COMET 191 L-3- sin. a.. Log. cos. e . . r .. Log. s.. Log. COS. (vf/ + e).. Q .. | = log. tau. B.. B.. Log. sin. B.. P cr s ..-9-9900575 ... + 9-9625442 Log. sin. a . Log. sin. e . P". Log. s. Log. sin. (<(/ + ). Q". P" Q77=log. tan. C. C. ...- 9-9900575 ... + 9-5999236 ...- 9-9526017 ... -9-5899811 .. + 9-9947958 .. + 9 6o21902 ...+9-9947958 ...- 9-9558944 ... + 9-6269860 ... -9-9506902 ...- 0-3256157 ... + 9-6392909 .295 17 23" 4 203 32 51"" -9 ...-9-9562445 Log. sin. C. ... -9-6015311 in. &9 -9963572 u.c... 9-9884500 Log. sin. B B = B + (*- fl).. Log. sin. C lu bi C=C + (a- Q). 34 46"-6 52 26" -0 ..279 54 8" 8 ...188 9 37" -3 A 38 B V v -104 We thus have, as the expressions are usually written, x-r. [9-4176428] sin ( 38 34 46 5 + i>) (All quantities be- y = r. [9-9963572] sin (279 54 8 8 + *)... J ing of course 2 = ?-. [9-9884500] sin (188 9 37 3 + u) ( logarithmic. The true anomaly reckoned from to 180, in a direct orbit, is to be applied to A , B , and C , vith a negative sign if tlie time for which we are calculating be before the perihelion passage, and with a positive sign if the time be subsequent thereto. In a retrograde, orbit the contrary rule is to be observed. In our comparison of the elements of Borrelly s comet with the second observation we found v= 104 52 26" 0, and log. r = 01258616; the calculation of the heliocentric co-ordinates and geocentric place with these values stands thus : B 279 54 8" -8 ...-104 52 26" C ...188 9 37 -3 v... -104 3 52 26" -0 A + v 293 42 20" -6 Log. sin - 9 Log. r Constant.. 9 9617163 1258616 4176428 E +v 175 1 42" 8 Log. sin + 8-9378148 Log. r 0-1258616 Constant 9 9963572 C +v 83 17 H"-3 Log. x -9-5052233 -0 -0 3200540 0835332 -0-4035872 y ........... +0-1148249 Y .......... -0-8992894 -0-7844645 Log. sin... Log. r... Constant. . . .. + 8-9970118 - .. 0-1258616 .. 9-9884500 Log. z... z. . Z... ..+0-lfl3260 .. + 1-2921890 ..-0-3901925 Z + z.. -0-9019965 Log. (Z + 2) +9 Subt. log. sin. 5 +9 95520 85425 0-10095 T Log. (Y + y) ........... -9-8945733 Log. (X + z) ........... -9-6059374 Log. tan. K. A .......... .^+0 -2886359 R. A ...... 24246 r 3~T" : 2 Log. (Z + z) +9-9552048 Log. cos. E.A -9-6603729 -9-6155777 Log. (X + z) -9-6059374 Log. tan. 5 +0 0096403 5.... + 4538 9"l For the demonstration of the method of determining a parabolic orbit, which has been here adopted, the reader may consult Olbers s work, already mentioned, and for various modifications and refinements he is referred to Encke s treatise, Ueber die Olbers -sc/te Met/iode zur Bestimmung der Cometenbakneii, in the appendix to the Berliner Astro- nomisches Jahrbuch for 1833; he will obtain much addi tional information from the treatise on Theoretical Astro nomy, by Prof. Watson of Ann Arbor, U.S., and from Prof. Oppolzer s work, Bahnbestimmung der Kometen und Planeten, Leipsic, 1870. On the solution of Lambert s equation, we may refer him to a paper by Mr Marth in Astronomische Nach- richten, vol. Ixv., Nos. 1557-60, which he will find accom panied by elaborately constructed tables. To obviate extending this article to inconvenient length, the introduc tion of tables has been avoided throughout; and should it fall under the notice of any one practised in such calcula tions, we must beg him to attribute any deviation from general rules to the wish to make the article complete in itself, so that the student may compute parabolic elements of any new comet, and its apparent track in the heavens therefrom, without extraneous assistance. For the method of calculating elliptical orbits, when decided deviation from the parabola is indicated, the reader ia referred to Gauss s classical work, Theoria Mot us Corporum Coelestium, originally published in 1809, a translation of which, by Commander Davis, U.S.N., was printed at Boston in 1857 ; in this volume he will also find the demonstration of the formulae employed in calculating geocentric places from the elements of the orbit. In presenting elements of comets of short period we shall include in Group A the comets for which periods of less than fifteen years are either established or have been assigned with greater or less degree of probability, and in Group B comets of longer periods, but not exceeding eighty years. We take the comets in order of length of period. GROUP A. I. Encke s Comet. T 1875, April 13 0682 e... G 849423 (the eccentricity). / // o...2 21105 (the semi-axis major).
- 1582131 Period 3 -288 years.
ft 334 40 48 18 C Di rec t. i 13 7 22 T is expressed in Greenwich mean time. The revolution of this comet in about 3J years was discovered by Encke on its appearance in 1818-19, when it was detected by Pons. Encke, having calculated the effect of perturbation by the planet Jupiter, showed that the comet had been previously observed in 1786, 1795, and 1805, though missed at the intervening returns. It has been observed, with more or less success, at every appear ance since 1819. Encke s investigations soon led him to infer that the comet s period had slightly diminished since 1795, and that this diminution might be owing to the effect of a resisting medium. The late researches of Dr von Asten of Pulkowa indicate that it is only in certain revolutions that an effect of this nature" can be sus pected, so that great doubt is thrown upon the validity of Encke s theory. II. Blanpain s Comet. T 1819, Nov. 20, 2148 .67 18 48 77 13 57 9 1 16 1819 1819, IV. e 0-686746. o 2-84931. Period... 4 81 years. Direct. These elements were calculated by Encke, who had ascertained that the motion of the comet could not be represented by a para bolic orbit. Clausen thought the comet was identical with one observed in 1743, which also exhibited a deviation from the para bola, and Olbers favoured his view, but no elliptical elements have yet been deduced directly from the observations of 1743. Ele ments which appear in some of the catalogues of comet-orbits with Clausen s name attached, were merely inferred from an assumed semi-axis major of 3 10, founded upon the hypothesis of identity with Blanpain s comet of 1819. The latter has not been observed since that appearance. III. BurcTchardCs Comet. T 1766, April 26 -9581 .251 . 74 13 11 1 45 1766 1766, II. e 0-86400. a 2-93368. Period... 5 025 years.
Direct.
