The scientific papers of John Couch Adams [microform]
rt, = 0'5 -', = 0-515 a' a' h,= 23"'98 &,= - 19"-07 /«,= 23'l 9 £,= -21*69 h.,= - 47-58 fc,= - 11-00 h,= - 57'30 £,= - 3'83 h3= - 1-93 A-3= - 7'64 /i3= - 3-40 £3= -• 576 p,= 9-93 q,= - 8-31 pi= G'52 Si35- 7'34 ^>s= - 8'54 «/„= - 55-36 pa= - 1 -1 ^'2 ry,= -54'39 ^3= 224-90 73=- 171-63 p3= 104'21 </3=-82'39 50. And by substituting these values in the equations (e), (»), (x), and (T/), we obtain IST HYPOTHESIS. 2ND HYPOTHESIS. "=0-5 -, = 0-515 a a' Se = - 49/77 Su = - o''702 8e =-4,3-23 Sri = - o''5417 &B,= -130-69 8y,= 222-38 8^= 177 8y,= 123-98 Sic.2= 1-02 Sy,= 2-83 801,= 1'13 S.^= 0'91 and the corresponding corrections of the elliptic elements will be £ CN — = 0-00000999 - = 0-00000771 a a 8e= 20-83 8sr = 127-27 5—2 36 ON THE PERTURBATIONS OF URANUS. [2 It will be seen that the corrections of the eccentricity and longitude of perihelion vary very rapidly with a change in the assumed mean distance. 51. If these quantities be substituted in the expressions before given, we obtain the following theoretical corrections of the mean longitude, each of these corrections being divided into two parts, of which the first is due to the changes in the elements of the orbit of Uranus, and the second to the action of the disturbing planet. HYPOTHESIS I. Ancient Observations. Year. „ „ „ 1712 -288-0 + 365-8= +77-8 1715 -283-1+357-1 = +74-0 1750 +210-5-2607= -50-2 1753 +218-1-267-0= -48'9 1756 +214-0-260-0= -46-0 1764 +154-0-186-7= -32-7 1769 + 79-6-100-7= -21-1 1771 + 27-6- 41-8= -14-2 Modern Observations. Year. „ „ „ Year. „ „ „ 1780 -126-12 + 129-27=+ 3'15 1813 - 125'59 + 147'72 = +22'13 1783 -180-28 + 188'70=+ 8-42 1816 • 68'21 + 91'02=+22'81 1786 -227-66 + 240-36= +1270 1819 10'40+ 33'18=+2278 1789 -26570 + 281-63= +15-93 1822 + 44'84- 23*64 =+21'20 1792 -292-25 + 310-38= +18-13 1825 + 94'69- 77'64=+17'05 1795 -305-84 + 325-27= +19-43 1828 + 13673 - 127'48 =+ 9'25 1798 -305-67 + 325-72= +20-05 1831 + 168'94- 172'17 = - 3'23 1801 -29177 + 312-05= +20-28 1834 + 189'85 -21T04= -2T19 1804 -264-95 + 285-38= +20-43 1837 + 198'51 -243'59= -45'08 1807 -22678 + 247-51= +2073 1840 + 194'54-269'36= -74'82 1810 -179-43 + 20076= +21-33 2] ON THE PERTURBATIONS OF URANUS. 37 HYPOTHESIS II. Ancient Observations. Year. 1712 -1337 + 211-9= +78-2 1715 -1177 + 191-5= +73-8 1750 + 85-2-134-4= -49-2 1753 + 73-8-122-2= -48-4 1756 + 59-1-105-2= -46-1 1764 + 27- 36-4= -33-7 1769 43-1+ 20-8= -22-3 1771 - 69-9+ 54-7= -15-2 Modem Observations. Year. 1780 - 133-10 + 1 35-9 8 =+ 2"-88 1783 -149-47 + 157-87=+ 8'40 1786 -160-15 + 172-99= +12-84 1789 -164-52 + 180-64= +1G-12 1792 -162-30+180-58= +18-28 1795 -153-59 + 173-07= +19-48 1798 -138-87 + 158-86= +19-99 1801 -118-95 + 139-08= +20-13 1804 - 94-96 + 115-21 = +20-25 1807 - 68-25+ 88-85 =+20-60 1810 - 40-33+ 61-61= +21-28 Year- // ,/ // 1813 -12-72+ 34-91= +22-19 1816 +13-08+ 9-88= +22-96 1819 +35-71- 1274= +22-97 1822 +54-04- 32-68= +21-36 1825 +67-18- 50-08= +17-10 1828 +74-52- 65-37=+ 9'15 1831 +75-74- 79-21= -• 3'47 1834 +70-85- 92-31= -21-46 1837 +60-08-105-25= -45-17 1840 +43-98-118-38= -74-40 52. Comparing these with the corrections of mean longitude derived from observation, we find the remaining differences to be the following : — 38 ON THE PERTURBATIONS OF URANUS. ANCIENT OBSERVATIONS. Observation - Theory. Year. Hypoth. I. Hypoth. II. MODERN OBSERVATIONS. 1712 + 67 1715 6-8 1750 • IT) 1753 + 57 1756 4-1 1764 5'1 1769 + 0'6 1771 +11-8 + 6-3 - 6-6 - 2-6 + 5-2 4-0 • 4-1 + 1-8 + 12'8 Observation - Theory. Tear. Hypoth. I. Hypoth. II. 1780 +6-27 + o'-54 1783 -0-23 -0-21 1786 -0-96 -1-10 1789 +1-82 +1-63 1792 -0-91 -1-06 1795 +0-09 +0'04 1798 -0-99 -0-93 1801 -0-04 +0-11 1804 +176 +1-94 1807 -0-21 -0-08 1810 +0-56 +0-61 Observation - Theory. Year. Hypoth. I. Hypoth. II. 1813 -0-94 -l"-00 1816 -0-31 -0-46 1819 -2-00 -2-19 1822 +0-30 +0-14 1825 +1-92 +T87 1828 +2'25 +2'35 1831 -1-06 -0-82 1834 -1-44 -1-17 1837 -1-62 -1-53 1840 +173 +1-31 The largest difference in the above table, viz. that for 1771, is deduced from a single observation ; whereas the difference immediately preceding it, which is deduced from the mean of several, is very small. 53. The results of the two theories agree very closely with each other, and with observation, till we come to the later years of the series ; and it is to be observed, that the difference between the theories becomes sensible at precisely the point where they both shew symptoms of diverging from the observations, the errors of the second hypothesis, however, being less than those of the other. Recent observations shew that the errors of the theory soon become very sensible, though decidedly less for the second hypothesis than for the first. The following are the differences of mean longitude, as deduced from theory and observation, for the oppositions of 1843, 1844, and 1845 : — Year. 1843 1844 1845 Observation - Theory. Hypoth. I. Hypoth. II. + 7-11 + 879 + 12-40 + 577 + 7-05 + 10-18 2] ON THE PERTURBATIONS OF URANUS. 