HISTORY OF PHYSICAL ASTRONOMY.

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i Memoirs of the Academy of Sciences for 1824, he has shewn that the1 disturbing forces of the sun and moon cannot produce, in the variableswhich determine the relative position of the earth’s axis, any secularinequalities which might ultimately become sensible. He also found thatthe 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 toi any variation depending on the action of the sun or moon.

! The conclusion at which Poisson arrived is fully borne out by an examina-tion 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 tothe same position relative to the horizon cannot constitute a fixed standard| of time; and consequently the interval between the present time and any1 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 historicalj records. It will follow also that if the diurnal motion constantly vary in; the same direction, the difference between the computed and the historic1 epochs will increase with the lapse of time. We may therefore conclude1 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 actualplaces as assigned by the recorded observations of astronomers ; and thisdifference 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 isreally invariable, the longitudes of the sun and moon, when computed forany ancient lunar eclipse, ought not to differ from 180° by a quantitygreater than the sum of their semi-diameters, and the difference maynaturally be expected to be in many cases much less. In the Gon-?iaissance des Temps for 1800, there is a paper by Laplace, containingcalculations of this nature for 27 eclipses recorded by the Chaldeans,Greeks, and Arabians, and the results in all instances go to prove theinvariability of the sidereal day. The greatest quantity by which thedistance between the centres of the sun and moon differs from 180°,amounts to 27' 41", and relates to an eclipse which happened in the year382 a.c. Even this difference, however, falls short of the sum of the solarand lunar semi-diameters, and, therefore, does not preclude the possibilityof an eclipse having taken place. It is clear, then, that the length of thesidereal day is not subject to any sensible inequalities, since the conclusionsdeducible from the supposition of its being constant accord so well withobservation. In order to illustrate this interesting fact more fully, Poisson .assumed that the length of the day had diminished by a ten-millionth partsince the most ancient of the Chaldean eclipses, which happened in the year720 a.c. ; and then, calculating the longitudes of the sun and moon for thatepoch, he found them to differ from 180° by 34'. This quantity beingj.greater than the sum of the semi-diameters of the two bodies, is incom-i patible with the occurrence of an eclipse, whence it follows that, duringthe lapse of 2500 years, the length of the sidereal day has not altered byso much as the ten-millionth part.

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

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