INVARIABLE PLANE, in celestial mechanics (see [Astronomy]), that plane on which the sum of the moments of momentum of all the bodies which make up a system is a maximum. It derives its celebrity from the demonstration by Laplace that to whatever mutual actions all the bodies of a system may be subjected, the position of this plane remains invariable.
A conception of it may be reached in the following way. Suppose that from the centre of gravity of the solar system (instead of which we may, if we choose, take the centre of the sun), lines or radii vectores be drawn to every body of the solar system. As the planet revolves around the centre, each radius vector describes a surface of which the area swept over in a unit of time measures the areal velocity of the planet. The constancy of this velocity in the case of the sun and a single planet is formulated in Kepler’s second law. Next pass any plane through the centre of motion and project the area just defined upon that plane. We shall thus have a projected areal velocity, the product of which by the mass of the planet is the moment of momentum of the latter. Form this product for every body or mass of matter in the system, and the sum of the moments is then invariable whatever be the direction of the plane of projection. In the case of a single body revolving around the sun this plane is that of its orbit. When all the bodies of the system are taken into account, the invariable plane is a certain mean among the planes of all the orbits.
In the case of the solar system the moment of Jupiter is so preponderant that the position of the invariable plane does not deviate much from that of the orbit of Jupiter. The influence of Saturn comes next in determining it, that of all the other planets is much smaller. The latest computation of the position of this plane is by T. J. J. See, whose result for the position of the invariable plane is inclination to ecliptic 1° 35′ 7″.74, longitude of node on ecliptic 106° 8′ 46″.7 (Eq. 1850).
INVENTORY (post-class. Lat. inventarium, a list or repertory, from invenire to find), a detailed list, schedule or enumeration in writing, of goods and chattels, credits and debts, and sometimes also of lands and tenements.
(i) In law, perhaps its earliest, and certainly its most important use has been in connexion with the doctrine of “benefit of inventory,” derived by many legal systems from the beneficium inventarii of Roman law, according to which an heir might enter on his ancestor’s inheritance without being liable for the debts attaching to it or to the claims of legatees beyond the value—previously ascertained by “inventory”—of the estate. The benefit of inventory exists in Scots law, in France (bénéfice d’inventaire), in Italy, Mauritius (Civil Code, Art. 774), Quebec (Civil Code, Art. 660), St Lucia (Civil Code, Art. 585), Louisiana (Civil Code, Arts. 1025 et seq.), and under the Roman Dutch law in Ceylon. In South Africa benefit of inventory is superseded by local legislation.
(ii.) In many systems of law, the duty is imposed on executors and administrators of making an “inventory” of the estate of the testator or intestate, in order to secure the property to the persons entitled to it. In England this duty was created by statute in 1529. In modern practice an inventory is not made unless called for, but the court may order it ex officio, and will do so on the application of any really interested party. Similar provisions for an inventory of the estate of deceased persons are made in Scots law (Probate and Legacy Duties Act 1808 (s. 38), and Executors (Scotland) Act 1900 (s. 5), and in most of the British colonies. In Scotland, prior to the Finance Act 1894 (which imposed a tax, called “estate duty,” on the principal value of all property, heritable or movable, passing on death), the stamp duty on movable property was termed “inventory duty.”
In the United States, the duty of preparing an inventory is generally imposed on executors and administrators; see Kent, Commentaries on American Law (new ed., 1896), ii. 414, 415; and cf. Gen. Stats. of Connecticut, 1888, s. 578; New York Stats. s. 2714; New Jersey (Orphans Court, s. 58).
(iii.) An analogous duty of preparing an “inventory” is imposed in many countries on guardians and curators. In Scotland judicial factors are charged with a similar statutory duty (Act of Sederunt, Nov. 25th, 1857, under the Bankruptcy (Scotland) Act 1856) as regards the estate of insolvent debtors.