HISTORY OF PHYSICAL ASTRONOMY.
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mass, the epoch, the eccentricity, and the longitude of the perihelionof the disturbing planet, together with its geocentric longitude for the30th of September, 1845* * * § . Mr. Adams was also anxious to communicatehis results to the Astronomer Royal, and for this puipose the kind offices ofProfessor Challis were again tendered. The letter of Professor Challis tothe Astronomer Royal on this occasion is dated the 22nd September, 1845 f.He mentions in it that Mr. Adams had completed his investigation re-lative to the supposed existence of a planet exterior to Uranus ; that hisresearches were founded on the observations which Mr. Airy was kindenough to send him some time previously, and that he was desirous ofcommunicating his results personally to him. He added, also, that fromMr. Adams’ character as a mathematician, and his practice in calculation,he considered that his conclusions had been accurately deduced from hispremises. Mr. Airy happened to be from home when Mr. Adams called atGreenwich, but a few days afterwards he wrote a letter to Professor Challis (,expressing the strong interest he felt in the subject of Mr. Adams’ re-searches, and mentioning that he would be happy to hear by letter fromhim respecting them.
On one of the last days of October, 1845, Mr. Adams called at theRoybal Observatory, and left a paper containing the elements of thenew planet, and the errors resulting from a comparison of the improvedtheory of Uranus with a great number of observations of the planet from1690 to 1840 §. These errors, which, by Bouvard’s tables, amounted fre-quently to 3', were now for the most part little more than 1". The fol-lowing are the elements of the planet, as given by Mr. Adams in thisimportant paper:—
Mean distance from the sun, the earth’s
distance being represented by unity . 38.4
Mean sidereal motion in 365.25 days . 1° 30'.9
Mean longitude, 1st October, 1845 . . 323°.34 /
Longitude of perihelion .... 315.55
Eccentricity . . . . . . .1610
Mass (that of the sun being unity') . . .0001656
These elements give 7° 39' for the mean anomaly of the planet on the 1stOctober, 1845, and 3° 3' for the equation of the centre. Hence, by addingthe latter to the mean longitude, we get 326° 37' for the true heliocentriclongitude of the planet. Now, if we compute the place of the planet forthe same instant by means of the elements derived from observation, weshall obtain 324° 48'for the .true longitude||. The difference, therefore,between the actual and theoretical places was only 1“ 49'; and it is clearthat if we had employed, as the epoch of comparison, the 23rd September,1846 (the epoch of the actual discovery of the planet), the result wouldnot have been materially different.
Thus it appears that, as early as the month of October, 1845, sevenmonths before any other person had arrived at a similar conclusion,Mr. Adams had solved the inverse problem of planetary perturbation;that, by means of his solution, he had discovered, theoretically, theexistence of a planet exterior to Uranus ; and that he had assigned to
* Challis’ Report to the Syndicate of the University of Cambridge ; see also Phil.
Mag., 1847.
f Airy’s Hist. Statement, No. 9. f Airy’s Hist. Statement, No. 10.
§ Ibid, No. 11.
II The elements here employed are those deduced from observation by ProfessorWalker of Washington.