39 For the observations of the last two years, I am indebted to the kindness of the Astronomer Royal. The three years nearly agree in shewing that the errors of the first hypothesis are to those of the second in the ratio of 5 to 4, from which I inferred, in a letter to the Astronomer Royal, dated September 2, 1846, that the assumption of 7 =sin 35° = 0'574, would probably satisfy all the observations very nearly. 54. The results which I have deduced from Professor Challis's obser- vations of the planet, strongly confirm the inference that the mean distance should be considerably diminished. It is of course impossible to determine precisely, without actual calculation, the alteration in longitude which would be produced by such a diminution in the distance. By comparing the values of 6 given by the two hypotheses, it may be seen, however, that if we took successively smaller and smaller values for the mean distance, the values found for the mean longitude in 1810 would probably go on diminishing, while at the same time the mean motion from 1810 to 1846 would rapidly increase, so that the corresponding values of the mean longitude at the present time would probably soon arrive at a minimum, and afterwards begin again to increase. This I believe to be the reason why the longitude found on the supposition of too large a value for the mean distance agrees so nearly with observation. In consequence of not making sufficient allowance for the increase in the mean motion, I hastily inferred, in my letter to the Astronomer Royal mentioned above, that the effect of a diminution in the mean distance would be to diminish the mean longitude. 55. I have already mentioned, that I thought it unsafe to employ Flamsteed's observation of 1690 in forming the equations of condition, as the interval between it and all the others is so large. The difference between it and the theory appears to be very considerable, and greater for the second hypothesis than for the first, the errors being + 44//-5 and + 50"'0 respec- tively. These errors would probably be increased by diminishing the mean distance. It would be desirable that Flamsteed's manuscripts should be examined with reference to this point. 56. The corrections of the tabular radius vector of Uranus may be easily deduced from those of the mean longitude by means of the following formula : 40 ON THE PERTURBATIONS OF URANUS. [2 Sr _ ldr~ lcZ8£ l8a_l_e8e _1 , .dA, 7= rdt b^~2ndt+±a 2 1 -e2 6^ * da i cos {i (?i< - n't + t - e') -nt-e + m} i cos {i (nt- n't + e - e') - nt - e + CT'} where S{ denotes the whole correction of the mean longitude at the time t, • -r- = e sin {nt + e — w| + ',- sin 2 {»? + e — rar} nearly, r ae 2 2 TO — -7^7 -- A- - 4 ,- 4 z (w — »') — n { da F 1 (?.TL1)_n f/oy iu,/l «» 4i(«-«')-^\( ^ i assuming all integral values positive and negative not including zero. 57. By substituting in this formula the values of tn', So, Se, &c., already obtained, and putting « = 19'191, we find the following results corresponding to the two assumed values of the mean distance. HYPOTHESIS I. a ~ a dr ^y a rfSt -8r=-j 8^-jr —,,-0-000089 r r de 2 ndt + 0-000069 cos {nt-n't + e-e?} + 0-000259 cos 2 {nt - n't + e - e'} + 0-000109 cos 3 {nt-n't + e-^} + 0-0000 16 cos {n't + f'-vr} -0-000168 cos + 0-000078 cos -0-000049 cos + 0-000209 cos {2nt - 3n't + 2e - Se' + or'}. 2] ON THE PERTURBATIONS OF URANUS. 41 HYPOTHESIS II. a s ar«Y a - dr = --j-S4—--7— Q'000144 r r rfe 2 + 0-000073 cos {nt-n't + e-e1} + 0-000266 cos 2 {nt - n't + e - e'} + 0-000115 cos3{nt-rit + e-t'} + 0-000016 cos {n't + f'-vr} -0-000188 cos + 0-000068 cos {nt - 2n't + e - 2e' + w'} - 0-000053 cos {Int - 3n't + 2e - 3e' + + 0-000165 cos 75 X 58. The values of S£ and , for some recent years are the following: — HYPOTHESIS I. Year. // // 1834 - 21-19 -20-93 1840 74-82 -32-34 1846 -148-65 -39-94 HYPOTHESIS II. 1834 21-46 -20-85 1840 74-40 -31-62 1846 -145-91 -38-30 Hence, by means of the above formulae, we find the corrections of the tabular radius vector to be Year. Hypothesis I. Hypothesis II. 1834 +0-00505 +0-00492 1840 +0-00722 +0-00696 1846 +0-00868 +0-00825 A. 6 42 ON THE PERTURBATIONS OF URANUS. [2 59. By far the most important part of these corrections arises from 1 sJSi Y the term r —-~ , and may therefore be immediately deduced from a com- £ nat parison of the observed angular motion of Uranus with that given by the tables. In fact, the corrections given by this term alone for the epochs above mentioned are Year. Hypothesis I. Hypothesis II. 1834 +0-00447 +0-00445 1840 +0-00694 +0-00678 1846 +0-00853 +0-00818 which, as we see, differ very little from the complete values just found. The correction for 1834 very nearly agrees with that which Mr Airy has deduced from observation in the Astronomische Nachrichten (No. 349). The corrections for subsequent years are rather larger than those given by the Greenwich Observations, the results of the second hypothesis, as in the case of the longitude, being nearer the truth than those of the first. 