HISTORY OF PHYSICAL ASTRONOMY.

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exhibits the retrograde motion of a planet, and assigns differences ofright ascension and declination, agreeing almost exactly with those indi-cated by the motion of the planet Neptune .

An examination of the mutual action of Uranus and Neptune illustratessome very interesting points in the theory of planetary perturbation.In consequence of the mean motion of the former of these planets beingonly a small fraction less than twice the mean motion of the latter, theperturbations which recur in every synodic revolution of the two planets,assume a resemblance to those which take place in the theories of thefirst and second, and of the second and third satellites of Jupiter . Thisnear commensurability of the mean motions, in fact, introduces into theorbit of each planet a considerable eccentricity, dependent wholly on per-turbation, and distinguishable from the permanent ecceutricit} r of the orbitby the constant coincidence of the line of apsides with the line of conjunc-tion of the two planets. In the case of Neptune disturbing Uranus , theaphelion of the movable ellipse is constantly turned towards the point ofconjunction. On the other hand, when the action of Uranus upon Neptune is considered, it is the perihelion that is turned towards the same point.In another respect the perturbations of the two bodies resemble those ofvarious other primary members of the planetary system. The near com-mensurability of the mean motions, combined with the permanent eccen-tricities of the orbits, gives rise to an inequality of long duration, similarto that in the theories of Jupiter and Saturn, or any of the other longinequalities to which wo have had occasion to allude. The magnitude andduration of this inequality cannot be ascertained with precision untilastronomers arrive at an accurate determination of the elements of thetwo planets. This remark applies more especially to the mean distances,a very small error in their relative values producing an enormous influenceon the final results. If we adopt 30.2020 for the mean distance of Neptune ,being one of the earlier values deduced from observation, the duration ofthe inequality will be 6820 yearn. On the other hand, if we employMr. Walker’s determination of the mean distance, which differs from thepreceding value only by T -t ¥ , the duration of the inequality will onlyextend to 4051 years. The magnitude of the inequality will vary in a stillgreater proportion with the change of mean distance *.

The mass of Neptune is an element which, in the present state of thetheory of the planet, is still involved in great uncertainty. A satellitewhich has been discovered by Mr. Lassel fortunately affords the means ofdetermining its value independently of the perturbative action of theplanet, but no satisfactory results on this point have been elicited by theresearches of astronomers. M. Otto Struve, by means of his own observa-tions, makes the period of the satellite 5 d 21 h 15™, and the semi-majoraxis of the apparent orbit 17".89. These numerical values indicate amass equal to T , the sun’s mass being represented by unity. On theother hand, Professor Pierce of Harvard College , U.S., guided by similarobservations of his countryman, Mr. Bond , has obtained -y-gg-jn f° r thovalue of the planet’s mass. This geometer has executed a detailed calcu-lation of the perturbations which Neptune produces on Uranus , and hasfound that the mass deduced from Mr. Bond ’s observations of the satellite

* It is worthy of remark that the inequality is greater in the former of these cases thanin the latter, although the disturbing body is then more distant. Both the magnitude andduration of the inequality increase ad infinitum as the mean distance increases towards avalue very nearly equal to 30.45014.