HISTORY OP PHYSICAL ASTRONOMY.

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CHAPTER IX.

Secular Variations of the Planets.—Elements of the Terrestrial Orbit—Variations of theEccentricity Motion of the Aphelion.—Obliquity of the Ecliptic —Its secular Varia-tion computed by Theory.—Euler. — Lagrange.—Laplace. — Influence of the displace-ment of the Ecliptic on the length of the tropical Year.—Indirect Action of the Planets

on the terrestrial Spheroid._Its effect in restricting the Variations of the Obliquity of the

Ecliptic and the length of the tropical Year_Invariable Plane of the Planetary Sys-

tem.—Theory of Comets.—Hevelius.—Borelli.—Dorfel.—Subjection of the Motionsof Comets to the theory of Gravitation by Newton.—Halley—Clairaut.—Researchesof Lagrange on Cometary Perturbation.—Lexell’s Comet. — Its Perturbations investi-gated by Laplace_Publication of the Mecanique Celeste.—General Reflections on

the Progress of Physical Astronomy.

The theory of - the secular variations of the elements of the planetaryorbits forms one of the most interesting subjects of physical astronomy.The actual existence of some of these variations was long a disputed pointwith astronomers; hut they have been established beyond all doubt inrecent times by the accuracy of modern observations. The secular varia-tions of the terrestrial orbit have naturally excited a more lively interestthan the others of the same class, on account of their connexion with thephysical condition of the earth. The investigation relative to the eccen-tricity is manifestly an object of the highest importance, since the indefiniteincrease of that element, at however slow a rate, would ultimately occasionsuch violent alternations of heat and cold at the earth’s surface, in the courseof every year, as utterly to destroy the existing economy of animal andvegetable life. The sublime researches of Lagrange have shewn, however,that such a condition cannot possibly ensue ; for the terrestrial eccentricitywill always he maintained by the action of the planets within certainnarrow limits between which it will perpetually oscillate. At present it isdiminishing at the rate of 18" in a century. An immense number of ageswill elapse before it reach its minimum state; but, when this takes place,it will then pursue a contrary order of variation, increasing at the sameslow rate as that at which it had previously diminished. We have seenthat the variation of this element forms the medium through which theaction of the planets is propagated to the moon ; occasioning thereby thesecular inequality in the mean motion of that body, which was so long thecause of embarrassment to mathematicians and astronomers, until itsphysical origin was at length discovered by Laplace.

The motion of the earth’s aphelion was first discovered by the celebratedArabian astronomer, A1 Bataui. As in the case of the lunar apogee, itadvances in the order of the signs, though at a much slower rate. Itsannual motion is estimated at 11" or 12". The variation of this elementis interesting on account of the clear evidence it affords of the disturbingaction of the planets on the earth; but it obviously cannot exercise anyinfluence on the physical condition of the latter.

But the question is very different when we consider the position of theearth’s orbit. A variation of this kind, by altering the obliquity of theecliptic, would manifestly affect the temperature and climate of the earthin an equal degree with the variation of the eccentricity. The true stateof the obliquity of the ecliptic was long a subject of controversy ; someastronomers asserting that it was invariable, while others maintained that

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