60. I made some attempts, by discussing the observations of latitude, to find approximate values of the longitude of the node and inclination of the orbit of the disturbing planet, but the results were not satisfactory. The perturbations of the latitude are, in fact, exceedingly small, and during the comparatively short period of three-fourths of a revolution are nearly con- founded with the effects of a constant alteration in the inclination and the position of the node of Uranus, so that very small errors in the observations may entirely vitiate the result. 61. The perturbations of Saturn produced by the new planet, though small, will still be sensible, and it would be interesting to enquire whether, if they were taken into account, the values of the masses of Jupiter and Uranus found from their action on Saturn would be more consistent with those determined by other means than they appear to be at present. The reduction of the Greenwich planetary observations renders such an inquiry comparatively easy, and it is to be hoped that English astronomers will not be the last to avail themselves of the treasures of observation thus laid open to the world. THE SEARCH FOR THE PLANET NEPTUNE BY PROFESSOR CHALLIS. [From the Astronomische Nackrichten. No. 583 (1846). Pp. 101—106.] CAMBRIDGE OBSERVATORY, October 21, 1846. My more immediate purpose in writing to you at present, is to give some account of observations which I undertook this summer in search of the recently-discovered planet. Mr Adams, a young Cambridge mathematician, had for a long time turned his attention to the perturbations of Uranus, and in the autumn of last year communicated to me and to Mr Airy, the Astronomer Royal, values which he had obtained of the heliocentric longitude, mass, eccentricity of orbit, and longitude of perihelion of a sup- posed disturbing planet, revolving at a mean distance from the Sun about double that of Uranus. These results were deduced entirely from a con- sideration of perturbations of Uranus not otherwise accounted for. M. Le Verrier, by an investigation published in June last, obtained almost precisely the same heliocentric longitude which Mr Adams had arrived at. This coincidence from two independent sources very naturally inspired confidence in the theoretical deductions, and accordingly Mr Airy shortly after suggested to me the employing of the Northumberland telescope of this Observatory in a systematic search after the planet. I commenced observing July 29. 6—2 44 THE SEARCH FOR THE PLANET NEPTUNE. [2 Unfortunately I was not then aware of the publication of hour XXI of the Berlin star-maps, and consequently had to proceed on the principle of comparison of observations made at intervals. On July 30 I recorded the approximate places of stars in a zone 9' in breadth, in such a manner as to be sure that none brighter than the llth magnitude escaped me, which a peculiar arrangement in the construction of the Northumberland Equatorial enabled me to do. On August 4 I took the places of the brighter stars in a zone 80' broad, and among these recorded a place of the planet. My next observations were on August 12, on which day I met with a star of the 8th magnitude in the zone which I had taken on July 30, which did not then contain this star. This again was the planet. So exactly had theory indicated the proper place for making the search, that in four days only of observing I had recorded two positions of the planet. Also according to the principle of search I had adopted, the observations of two of those days (July 30 and August 12) were sufficient to discover it. My time, however, was so occupied with comet reductions, and so little expec- tation had I of discovering the planet by a brief search, that I was only just preparing to map the places of the stars to see what success I had had, when the announcement of the discovery reached me. My observations after August 12 were purposely made early in Right Ascension for the sake of being able to carry them on during a longer portion of the year. Accordingly I did not again meet with the planet till September 29, on which day I saw for the first time the results of M. Le Verrier's last investigations. By these I was induced to return again to the theoretical position of the planet, and to endeavour to detect it by the appearance of a disk. In fact on the night of September 29, out of a very large number of stars whose approximate places I recorded, I fixed upon one which appeared to me to have a. disk, and which proved to be the planet. On October 1 I had intelligence of Dr Galle's discovery. The foregoing account, while it shews that I cannot lay claim to any discovery, may perhaps be regarded with some degree of interest. In particular, the places which I have obtained for the planet on August 4 .and August 12, though they cannot pretend to great accuracy, for the present possess a value which they will lose when accurate observations have been continued for a longer period. I have, therefore, thought it worth while to send them to you, and to describe in detail the manner in which they have been deduced, that an opportunity may be given of judging of the degree of confidence they deserve. 