approximation to the truth which has yet been arrived at by philosophers*. It is remarkable that Newton conjectured that the mean density of the earth is about five or six times the density of watert.

The Schehallien experiment for determining the mean density of the earth is purely statical; on the other hand, the experiment with the torsion balance is founded on dynamical principles, being in fact a case of the horizontal pendulum. The vertical pendulum has also been employed for a similar purpose. The attraction on the top of a high mountain may be decomposed into two parts; one of which is the attraction at the level of the sea diminished in the inverse ratio of the square of the distance, and the other is the attraction of the mountain itself. Hence, if the intensities of gravity on the mountain and at the level of the sea be determined by observation, the difference of the two forces will indicate the attraction due to the mountain, and, by a process similar to that employed in the Schehallien experiment, we shall be enabled to ascertain the mean density of the earth. Experiments for this purpose were made by Carlini at the hospice of Mount Cenis, which has an elevation of 6375 feet above the level of the sea; and the conclusion at which he arrived was that the mean density of the earth is 4.39, that of water being unity.

We have mentioned already that D'Alembert succeeded in accounting completely for the motion of the earth's axis in space, arising from the action of the sun and moon upon the redundant matter accumulated round the equator. It still remained, however, for geometers to ascertain whether the disturbing forces affected the position of the axis relative to the surface of the terrestrial spheroid, or whether they occasioned any change in the velocity of rotation. Observation, indeed, gave a negative answer to both of these questions; for neither the latitudes of places on the earth's surface nor the length of the day appeared to have undergone any variation from the earliest period of history. It was desirable, however, to establish these facts by demonstrative reasoning founded on the theory of gravitation ; for, in the absence of such conclusive evidence, there existed no grounds for supposing that the position of the axis and the velocity of rotation might not be affected by secular inequalities, which, though slow in their developement, would in the lapse of ages become sensible by continual accumulation. If the axis experienced any such displacement, the position of the equator would be constantly shifting with inconceivable slowness, and the sea, by always flowing towards the new position to restore the equilibrium of the particles, would eventually occasion a total change in the relation of land and water on the earth's surface. It is clear also that the latitudes of places would be ultimately affected by the displacement, and hence would ensue a corresponding alteration of the seasons. Poisson first examined this point with all the attention due to its importance. In an admirable paper, which was published in the

* Notwithstanding all the precautions used by Mr. Baily, he found that the resting points of the balls and the times of oscillation were subject to disturbances, the cause of which he was unable to explain. In the Philosophical Transactions for 1847, there is a paper by Mr. Herne, of the Royal Military College of Sandhurst, in which he attempts to account for these anomalies by the supposition of a magnetic state of the masses and balls.

+ Verisimile est quòd copia materiæ totius in Terrâ quasi quintuplo vel sextuplo major sit quam sit tota ex aqua constaret.—Princip., lib. iii. prop. 10.

Memoirs of the Academy of Sciences for 1824, he has shewn that the disturbing forces of the sun and moon cannot produce, in the variables which determine the relative position of the earth's axis, any secular inequalities which might ultimately become sensible. He also found that the velocity of rotation could not be sensibly affected by the same cause; whence it followed that the length of the sidereal day is not subject to any variation depending on the action of the sun or moon.

The conclusion at which Poisson arrived is fully borne out by an examination of ancient eclipses. It is clear that, if the diurnal motion of the earth be variable, the period comprised between two successive returns of a star to the same position relative to the horizon cannot constitute a fixed standard of time; and consequently the interval between the present time and any remote epoch, when expressed in terms of the sidereal day as determined by modern observation, will not correspond to the number of revolutions which the earth has actually accomplished, as indicated by historical records. It will follow also that if the diurnal motion constantly vary in the same direction, the difference between the computed and the historic epochs will increase with the lapse of time. We may therefore conclude that the places of the planets, when computed for any remote epoch by means of the modern value of the sidereal day, will differ from their actual places as assigned by the recorded observations of astronomers; and this difference will be more considerable for the moon than for any other body, on account of her rapid motion. Now, if the rotation of the earth is really invariable, the longitudes of the sun and moon, when computed for any ancient lunar eclipse, ought not to differ from 180° by a quantity greater than the sum of their semi-diameters, and the difference may naturally be expected to be in many cases much less. In the Connaissance des Temps for 1800, there is a paper by Laplace, containing calculations of this nature for 27 eclipses recorded by the Chaldeans, Greeks, and Arabians, and the results in all instances go to prove the invariability of the sidereal day. The greatest quantity by which the distance between the centres of the sun and moon differs from 180°, amounts to 27′ 41′′, and relates to an eclipse which happened in the year 382 A.C. Even this difference, however, falls short of the sum of the solar and lunar semi-diameters, and, therefore, does not preclude the possibility of an eclipse having taken place. It is clear, then, that the length of the sidereal day is not subject to any sensible inequalities, since the conclusions deducible from the supposition of its being constant accord so well with observation. In order to illustrate this interesting fact more fully, Poisson assumed that the length of the day had diminished by a ten-millionth part since the most ancient of the Chaldean eclipses, which happened in the year 720 A.c.; and then, calculating the longitudes of the sun and moon for that epoch, he found them to differ from 180° by 34'. This quantity being greater than the sum of the semi-diameters of the two bodies, is incompatible with the occurrence of an eclipse, whence it follows that, during the lapse of 2500 years, the length of the sidereal day has not altered by so much as the ten-millionth part.

