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HISTORY OF PHYSICAL ASTRONOMY.

a very marked discordance with the real orbit, as indicated hy observation.It was found that the orbit in which the planet actually revolved was muchsmaller than either of those deduced from theory, and that, instead of beingvery eccentric, it approached very nearly to a circular form. The followingare the elements calculated from observation by Mr. Walker of Washing­ ton , U.S. :

Mean distance. 30.0303

M. Long. January 1, 1847; M. T. Greenwich 328° 32' 44".20

Eccentricity . ..00871940

Long, of Perihelion.47° 12' 0".50

Long, of Ascending Node .... 130 4 20 .81Inclination. 1 46 58 .97

Mean Daily Motion ..... 21".55448

Periodic Time ..... 104.0181 trop. years.

Elements of the planet’s orbit were also calculated by other astronomers,and the results were found to agree very nearly with those above given.It appears that the mean distance, instead of being nearly double themean distance of Uranus , amounts only to about two-thirds of it. The lawof Bode, therefore, which is so remarkably applicable to the other mem-bers of the planetary system, totally fails in this case. The generaldiscordance of the elements with those severally assigned by the twogeometers who were led to the theoretical discovery of the planet, at firstoccasioned considerable surprise, and it was suspected that some difficultywould be experienced in rendering a satisfactory account of its origin. Alittle reflection, however, served to arrive at clearer views on the subject.In order that the reader may understand how elements so remote from thetruth as those of Le Verrier and Adams, could have sufficed to effect thetheoretical discovery of the planet, it is necessary to form a distinct con-ception of the nature of the problem, by the solution of which these geo-meters were conducted to their respective results. The data of thisproblem were the observed perturbations of Uranus , and the main objectto be accomplished was to determine the position in the zodiac occupiedat any assigned instant by the disturbing body so as to arrive at its actualdiscovery. Now, the derangement occasioned in the motion of any planetby the action of another planet upon it depends on the intensity anddirection of the disturbing force at each instant; and these again dependon the mass of the disturbing body, and on its distance and longitude withrespect to the sun. It is manifest, therefore, that only those elementswhich will accurately assign the distance and longitude of the disturbingbody will render a complete account of the perturbations of Uranus . Butif the values of the heliocentric co-ordinates should not be absolutely cor-rect, still, if they approach with tolerable approximation to the true values,it is not difficult to perceive that by a due adjustment of the mass, theintensity and direction of the disturbing force will be represented with acorresponding degree of precision. Under such circumstances the anoma-lies of the disturbed planet will be accounted for with nearly as greatfidelity as if the disturbing planet were in its true place, for the error ofperturbation is obviously of an order inferior to the error in the place ofthe disturbing body. Now, although it is impossible permanently to re-present, even with tolerable accuracy, the heliocentric co-ordinates of a bodyrevolving in an elliptic orbit by means of any elements which differ from