2] THE SEARCH FOR THE PLANET NEPTUNE. 45 My observations were all made with the large Northumberland "Refractor, and with a magnifying power of 170. On August 4, the Hour Circle being fixed, the telescope was moved in declination, and the transits were all taken at the same part of the field, at the toothed edge of the comb of a micrometer eye-piece. Differences of declination were measured by means of a graduated sector-arc, which was read off by a microscope-micrometer, one revolution of which is 10". The stars were accurately bisected by a fixed wire equator! ally adjusted, but to gain time the micrometer was read off to integral revolutions, and by estimation to a fourth part of a revo- lution. The error of reading off in this way could hardly be more than 3", and the error of comparison with a single star might possibly amount to 6". On August 12, the telescope was absolutely fixed, and the zone, which was 9' in breadth, was limited by the field of view. The transits were taken at the toothed edge of the comb carefully adjusted, and the differences of declination were measured by revolutions of the eye-piece micrometer, read off in integral revolutions, and by estimation to a fourth part of a revolution, by means of the teeth of the comb. Occasionally, as it happened in the instance of the planet, the tenth part of a revolution was estimated. The value of one revolution of this micrometer is 17", and I should therefore estimate the error of comparison with a single star, so far as it depended on error of reading off, to be at most 8". I now give the places of the planet resulting from a comparison with every known star that was taken in the same series on each of the two days. August 4 Star of Comparison and authority . h f pj „ d f p, t for its place. . . . 01 <> . fBritish Association Catalogue ... 2 1 58 14' 13 ...... - 12 57 18'4l „ g h. m. s. 50 Capncorm ...... ...... British Association Catalogue 7599 ............ 14'89 ...... 32'0 38 Aquarii B. A. C. 7722 h. m. s. ...... 14-86 ...... 41'9* Bessel Z. 127 and Z. 129 215910 ...... 14-48 ...... 33-6 127 and Z. 129 22 5 6 ...... 14'80 ...... 34'9 -- 127 214534 ...... 14'69 ...... 28'4 127 213454 ...... 14-18 ...... 35'1 -- 127 213230 ...... 14-94 ...... 30'2 - 127 214850 ...... 14-77 ...... 33'6 * There can be little doubt that there is an error of 10" in these from error in the number of micrometer revolutions. h. m. B. h. m. s. o / // 22 051... ...21 57 26-14... ...-13 1 55-2 22 5 6... 25-98... 64-0 22 8 15... 26-27... 59-3 22 10 53... 26-05... 61-5 22 11 18... 26-10... 61-9 22 18 20... 25-99... 627 22 19 26... 26-32... 60-9 22 24 45... 26-35... 54-4 22 32 7... 26-21... 57-8 22 27 31... 25-99... 65-2 22 36 51... 25-84... 627 26-34.. 57-1 46 THE SEARCH FOR THE PLANET NEPTUNE. [2 August 12 Star of Comparison. B.  127 and 129 129 127 75 Aquarii B. A. C. 7976. Not knowing whether Bessel's place of 50 Capricorn! or that of B. A. C. is preferable, I have adopted the mean of the two. The following are the places of the planet given by the means of the above determinations. Greenwich mean time. B. A. Decl. h. m. s. h. m. s. 0 , ,, August 4 13 36 25 21 58 1470 - 12 57 32'2 12 13 326 215726-13 -13 2 0'2 in which the errors of R. A. are probably not greater than those incident to results depending on single transits, and the errors of declination, ac- cording to the estimate already given, may amount to 3 or 4 seconds. From these places, compared with recent observations extending to October 13, Mr Adams has obtained the following results: — Distance of the planet from the Sun 30 '05 Inclination of the orbit 1° 45' Longitude of the descending node 309 '43 Heliocentric Longitude, August 4 326'39 The present distance from the Sun is therefore about a tenth less than theory had predicted. Guided by these results I have been seeking for previous accidental observations of the planet, but without success. The position at the date of the Histoire Celeste is now too near the Sun. DETERMINATION OF THE ORBIT OF THE PLANET NEPTUNE (PROFESSOR CHALLIS). [From the Astronomische Nachrichten. No. 596 (1847). Pp. 309 — 314.] IN conformity with a wish expressed by the Vice-Chancellor and the Observatory Syndicate at their ordinary terminal meeting, held on March 15, I propose in this Report to carry on, for the information of members of the Senate, the account of proceedings in the Observatory relative to the new planet, a first Report of which was made on December 12 of last year. The theoretical grounds on which a search for the planet was insti- tuted, the manner in which the search was conducted, and the degree of success that attended it, were stated in the former Report, which brought the history of proceedings down to the date at which the planet was dis- covered. I have now to give an account of the subsequent observations both of its position in the heavens, and of its physical appearance, and