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HISTORY OF PHYSICAL ASTRONOMY.
surmise has been fully borne out by the results derived from actual obser-vations of the planet; and, while it is highly creditable to Mr. Adams’sagacity, it also shews the thorough insight he had obtained into themutual bearings of the various parts of the intricate problem with whichhe was engaged. The following are the elements he deduced from hissecond hypothesis of the mean distance :—
323° 2'299° 11'.12062.00016003
Mr. Adams gave examples of the correction to the tabular value of theradius vector. The correction for 1834 almost coincided with that whichMr. Airy had deduced from observation. The corrections for later yearswere not quite so satisfactory; but in this respect also the second hypo-thesis presented a better agreement with observation than the first did.Mr. Adams mentioned that he was then engaged in determining the in-clination and place of the node, and that he hoped to complete his investi-gation in a few days.
The corrections to the tabular radius vector transmitted, on this occa-sion by Mr. Adams to the Astronomer Royal, naturally suggest a fewremarks. We have already mentioned that the latter attached muchvalue to this part of the theory, as affording a criterion for testing theaccuracy of the results derived from the researches on the motion inlongitude. We can easily imagine that some of our readers will be slowto concur with the views of the Astronomer Royal on this point. If indeedthe cause of the irregularities of Uranus was doubtful, it is not difficult toperceive that the explanation of the errors of radius vector by the pertur-bations of an assumed planet would possess much weight in establishingthe legitimacy of such an hypothesis ; for, granting that the irregularitieswere due to some other cause, although it is conceivable that the theory ofgravitation might be made to represent the errors in longitude by a suit-able evaluation of the constants of the problem, it is utterly im-probable that the same constants and the same values of them would alsoaccount for the errors of radius vector, with which they had no physicalconnexion. But the necessity of computing the errors of radius vector inaddition to those of longitude does not appear so obvious, if it be admittedthat the irregularities of Uranus are really due to a disturbing planet, andthat the sole point to be decided was the accuracy of the results. In thiscase it was known a priori that the constants which entered into the ex-pressions of the errors, both of longitude and radius vector, were the bondfide representatives of the physical elements of the problem. It wasalso known that these expressions were legitimately deduced from esta-blished principles, and consequently were not mere empyrical formulae.Hence it might be presumed that results which accounted so satisfactorilyfor the errors in longitude throughout a period embracing more than arevolution and a half of the planet could hardly fail to account with equalfidelity for the errors of radius vector. This reasoning involves the tacitassumption that, if certain values of the unknown quantities of the problemsatisfy the errors of one of the co-ordinates of the planet, they musteither be absolutely correct, or must constitute very near approxima-tions to the truth. This principle, however, is at variance with theresult of researches in physical astronomy, for it has been found, in