An interesting question which Laplace first considered in connexion with the length of the sidereal day, is that relating to the mean temperature of the earth. Various facts concur to strengthen the opinion that the earth was originally a fluid mass, which subsequently became solid by a process of cooling, which is even still going on. This gradual diminution of temperature being necessarily accompanied by a corresponding diminution

++M

of the earth's mass, the particles composing the latter will all in consequence approach nearer to the axis. Now, it follows immediately from a well-known principle in Mechanical Science, that when a body is endued with a rotatory motion, and is not exposed to the action of any extraneous forces, the principal moment of inertia, or, in other words, the sum of the products formed by multiplying each particle into its angular velocity and the square of its distance from the axis of rotation, is a constant quantity. The number of particles then remaining the same, if their distances from the axis be diminished, their angular velocities must be increased, and vice versa. Hence, if the dimensions of the earth be in a state of contraction from cooling, the velocity of rotation must be increasing, and the length of the sidereal day must be diminishing. It is not difficult, however, to show that if the earth is really becoming cooler, the diminution of temperature must be proceeding at a very slow rate. We have seen that, during a period of 2500 years, the sidereal day has not been shortened by so much as the ten-millionth part. Now, the principles of Mechanics teach us that this result would ensue if the earth's radius experienced a diminution of only one twenty-millionth part of its length. It follows, then, that during the period which has elapsed since the earliest Chaldean observations, the mean temperature of the earth has not varied to such an extent as to cause the terrestrial radius to contract by one twenty-millionth part of its length.

The important question of the Tides has recently attracted considerable attention in this country. The Encyclopædia Metropolitana contains a valuable essay on the mathematical part of the subject, by Mr. Airy, founded on the theory of undulations. Sir John Lubbock and Dr. Whewell have been engaged during many years in determining the laws of the tides by observation, and in tracing their connexion with the places of the sun and moon. The results to which they have been conducted by their researches are contained in a series of admirable papers, which continue to be published from time to time, in the volumes of the Royal Society. These distinguished philosophers are now endeavouring to do for the theory of the tides what astronomers had done for the lunar theory previous to the establishment of the theory of Gravitation. Let us hope that their efforts will be attended with similar success, and that the day is not very remote when this important branch of Physical Astronomy will be in a condition to invite the researches of the geometer, and to reward him with a rich harvest of results.

It is clear that if the sun and moon by their action on the earth occasion oscillations in the waters of the ocean, they ought to produce a similar movement in the atmospheric fluid. Laplace investigated the theory of this subject upon a somewhat restricted hypothesis*, and Bouvard undertook an extensive series of observations of the height of the barometer, with the view of detecting periodical oscillations depending on the places of the disturbing bodies. The effects, however, were so very minute as to be almost entirely masked by irregularities arising from other causes, and no satisfactory conclusion could be deduced from the observations.