to state the results respecting the orbit which have been deduced from the observations by calculation. A regular series of observations of the planet was commenced on October 3, 1846, and continued at all available opportunities, partly with the meridian instruments, and partly with the Northumberland Equatorial, to December 4, soon after which the planet became too faint to observe on the meridian on account of daylight. The observations were subsequently carried on with the Equatorial to January 15. The series was much interrupted by cloudy weather, particularly in the months of December and January. On the whole I have obtained 28 positions of the planet with the meridian instruments, and 25 positions with the Northumberland Equatorial by means of 92 differential observations of Right Ascension and as many of North Polar Distance. The Equatorial measures were all referred to the same star, No. 7648 of the British Association Catalogue, the exact place of which was determined by 16 observations with the Transit, and 8 observations with the Mural Circle. I have reason to think that the positions obtained with the equatorial are entitled to very nearly the same weight as those 48 DETERMINATION OF THE ORBIT [2 obtained on the meridian. All the above observations I have completely reduced, and have placed the results at the disposal of Mr Adams for deducing elements of the planet's orbit. On January 12, I had for the first time a distinct impression that the planet was surrounded by a ring. The appearance noticed was such as would be presented by a ring like that of Saturn, situated with its plane very oblique to the direction of vision. I felt convinced that the observed elon- gation could not be attributed to atmospheric refraction, or to any irregular action on the pencils of light, because when the object was seen most steadily I distinctly perceived a symmetrical form. My assistant, Mr Morgan, being requested to pay particular attention to the appearance of the planet, gave the same direction of the axis of elongation as that in which it appeared to me. I saw the ring again on the evening of January 14. In my note-book I remark, "The ring is very apparent with a power of 215, in a field considerably illumined by lamp-light. Its brightness seems equal to that of the planet itself." On that evening, Mr Morgan, at my request, made a drawing of the form, which on comparison coincided very closely with n drawing made independently by myself. The ratio of the diameter of the ring to that of the planet, as measured from the drawings, is about that of 3 to 2. The angle made by the axis of the ring with a parallel of declination, in the south-preceding or north-following quarter, I estimated at GOC. By a measurement taken with the position-circle on January 15, under very unfavourable circumstances, this angle was found to be 65°. I am unable to account entirely for my not having noticed the ring at an earlier period of the observations. It may, however, be said that an ap- pearance like this, which it is difficult to recognize except in a good state of the atmosphere, might for a long time escape detection, if not expressly and repeatedly looked for. To force itself on the attention, it would require to be seen under extremely favourable circumstances. Previous to the observations in January, the planet had been hid for more than three weeks by clouds. The evenings of January 12 and 14 were particularly good, and the planet was at first looked at in strong twilight. Under very similar circumstances I have twice seen with the Northumberland telescope the second division of Saturn's King. I communicated to Mr Lassell of Liverpool, who was the first to suspect the existence of a Ring, my observations upon it, accompanied with a drawing ; and I have received from him in return a drawing of the appearance presented in his twenty-feet reflector, closely resembling mine 2] OF THE PLANET NEPTUNE. 49 both as to the form and the position of the Ring. Mr Lassell writes, " I cannot refuse to consider that your observation puts beyond reasonable doubt the reality of mine." In this conclusion I concur, and accordingly in communications to the Royal Astronomical Society and to Schumacher's Astronomische Nachrichten, containing my reduced observations, I have ven- tured to express my conviction of the existence of a Ring. By micrometer measures taken with the Northumberland telescope, I find the apparent diameter of the body of the planet to be very nearly 3". The above account includes all the observations on the planet I could obtain before its disappearance in the solar rays. By the kindness of Mr Adams I am able to add some particulars respecting its orbit, which he has derived by calculation from the reduced places with which I fur- nished him. As was stated in the former Report, Mr Adams calculated first approximations to the elements, by employing the places I obtained on August 4 and August 12 in the course of searching for the planet, with observations since the