HISTORY OF PHYSICAL ASTRONOMY.

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I equinoxes, is of much more recent date. Laplace found by computationI that it fell in the year 1250 a.d. The solar perigee then coincided with! the winter solstice. He therefore proposed that the year 1250 a.d. should| be used as a universal epoch, and that the first day of the year should[ begin with the passage of the sun through the vernal equinox* * * § .

| An interesting discovery to which Laplace was conducted by his re-, searches on the planets was the existence of an invariable plane in thei solar system. It is well known that astronomers generally fix the posi-! tion of a celestial bod}^ by determining its distances with respect to two; great circles of the celestial sphere at right angles to each other. If thej planes of these circles be immoveable, it is clear that observations, however! numerous or distant from each other, may be referred to them, and anyj changes of position which may have occurred will be discovered by a com-parison of the recorded distances from each circle. On the other hand,j if the position of the correlative planes be variable, it is equally undeni-; able that any conclusions drawn from such a comparison will be totallyj vitiated, at least unless due account be taken of the altered position ofi the planes at the time of each observation. Now as the orbits of all the! planets are continually shifting their positions, in consequence of the' mutual attraction of the several bodies, it is impossible to use any oftheir planes as the plane of one of the great circles of reference ; and thesame may be said of the plane of the equator, the position of which iscontinually varying from the action of the sun and moon upon the terres-trial spheroid. It becomes, therefore, highly desirable to discover someplane, the position of which shall be independent of the mutual perturba-tions of the planets, and which may, therefore, be used as a common groundfor comparing distant observationsf. This important object was effected byLaplace, who ascertained that, amid the disturbances to which the planetsare continually exposed by their mutual attraction, there exists an invari-able plane, about which the orbits perpetually oscillate, deviating from itonly to a very small extent on either side. This plane passes through thecentre of gravity of the solar system, and it is so situated, that if all theplanets be projected on it, and if the mass of each planet be multiplied intothe area, corresponding to any given time which is described by the pro-jected radius vector, the sum of such products will be a maximum. Bymeans of this property, which is independent of any particular epoch, itwill be easy for astronomers in future ages to determine the exact positionof the plane, and to compare observations together by means of itj.

This plane is not peculiar to the solar system. It exists in all thosesystems wherein the bodies are not exposed to any other forces than thosearising from their mutual attraction. Its position in the solar system hasbeen calculated, by referring it to the plane of the ecliptic, correspondingto the year 1750. In this manner it is found that the inclination of theplane is 1° 85' 31", and the longitude of the ascending node 102° 57'80". If a similar calculation he made for the year 1950, the inclinationwill be 1° 35' 31", and the longitude of the node 102° 57' 15". Theagreement of these results is very surprising when we take into account theuncertainty that prevails respecting the masses of several of the planets §.

* Mec, Cel., liv. vi. chap. x.

f Of course the relation between the two planes determines the position of the otherplane.

$ Journal de V Ecole Polytechnique, Annee, 1798; see also Mec. Cel., liv. ii. chap.vii

§ Mec. Cel., liv. vi. chap. xvii. See also Ponfecoulant’s Theorie Analytique duSysteme du Monde>X\\ t vi. chap. xxii.