Page:Encyclopædia Britannica, Ninth Edition, v. 6.djvu/215

Rh COME T 187 We have now to calculate the true anomaly at the first observation from the radii-vectores r, r&quot; and the included angle u -u, which is = v -v, and for this purpose will employ both expressions for tan. U&amp;lt; in YTX. 1 )- No purpose By the first formula. Log. cotan. %(u &quot;-u ) ............ +1-0332699 ) = (Nat. cotan. l(u &quot;-u }} ............ + 10796174 Log. / ............ &quot;~0~-070&quot;8694 Log. r &quot; ............ G 1742799 9-8965895 iploy both expressions for tan. By the second formula. Log. V/ 7 ............ 0-0871400 Log. cos. (u &quot;-u ) ............ + 9-9681449 0-0852849 in (IX.)- /F V/ 7 9-9482943 Log. sin. %(u &quot;-u ): ........... + 8-9648750 No. 1 ......................... +1-2169840 Log. v9 ............ 0-0354347 No. 2 ....................... + 1 -0850125 No. 1-No. 2 ............. + 0-1319715 Log ............. + 9-12048of + 0-9834198 Log. (sin. (u &quot; - u }J r &quot;} ............ + 9 05201 50 No. 2 ....................... +9-625422 No. (l.)-No. (2) = Nat. tan. v +1-170752 Log. tan. v + 0-0684649 v + 4929 51&quot;-5 Log. tan. v + 0-068-1651 i/... ,..+49 29 51 &quot;-5 The perihelion distance (g] = r, cos. 2 -JV, or Log. cos. v .... 9-8125654 Log. cos. 2 v 9-6251308 Log. r 0-0708694 Log. q. .9-6960002 q .0-4969525 The longitude of the perihelion (TT) = 282 12 48&quot; l + 98 59 43&quot; - 114 22 57&quot;&quot;6 = 26649 33&quot; 5 It remains only to determine the time of perihelion from (XII.), computing both from v and v&quot; = v +(u &quot; it ) = 10934 45&quot;-0, so as to have the final verification of the work lv = 49 29 51 -4 i v &quot; = 54 47 22&quot; 5 Log. tan. Jt/=+ 0-0684649 Log. tan. v &quot; ... + 151 3832 Log. tan. 3 i/= +0-2053947 Log. tan. 3 ij/&quot;... + 4541496 Log. ... 9-5228787 , 9 52287S7 + 9-7282734 No.. .. + 0-534901 Nat. tan. v ... 1 -170752 + 9-9770283 No.. ..+0-948480 Nat. tan. v &quot;... 1-417043 Log. q.... Log. 2.... 1 705653 9 6960002 301 0300 2-365523 Log. x... 0-3739272 Log.- 9-9970302 i-Log. (2g)... 9-9985151 Log. (2g)i.. 9-9955453 Log. 2k... 8-5366114 i -4KQQQQQ Add Log. *.... -2318907 1-8328611 No. = days from 3d obs. to perihelion J Rate of 3d observa- tion &amp;gt; December 26-24751 Perihelion passage, October 1919234 No - days from 1st ) 49 d. 7097 obs. to perihelion ) Date of 1st observa tion, December 7 26339 Perihelion passage, October 19-19242 We have now the whole of the elements of the parabolic orbit, viz., as usually written and entered in catalogues, Perihelion Passage, 1874, October 19-1924, Greenwich Mean Time. TT 266 49 33&quot; 5 ) Mean equinox fl 28212 48&quot;-1 1875-0 i 8056 27&quot; 5 Log. q 9-6960002 Motion retrograde. As already remarked, it is always desirable to ascertain how the comet s geocentric position, calculated from the- elements thus obtained, agrees with the observed position. A close agreement where good observations have been em ployed, of course, indicates that the real path of the comet in space does not much differ from a parabola, while a considerable difference, i.e., one exceeding the probable error of the observation, may be due to the ellipticity of the orbit, and the comet may prove to be one of no long period. We will, therefore, proceed to compute the longf- tude and latitude from the above elements for the time of the second observation. Perihelion passage (T), October 19 19240 Date of second observation (t&quot;), December 16 68190 t&quot;-T + 58-48950 Instead of using Barker s table, we will compute the true anomaly directly by the formulas (XIII.) ; thus, Log. (3*)... 8-7127027 Log. (r-T)... + 1-7670779 3 +0-4797806 Log. (27) 2 ... 9 9955453 Log. cotan. 2^... +0 4842353 2f... 18 9 18&quot; -8 Log. cotan. v... 7964958 Log. cotan. = Log. v cotan. v 0-2654986 v... 9 4 39&quot; 4 Log. cos. 4t,&quot;... = 9 7850693 Log. cos. &quot;*v&quot;... Log. q... Lo. r&quot;... 9-5701386 9-6960002 ...28 29 7&quot; 6 2...565S 15&quot;-2 Log. cotan. 2|.... 9 8130004 Log. 2 .... 0.3010004 tan. v&quot; ... 0-1140304 &&quot;...+ 5226 13&quot;-0 01258616 We then obtain the comet s heliocentric longitude on the ecliptic (#&quot;} and heliocentric latitude (X&quot;), the motion in the orbit being retrograde, from equations (XV.) : fl ...282 12 481 v&quot; ...104 52 26-0 27 5 14-1 7T...266 49 33-5 &quot;+ fl-ir 120 15 40 6 Log. sin. (v&quot;+ & -ir).. +9 936381 2 ... Log. cos. Z... + 9-1971480 + 9-1335292 Log.cos.(t/ + fl -TT)...- 9 7023823 Log. tan. (Q-6&quot;) -9-43114C9 R -0&quot;...164 53 51&quot;-4 R ...282 12 48&quot;-1 +9-9363812 Log. sin. i.... 9 9945489 Log. sin. A&quot;... + 9 -9309301 &quot;...+5832 7&quot;.5 18 56&quot;7