discovery extending to October 13. For the sake of comparison with the second approximations, I now give the first results. Heliocentric Longitude 32639 Aug. 4, 1846 Longitude of the Descending Node 309 43 Inclination of the Orbit 1 45 Distance of the Planet from the Sun 30'05. In calculating the following second approximations Mr Adams used the mean of the two places of August as a single place, and of the others he selected nine which seemed to be the best determined, and which were separated by convenient intervals. All the results are calculated for the epoch of 1846, August 8'0, mean time at Greenwich. Heliocentric Longitude of the Planet referred to the o / // mean Equinox of 1847'0 326 41 12'3 Heliocentric motion in Longitude in 100 days 36 5 '52 Heliocentric Latitude South 30 34'4 Change of Heliocentric Latitude in 100 days 1 4 '44 Longitude of the Descending Node 310 3 44'0 Inclination of the Orbit 1 46 49'1 Distance of the Planet from the Sun '. 30 '008 Half the Latus Rectum of the Orbit 30'228. A. 7 50 DETERMINATION OF THE ORBIT [2 The first position on which the above results depend, that of August 4, was obtained 16 clays before the planet was in opposition, and the last position, that of January 15, 32 days before it was in conjunction. The great variation of the planet's elongation from the Sun in this interval is favourable to the correctness of the above determinations, which, although they cannot pretend to extreme accuracy on account of the short period over which the observations extend, are yet entitled to considerable weight. Mr Adams has in fact calculated the probable errors of the above results by supposing each observation of Right Ascension or of North Polar Distance to be liable to an error of 3", and he finds that there is little probability of their receiving any great amount of correction by taking account of future observations. It may be remarked that the first and second approxi- mations do not differ by any large quantities. Hence it may be inferred that the places of August are deserving of confidence, and that, on account of the extension given to the period of observation by including those places, this second approximation to the elements is more accurate than it would have been if it depended solely on observations made since the discovery of the planet. The calculations give 59' 8" for the planet's heliocentric motion from August 4 to January 15. This is so small an arc that it is not possible to deduce with any degree of certainty those elements the determination of which depends on change of the heliocentric distance. Mr Adams has, how- ever, discussed the observations with this object in view, and has obtained certain limiting results, which, as possessing considerable interest, I here subjoin. The eccentricity of the orbit cannot exceed 0'18. The most probable value is 0'06, which differs but little from the eccentricities of the orbits of Jupiter, Saturn, and Uranus. The most probable longitude of perihelion is 49° 58', and the probable true anomaly 276° 43', according to which the planet is near the extremity of the latus rectum and is descending towards perihelion. These results are extremely uncertain. The mean distance is 30'35, with a probable error of 0'25 ; and the corresponding sidereal period is 167 years, with a probable error of about 2 years. It is remarkable that the periodic time is very nearly double that of Uranus ; so that these two bodies will offer an instance of mutual 2] OF THE PLANET NEPTUNE. 51 perturbations of large amount, differing in character from those of the older planets, but analogous to the mutual perturbations of the first and second, and second and third satellites of Jupiter. According to Bode's law of the planetary distances, the mean distance of the new planet would be nearly 38. The actual mean distance differs so much from this, that we are compelled to conclude that this singular law fails in this instance. Since the apparent diameter of the new planet is to that of Uranus nearly in the ratio of 3 to 4, according to the foregoing determination of the distance its bulk is to that of Uranus in the ratio of 8 to o. The above is the sum of the results derivable from the first series of observations. For further and more exact information we must wait till the planet emerges from the solar rays. Before concluding this Report, I am desirous of saying a few words respecting the name of the planet. I recently had the satisfaction of receiving from M. Struve the copy of a communication read by him at the general annual meeting of the Imperial Academy of Sciences of St Petersburg on December 29, in which he states the reasons that have induced himself and the other Poulkova astronomers to adhere to the name of Neptune, which name was first proposed by the French Board of Longitude, shortly after the discovery of the planet. These reasons are thus briefly expressed in a note addressed to me personally : " The Poulkova astronomers have resolved to maintain the name of Neptune, in the opinion that the name of Leverrier would be against the accepted analogy, and against historical truth, as it cannot be denied that Mr Adams has been the first theoretical discoverer of that body, though not so happy as to effect a direct result of his indications." M. Struve's communication has been published in this country by the Astronomer Royal, who has expressed his assent to the reasons therein contained, and his determination to adopt the name of Neptune. Professor Gauss and Professor Encke have also, as I understand, adopted this name. I have only to add that it is my intention (and I am permitted to say, the intention of Mr Adams also) to follow the example set by these eminent astronomers. 