13 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[J^ 



The remainder of the letter was principally occupied with the details of 

 a plan of observing dill'erent from mine, and of which the advantage was 

 fully proved in the practical observation. 



On August 7, I'rofessor Challis, writing to my conBdenlial assistant 

 (Mr. Main) in my supposed absence, said,— 



No. 18. — Professor Challis to the Rev. R. Wain, 

 [extract.] 

 " CitmbrUlge Observatory, Aiigvst 7,1846. 

 " I have undertaken to search for the supposed new planet more distant 

 than Uianus. Already I have made trinl of two different melhods of 

 observing. In one method, recommended by Mr. Airy * • • I met 

 with a difficulty which I had anticipated. • • • I adopted a second 

 method." 



From a subsequent letter (to be cited hereafter), it appears that Profes- 

 sor Challis had commeuced the search on July 29, and had actually ob- 

 served the planet on August 4, 1840. 



Mr. Main's answer to the other parts of this letter, written by my direc- 

 tion, is dated August 8. 



At Wiesbaden (which place I left on September 7), I received the fol- 

 lowing letter from Professor Challis : — 



No. 19. — Professor Challis to G. B. Airy. 

 [lxteact.] 



" Cambridge Observatory, Sept. 2, 184G. 

 " I have lost no opportunity of searching for the planet ; and the Lights 

 having been generally pretty good, I have taken a considerable number of 

 observations : but I get over the ground very slowly, thinking it right to 

 include all stars to 10-11 magnitude; and I find, that to scrutinise, 

 thoroughly, in this way the proposed portion of the heavens, will require 

 many more observations than I can take this year." 



On the same day on which Professor Challis wrote this letter, Mr. 

 Adams, who was not aware of my absence from England, addressed the 

 following very important letter to Greenwich : — 



No. 20.— J. C. Adams, Esq., to G. 15. Airy. 



" St. John's College, Cambridge, Sqit.i, 1346. 

 " In the investigation, the results of which 1 communicated to you last 

 October, the mean distance of the supposed disturbing planet is assumed 

 to be twice that of Uranus. Some as.-iumption is necessary in the first in- 

 stance, and Bode's law renders it probable that the above distance is not 

 very remote from the truth : but the investigation could scarcely be con- 

 sidered satisfactory while based on any thing arbitrary; and 1 iherefore 

 determined to repeat the calculation, makiu;; a different hypothesis as to 

 the mean distance. The ecceuuicity also resulting from my former calcu- 

 lations was far too large to be probable; audi found Ihat, although the 

 agreement between theory and observation continued very satisfactory 

 dowu to 1840, the difference in subsequeut years was becoming very sensi- 

 ble, and 1 hoped that these errors, as well as the eccentricity, might be 

 diminished by taking a diffLrent mean distance. Not to make too violent 

 a change, I assumed this distance to be less than the former value by about 

 jUh part of the whole. The result is very satisfactory, and appears to 

 show ihat, by still further diminishing the distance, the agreement between 

 the theory and the later observations may be runJered complete, and the 

 eccentricity reduced at the same time to a very small quantity. The mass 

 and the elements of the orbit of the supposed planet, which result from the 

 two hypotheses, are as follows : — 



Hypothesis I. Hypothesis II. 



1705 4-0 -09 -fO -01 



1798 --0 -OS* —0 -93 



1801 —0 -04 +0 -11 



1804 -fl -76 +i -94 



1807 —0 -21 —0 -08 



1810 -fO -56 +0 -61 



1825 +1 -92 -fl -87 



1828 +'2 -25 +2 '35 



1831 —1 -OS —0 •«2 



1834 —I -44 —1 17 



1837 —1 -62 —1 -53 



18)0 +1 -73 -t-1 -31 



(^-0 (-="-"0 



Mean Longitude of Planet, 1st Oct. 1816 323° 8' 323° 2' 



Longitude of Perihelion .. 315 57 299 11 



Eccentricity .. .. 010103 0120C2 



Mass(that of Sun being 1) .. 0-0001G50S 0-00015003 



"This investigation has been conducted in the same manner in both cases, 

 so that the differences between the two sets of elements may be considered 

 as wholly due to the variation of the fundamental hypothesis. The fol- 

 lowing table exhibits the differences betwieu tlie tlieoiy and the observa- 

 tions wliich were used as the basis of calculation. The quantities given 

 are the errors of »nea7i longitude, which 1 found it more convenient to em- 

 ploy in my investigations than those of the true longitude. 



Ancient Observations, 



(Obs. — Theory.) 

 Pate. Hypoth. I. Hypoth. II. 



1756 — 4"-0 — 4" 

 1764 —5-1 —4-1 

 1769 -f -6 -f 1 -8 

 1771 4-11 -8 4-12 -8 



Modern Observations. 