The oscillations of the atmospheric tide will manifestly be greatest near the equator, and the most favourable station for detecting them would

Méc. Cél. liv. iv. chap. iv., liv. xiii. chap. vii. The temperature of the atmosphere was assumed to be uniform, and the density at each point proportional to the compressing force.

be some small island in the middle of the ocean, because the barometer would in that case be least liable to be affected by the fluctuations arising from the irregularities of the earth's surface. With the view of throwing some light on this delicate subject Captain Lefroy, of the Royal Artillery, undertook a series of barometrical observations at the island of St. Helena. These observations were conducted solely with reference to the place of the moon, as the effect of the sun's influence was naturally expected to be insensible. They extended from August, 1840, to December, 1841, and therefore comprised a period of seventeen months. The mean result of these observations clearly indicated the existence of a lunar atmospheric tide. It gave 28.2714 inches for the height of the barometer when the moon was on the meridian, and 28.2675 when she was on the horizon. The difference was therefore .0039 inches*. The observations were subsequently resumed by Captain Smythe in October, 1842, and were continued till September, 1843. The average of all the results obtained during this period gave .00255 inches for the excess of the altitude of the barometer, when the moon was on the meridian, over the altitude when she was six hours distant from it. The observations for the following two years were compared together by Lieutenant Colonel Sabine at Woolwich, and the results he derived from them presented a satisfactory accordance with those previously obtained by Lefroy and Smythe. The average excess of barometrical pressure during this period amounted to .00365 inches, or in round numbers to .004 inches. It is manifest that the effect of the moon's action ought to be greatest when she is in perigee, and least when she is in apogee. This is unequivocally indicated by the observations, as appears from the following results of the mean barometrical excess, obtained by a comparison of observations made when the moon was on the medidian, and when she was six hours distant from it :

These quantities are small, but still they are sufficiently sensible to establish beyond doubt the existence of oscillations in the atmosphere, similar to those which affect the waters of the ocean. This is not the least interesting of the many facts in physical science which would have for ever escaped detection, if their existence had not been suggested by the theory of gravitation.

* Phil. Trans., 1847.

CHAPTER XII.

Introductory Remarks.—Ancient Observations of Uranus.-Calculation of Tables of the Planet by Delambre.-Tables of Bouvard.—Irregularities of the Planet.-Speculations respecting their Origin.-Errors of Radius Vector.- Researches of Geometers.-Bessel. -Adams.-Inverse Problem of Perturbation.-Account of Adams' Researches relative to the existence of a Planet exterior to Uranus.-Results obtained by him.-Researches of the French Astronomers on the Theory of Uranus. - Eugene Bouvard.-Le Verrier. -Account of his Researches.-Near agreement of his Results with those of Adams.-Steps taken by Airy and Challis for the purpose of discovering the Planet.-New Results obtained by Adams.-Explanation of errors of Radius Vector.-Account of the second part of Le Verrier's Researches on the Trans-Uranian Planet.-Address of Sir John Herschel at Southampton.-The Planet discovered at Berlin by Galle.— Admiration excited by the Discovery.-Account of Challis' Labours.-Public Announcement of Adams' Researches.-Impression produced by it.-Historical Statement of the Astronomer Royal.-Publication of the Researches of Le Verrier and Adams.-Remarks suggested by the Discovery of the Planet.

THE Theory of Gravitation is not more remarkable for the sublimity of its results than for its varied and effective character, when considered as an instrument applicable to the discovery of truth. By unfolding its principles, the astronomer, without leaving his observatory, has been enabled to determine the distances of the sun and moon from the earth, to weigh the planets as in a balance, and to educe order and stability from the countless irregularities of their motions. It has conducted him to a knowledge of the figure of the earth by merely watching the motion of the moon or the swinging of a pendulum, and it supplies the means of ascertaining the figures of the celestial orbs without measuring their apparent dimensions. The eccentric aberrations of comets, the ebbing and flowing of the tides, and the oscillations of the atmosphere, all equally attest the value of its guidance in exploring the hidden operations of nature. But a still more striking triumph of this magnificent theory was reserved for our own day, when the mathematician, by meditating in his chamber upon its principles, has succeeded in revealing the existence of a new planetary world, vastly exceeding the earth in magnitude, which had hitherto escaped the scrutinies of astronomers, aided by all the powerful appliances of optical

science.

Soon after the discovery of Uranus by Sir William Herschel in 1781, it was ascertained that astronomers had observed it on many previous occasions without recognising it to be a planet. Even as early as 1690, Flamstead had designated it as a star of the sixth magnitude; and from that year, down to 1781, astronomers had determined its position no fewer than nineteen different times, under an erroneous impression of its real nature *.

⚫ Bode first discovered two ancient observations of Uranus; one in the Historia Celestis of Flamstead (the observation of 1690), and the other in one of Mayer's Catalogues. Soon afterwards Lemonnier detected three positions of the planet among his own observations. Bessel, while engaged in reducing Bradley's observations, found that the position of Uranus