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APPENDIX.

planet, which involves all the consequences liable to be developed in thelapse of indefinite ages. Hence it is manifest that the absence of any re-semblance between the theory of the hypothetical planet of Le Verrierand that of the planet Neptune , cannot he considered as affecting in theslightest degree the merit of Le Vender's researches, in so far as they hadfor their object the discovery of the disturbing body. Even in the case ofNeptune , the terms to which Mr. Gould alludes do not exercise anysensible influence on the action of the planet between the years 1690and 1845.

(95.) With reference to the same geometer Mr. Gould makes the followingstatement:—“ His laborious and elegant researches have been crownedwith brilliant success, and M. Le Verrier himself rewarded by the con-sciousness of having been the immediate occasion of the discovery ofNeptune . And although the agreement of Neptune 's direction at thetime of the discovery with the direction of the theoretical planet was hutaccidental, it almost seems as though the heavens strove to show themselvespropitious, so happy teas the accident, so wonderful the coincidence." *

(96.) Leaving the above passage to the reader’s own reflections, we proceedto notice one or two other statements of Mr. Gould’s. Referring to theassertion of Sir John Herschel , in his “ Outlines of Astronomy," that thelongitude and radius vector of the hypothetical planet, whether of Adamsor Le Verrier, very nearly coincided with the longitude and radius vectorof Neptune during the period of its action being sensible, Mr. Gouldremarks:—“ But surely it cannot be considered as an analogy betweenthe two orbits, that the perihelion of the one was so near the aphelion ofthe other.”

The analogy between the two orbits, demanded by the question relativeto the disturbing body, was confined solely to a pretty close coincidenceof the paths of the hypothetical and real planets during the period of thedisturbing force being sensible. Even in this case it was a near agreementof the longitudes, rather than of the distances, which was required by theconditions of the problem. With respect to the absolute identity of thetwo orbits, the establishment of such a condition was an object of no im-portance in so far as the discovery of the disturbing body was concerned.Sir John Herschel , in the work to which Mr. Gould refers—so far fromattempting to demonstrate any resemblance between the elements of Nep­ tune on the one hand, and those of the hypothetical planet of eitherLe Verrier or Adams on the other—on the contrary, utterly repudiatesthe existence of any necessary connexion between such an analogy andthe question relative to the discovery of the disturbing body. But, apartfrom all consideration of this circumstance, it seems surprising that Mr.Gould should urge such an objection to the identity of the two orbits asthat above cited, when it is borne in mind that in the one case the orbitis very eccentric, and in the other case is almost circular.

(97.) Mr. Gould concludes his Report with a remark the object of whichis to reconcile the conflicting results of observation and theory. “ Thecombined labours of Le Verrier and Peirce,” says he, “ have incontro-vertibiy proved that, by reducing the limits of error assumed for themodern observations to 3", there can be but two possible solutions of theproblem. There are two different mean distances of least possible error,one of which is 36, and the other 30. The one is included within the

Report, p. 51.