1780 -t-0"27 -f0"-54 1810 -fl"-.56 -l-0"-61 



17S3 —0 -23 —0 -21 1813 —0 -94 —1 00 



J786 _o -36 —1 -00 1816 —0 -31 —0 -46 



1789 ^-1 -82 +1 -63 1819 —2 -00 —2 19 



J792 _o '91 —1 -06 ! 1822 +0 '30 -f -14 



"The greatest difference in the above table, viz. that for 1771, is de- 

 duced from a single observation, whereas the difference immediately pre- 

 ceding, which is deduced from the mean of several observations, is much 

 smaller. The error of the tables for 1780 is found by interpolating between 

 the errors given by the observations of 1781, 1782, and 1783, and those of 

 liCU and 1771. The differences between the results of the two hypotlieses 

 are exceedingly small till we come to the last jears of the series, and be- 

 come sensible precisely at the point where both sets of results begin to 

 diverge from the observations ; the errors corresponding to the second hy- 

 pothesis being, however, uniformly smaller. The errors given by the 

 Greenwich Oliservutious of 1843 are very sensible, being for the first hypo- 

 thesis 4- 6"-84, and for the second -f 5"-50. By comparing these errors, it 

 may be inferred that the agreement of theory and observation would be 



a 

 rendered very close by assuming — — 0'»7, and the correspondiDg mean 



longitude on the 1st October, 1846, would be about 313° 20', which I am 

 iucliued to think is not far from the truth, it is plain also that the ecceu- 



a 

 tricity corresponding to this value ^ would be very small. In conse- 

 quence of the divergence of the results of the two hypotheses, still later 

 observations would be most valuable for correcting the distances, and I 

 should feel exceedingly obliged if you would kindly communicate to me 

 two normal places near the oppositions of 1844 and 1845. 



"As Klamsteed's first observation of t7i-anas(iu 1690) is a single one, 

 and the interval between it and the rest is so large, 1 thought it unsafe to 

 employ this observation informing the equations of condition. On com- 

 paring it with the theory, I find the difference to berather large, and greater 

 for the second hypothesis than for the first, the errors being 4- 44"5 and 

 -\- 50"0 respectively. If the error be supposed to change in proportion to 



a 

 the change of mean distance, its value corresponding to — = 0-57, will be 



a* 



about 4- 70", and the error in the time of transit will be between 4' and 5'. 

 It would be desirable to ascertain whether Klamsteed's manuscripts throve 

 any light on this point. 



"The corrections of the tabular radius vector of tVaiiiw, given by the 

 theory for some late years, are as follows : — 



Date. Hypoth. I. Hypoth II. 



1834 4-0-005051 4-0 004923 



1810 4-0007219 4-0006U62 



1846 4-0-008676 4-OOO820O 



"The correction for 1831 is very nearly the same as that which you have 

 deduced from observation, in the Astronomisctie NaciiricUten ; but the in- 

 crease in later years is more rapid than the observations appear to give it : 

 the second hypothesis, however, still having the advantage. 



" I am at present employed in discussing the errors in latitude, with the 

 view of obtaining an approximate value of the inclination and position of 

 the node of the new planet's orbit; but the perturbations iu latitude are so" 

 very small that I am afraid the result will not have great weight. Accord- 

 ing to a rough calculation made some time since, the inclination appeared 

 to be rather large, and ihe longitude of the ascending node to be about 300°; 

 but I am now treating the subject much more completely, and hope to ob- 

 tain the result in a few days. 



" I have been thinking of drawing up a brief account of ray iuvestigatioa 

 to present to the British Association." 



Mr. Main, acting for the Astronomer Royal in his absence, answered 

 this letter as follows : — 



No. 21. — The Rev. R. Main to J. C. Adams, Esq. 



" Royal Observatory, Greenwich, 1846, Sept. 6. 

 " The Astronomer Royal is not at home, and he will be absent for some 

 time ; but it appears to me of so much importance tluit you should have 

 immediately the normal errors of Uranus for 1844 aud 1845, that 1 here- 

 with send you the former (the volume for 1844 has been published for 

 some lime), and I shall probably be able to send you those for 1845 oa 

 Tuesday next, as 1 have given directions to have the computations Uuished 

 immediately. If a place (geocentric) for the present year should be of 

 value to you, I could probably send one in a few days." 



In acknowledging this letter, Mr. Adams used the following expression : 

 No. 22. — J. C. Adams, Esq. to the Rev. R. Main, 

 [extract.] 

 " St. John's College, Cambridge, 7/A Sept. 1846. 

 " I hope by tomorrow to have obtained approximate values of tlie in- 

 clination and longitude of the node." 



On the same day, Sept. 7, Mr. Main Irausmitled to Mr. Adams the 

 normal places for 1845, to which allusiou was made iu the letter of Sep- 

 tember 5. 



Ou the 31st of August, M. Le Verrier s second paper on the place of the 