7—2 OBSERVATIONS OF THE PLANET NEPTUNE, BY PROFESSOR CHALLIS. [From the Monthly Notices of the Royal Astronomical Society. Vol. VII. (1847.)] CAMBRIDGE. In the Meridian. 1846 Greenwich M. 1 '. B. A. N. P. D. h. m. s. h. m. s. O / // Oct. 8 8 43 27 21 52 13-29 103 29 43-4 TO 8 35 29 21 52 6-42 103 30 18-7 13 8 23 21 21 51 56-90 103 31 8-7 15 8 15 34 21 51 51-05 103 31 37-5 16 8 11 35 21 51 48-43 103 31 53-9 17 8 7 37 21 51 45-89 103 32 6-4 19 7 59 40 21 51 40-98 103 32 31-2 20 7 55 42 21 51 38-76 103 32 41-6 23 7 43 48 21 51 32-60 103 33 7-1 30 7 16 7 21 51 22-86 103 33 58-9 Nov. i 7 8 13 21 51 21-16 103 34 9-7 4 6 56 25 21 51 19-91 103 34 14-3 1 1 6 28 54 21 51 20-78 103 34 6-1 16 6 9 19 21 51 25-63 103 33 38-7 18 6 1 30 21 51 28-43 103 33 23-8 19 5 57 36 21 51 30-42 103 33 13-4 20 5 53 43 103 33 3'3 21 5 49 48 21 51 33-71 103 32 52-8 22 5 45 54 21 51 35-40 103 32 417 24 5 38 6 21 51 40-03 103 32 17-1 26 5 30 19 21 51 44-91 103 31 527 28 5 22 33 21 51 50-25 103 31 22-6 30 5 14 47 21 51 56-30 103 30 50-6 Dec. i 5 10 55 21 51 59-58 103 30 33-4 3 539 21 52 6-11 103 29 56-6 4 4 59 17 21 52 9-38 103 29 39-6 With the Northumberland Equatorial. Greenwich M. T. R. A. N. P. D. No. of Measures. 1846 Oct. h. m. s. h. m. s. o / // 3 8 2 58 21 52 32-58 103 28 2-5 7 10 22 45 21 52 32-22 103 28 4-2 6 5 10 57 13 21 52 24-24 103 28 47-2 6 8 10 49 27 21 52 13-14 103 29 44-5 6 13 7 29 46 21 51 57-08 103 31 5'7 6 2] OBSERVATIONS OF THE PLANET NEPTUNE. 53 1847 Greenwich M. T. E. A. N. P. D. No. of 1 Oct. 17 h. 7 m. 56 s. 21 h. 21 m. s. 51 45 •92 103° / // 32 4 7 9 30 6 30 17 21 51 22 •84 103 34 1 •5 8 Nov. 2 8 42 56 21 51 20 •97 103 34 13 •1 6 3 9 52 17 21 51 20 •20 103 34 10 •9 6 16 7 4 42 21 51 25 •77 103 33 35-0 5 18 7 26 54 21 51 28 •68 103 33 23 7 3 19 6 50 47 21 51 30 •21 103 33 14 •5 6 26 6 0 16 21 51 44 •83 103 31 49 •8 4 Dec. 1 1 6 50 37 21 52 38 •64 103 27 6 •6 6 12 7 12 35 21 52 43 •13 103 26 40 •2 6 13 6 5 49 21 52 47 •60 103 26 15 •1 6 H 7 42 37 21 52 52 •59 103 25 50 •4 4 15 5 50 57 21 52 57 •02 103 25 27 •6 3 18 4 52 3 21 53 12 •19 103 24 5 •3 4 Jan. 1 1 5 35 20 21 55 46 •97 103 10 27 •4 6 12 5 37 43 21 55 54 •87 103 9 45 •9 6 H 5 45 48 21 56 9 •82 103 8 27 •3 6 15 5 49 9 21 56 18 •04 103 7 42 •4 6 The star of reference throughout is No. 7648 of the British Association Catalogue, the assumed mean place of which, January 1, 1846, determined by 16 transit and 8 circle observations, is R. A. = 21h 50m 58'91, N. P. D. = 103° 23' 55"'56. I found the apparent diameter of the planet by micrometer measures taken October 3 to be 3"'07. I have been able with the Northumberland telescope to verify Mr Lassell's suspicion of a ring. I first received the impression of a ring on January 12. Two independent drawings, made by myself and my assistant, Mr Morgan, gave the same representation of its appearance and position. The ring is very little open. Its diameter makes an angle in the south preceding quadrant of 66° with the parallel of declination, according to a measurement (not very satisfactorily taken) on January 15. The ratio of the diameter of the ring to that of the planet is by estimation that of 3 to 2. I am unable to account for my not having noticed the ring earlier. 3. CORRECTED ELEMENTS OF XEPTUNE. [From the Monthly Notices of the Royal Astronomical Society (1847). Vol. vn.] THE following results respecting the orbit of the recently discovered planet Neptune may, perhaps, not be uninteresting to the Society. They are deduced from the early Cambridge observations of August 4 and August 12, combined with nine later ones made at the same observatory, those being generally selected where the planet was observed with the equatorial and meridian instruments on the same day. To each element found I have annexed the probable error to which it is subject, in order that it may be judged what reliance may be placed upon the value obtained. It will be seen that some tolerably definite information respecting the orbit is already afforded by the observations, though they are, of course, insufficient to determine, even roughly, all the elements. Epoch 1846, Aug. 8-0, G. M. T. True Long, of the Planet, M. Eq. 1847-0 326° 41' 12"'3± 2"'55 Motion in Longitude in 100 days 36'5//>52± 2"'82 Distance of Planet from the Sun 30'008±0'0312 Change of distance from the Sun in 100 days ... -0 '01 947 ±0-0365 Heliocentric Latitude, South 30'34"-35± 2"'24 Increase of Heliocentric Latitude in 100 days 1' 4"'44± 2"'05 3] CORRECTED ELEMENTS OF NEPTUNE. 