HISTORY OF riTYSTOAL ASTRONOMY.

201

not appear to have occurred to any of the great geometers whose names areassociated with the development of the theory of gravitation. Nor is thiscircumstance calculated to excite surprise, for the actual state of PhysicalAstronomy had not yet demanded such an advanced step. It was onlywhen all the consequences resulting from the mutual action of the planetsalready known had been fully deduced, and the outstanding irregularitieshad assumed the form of residual phenomena depending on some foreigninfluence, that further speculation suggested the expediency of invertingthe usual order of investigation. It is manifest from this circumstance,that the complete establishment of the formulae of planetary perturbationmust have preceded any attempt to ascend from the effects produced byan unseen planet to the determination of its actual position. The accom-plishment of this latter object is therefore an indication of the highly-advanced state of physical astronomy, since it implies not only that thedifficulties peculiar to the inverse problem of perturbation have beensuccessfully overcome, but also that the irregularities occasioned by themutual action of the planets have been deduced from the principles of theNewtonian theory, and have, in all instances, been found to accord withthe results derived from observation. This remark does not, of course,apply to the planet which theory has recently revealed to us, since a con-siderable time must elapse before an accurate knowledge of the inequalitiesof its motion can be obtained. It will then be an interesting point toascertain whether these inequalities do not in their turn afford indicationsof the existence of a still more remote member of the solar system. Theastronomer is thus led to speculate on the theoretical discovery of planets,reflecting too feeble a light on account of their immense distance from thesun, to be ever visible, even by the aid of the most powerful telescopes.It is to he hoped, that notwithstanding the abundant harvest, which hasbeen already reaped in Celestial Mechanics , that magnificent region isdestined still to afford more profitable fields for the application of the re-sources of analysis than that which the imagination here suggests.

CHAPTER XIII.

The Elements of the Planet Neptune deduced from Observation.—They are found to beDiscordant with the Results of Theory. —The cause of Discordance assigned.—The

Planet observed by Lalande.—Theory of its Perturbations_Researches on the Value

of its Mass.—Uncertainty respecting this Element.—Researches of M. Hansen on theLunar Theory.— Conclusion of the History of Physical Astronomy.

As soon as astronomers received intelligence of the discovery of the PlanetNeptune, the new member of the solar system was regarded with intenseinterest, and accurate observations of it were made both in Europe andAmerica . When the elements of the orbit were calculated from these ob-servations, a comparison of the results with those assigned by the theoriesof Le Verrier and Adams led to rather unexpected conclusions. Althoughthe orbits assigned by these geometers to the disturbing planet did notdiffer materially from each other, they both, on the other hand, exhibited