of the earth's surface is shown by the level which the water of the ocean spontaneously assumes, and hence grew the belief that the shape of our globe could not be that of a perfect sphere. For were the solid nucleus of the earth perfectly spherical, the waters of the ocean must have accumulated themselves by virtue of the centrifugal force in a zone on each side of the equator. In order that a mass of fluid acted upon by its own gravitation, and the centrifugal force arising from its solution around its fixed axis, should be at rest, and have no tendency to move either towards its poles or its equator; it is necessary that the weights of all the columns of the fluid, reaching from the centre to the surface, should be equal to each other; and that these several columns, if supposed to be enclosed in tubes, communicating with each other at the centre, should be in equilibrio. But a column beneath the equator, being formed of matter whose gravity is diminished by the