OF ARTS AND SCIENCES. 145 



is not more than seven degrees from it; and in another solution which 

 I have obtained, the present direction is almost identical with Nep- 

 tune's. But the coincidence fails in a most important point; for, 

 whereas Walker and Adams both demonstrate, from incontrovertible 

 data and a simple but indisputable argument, that the new planet can- 

 not be more than ninety degrees from its perihelion, either of these 

 two latter geometrical planets would now be in aphelion and at much 

 too great a distance from the sun. 



" All my attempts to reconcile the observed motions of Neptune with 

 the assumption that it is the principal source of the unexplained irreg- 

 ularities in the motions of Uranus, have been frustrated. Whatever 

 orbit is attributed to this planet in my analysis, whether Walker's, or 

 Valtz's, or Encke's, or Adams's, or any other which I can suppose, 

 and which is not unquestionably irreconcilable with observation, and 

 whatever may be supposed to be its mass, I cannot materially diminish 

 the amount of residual perturbation, but leave it full as great as it was 

 previously to Galle's discovery. Notwithstanding my repeated exam- 

 inations, it would be presumptuous in me to claim for my investiga- 

 tions a freedom from error which the greatest geometers have not es- 

 caped, especially in the face of the vastly improbable conclusion to 

 which my analysis tends ; namely, that the influence of the new planet 

 is wholly different from that demanded by the problem whose solution 

 led to its discovery. It may, however, be asked whether the attraction 

 of Uranus might not be exhibited in the motions of Neptune, in such 

 a way as to modify the orbit deduced from observation, and thus rec- 

 oncile it with theory ; but this question cannot be answered without 

 further investigation." 



Professor Peirce stated that the above solutions were not 

 to be regarded as actual solutions, but merely as theoretical 

 and possible ; that is, if a planet had moved in either of the 

 above orbits, the perturbations which it would have produced 

 in Uranus would have been precisely those which have been 

 manifested. But the influence of the planet Neptune has been 

 wholly disregarded in obtaining these solutions, precisely be- 

 cause the nature of that influence must remain unknown, 



a previous communication to the Boston Courier, and which was vitiated by 

 an oversight in the date for which the computations had been made. 



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