55 Hence we find, Inclination of the Orbit 1°46'49"'1+ 3' 7" Longitude of Descending Node 310° 3' 44"'0 + 30' 37" Semi-latus Rectum 30'228 + 0'0922. Also, if e be the eccentricity of the orbit and a the true anomaly, ecosa= 0-00733 ±0-00235 esina= -0'06223 ±0'1167. Hence the most probable values of the eccentricity and longitude of the perihelion appear to be, Eccentricity = 0'06266. Longitude of Perihelion = 49° 58'. These latter are merely given as the results of the calculation, the magnitude of the probable error of e sin a shewing that no weight is to be attached to them. It may be seen, however, that the eccentricity cannot be large. The most probable value of the mean distance = 30'35, with a probable uncertainty of about 0"25 : the corresponding periodic time=167"2 sidereal years, which is very nearly double that of Uranus. Hence the mutual dis- turbances of these two planets will present some remarkable peculiarities analogous to those of the first and second, and of the second and third satellites of Jupiter. The probable errors given above have been found by considering the probable error of each observation to be 3", the mean of the observations on August 4 and August 12 (which, however, agree very well with each other) being taken as a single observation. This estimation appears to be quite high enough, as the remaining differences between theory and observation only exceed that amount in two instances. 56 CORRECTED ELEMENTS OF NEPTUNE. [3 NOTE. Extract of a Letter from Professor Schumacher. " I have received to-day a very interesting letter from M. Le Verrier. The star observed by Lalande on May 10, 1795, is undoubtedly the planet (Neptune). On consulting the original MSS. it appears that he observed the planet on May 10, and also on May 8 ; but in printing the Histoire Celeste, these two observations, supposed to be of the same fixed star, were found discordant. Hence the observation of May 8 ivas not printed at all, and to that of May 10 were affixed the two points, signifying doubt, which are not in the MSS. The MSS. observations stand thus:"*- Middle Wire. Third Wire. Zenith Distance, h. m. s. h. m. s. 0 / // May 8 7'8 141124 595440 Planet 11 36'5 60 8 17 10 Planet 11 23 '5 60 7 19 14 11 50-5 59 54 40. Observations of Neptune since its Reappearance. CAMBRIDGE. Northumberland Equatorial. (Prof. Challis.) Greenwich M. T. li. A. N. P. D. h. m. s. h. m. s. 0 / // 1847 May 6 15 13 49 22 9 53'40 101 55 53'1 ii 15 24 11 21 10 9-03 101 54 38'0 "Neptune was compared with a star in Bessel's Zones 127, 129, R. A. = 22h 15m 11s, and Bessel's place was employed. On May 6th, the ob- servation was difficult from twilight and unfavourable atmosphere." Greenwich M. T. R. A. N. P. D. h. m. s. h. m. s. o / // 1847 May 26 14 58 36 22 10 3672 101 52 33'5 June i 14 5 4 22 10 39'86 101 52 27'0 " The planet was compared on May 26 three times with B. A. C. 7740 and twice with a star in Bessel's zones 127 and 129, R A. = 22h 15m 11s. On June 1 it was compared five times with the former star and four times with the latter. The places of the stars are taken from the British Association Catalogue and from Bessel." * The mean places of the star for 1800, by Schumacher's Tables, are R. A. 14 12 0-83 N. P. D. 101 8 19-4 11 59-81 8 17-8 There is probably an error of I* in one of the observed R. Ascensions. 4. NEW ELEMENTS OF NEPTUNE. [From the Monthly Notices of the Royal Astronomical Society (May, 1847), Vol. vn.] THE following elements of Neptune have been obtained by taking into account Professor Challis's Observations made since the reappearance. * The elements are now sufficiently correct to enable me to approximate to the perturbations of Neptune by the action of Uranus, in order to compare more accurately the ancient observations of 1795 with those .... made re- cently. I have used the old observations, supposing the elements not to have changed. I hope immediately to set about a new solution of the perturbations of Uranus, starting with a very approximate value of the mean distance. * * * I do not think with Professor Pierce, that the near commensurability of the mean motions will interfere seriously with the results obtained by the treatment of perturbations ; but it will be interesting to see how nearly the real elements can be obtained by means of the pertur- bations. Elements of the Orbit of Neptune. Mean Longitude, Jan. 1, 1847, G. M. T 328 13 54'5j Longitude of Perihelion (on the Orbit) 11 13 41 "5 1 M. Eq. 1847'0 Ascending Node 130 5 39'OJ Inclination to Ecliptic 1 47 1'5 Mean Daily Motion 21-3774 Semi-axis Major 30'2026 Eccentricity of Orbit 0'0083835 A. 8 5. EPHEMERIS OF NEPTUNE AND MERIDIAN OBSERVATIONS. [From the Astronomische Nachrichten. xxvi. (1847). No. 604, pp. 51, 52.] Communicated by Rev. R. Sheepshanks. Ephemeris of Neptune for Mean Midnight Greenwich. B. A. N. P. D. 1847 April 30 h. m. s. 