Historical Identification: Per Dreyer, NGC 1800 (= GC 1013 = JH 2732, 1860 RA 05 11 11, NPD 122 08.7) is "pretty bright, pretty much extended, gradually pretty much brighter middle, 13th magnitude star to east".
Physical Information: Apparent size 2.0 by 1.1? arcmin.

Historical Identification: Per Dreyer, NGC 1801 (= GC 1014 = JH 2739, (Dunlop 115), 1860 RA 05 01 34, NPD 159 48.5) is "faint, pretty large, round, very gradually a little brighter middle, preceding (western) of 2", the other presumably being NGC 1809.
Physical Information: Apparent size 2.2? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1802 (= GC 1015 = WH VIII 41, 1860 RA 05 01 44, NPD 66 04.8) is a "cluster, stars considerably scattered".
Physical Information: Apparent size 20? arcmin.

Historical Identification: Per Dreyer, NGC 1803 (= GC 1016 = JH 2737, 1860 RA 05 01 52, NPD 139 45.8) is "faint, small, round, very gradually a little brighter middle, 11th magnitude star to the southeast, perhaps nebulous". The position precesses to RA 05 05 28.5, Dec -49 34 25, less than half an arcmin southeast of the center of the galaxy listed above, the description fits and there is nothing nearby save for the nebulous "star" noted in the description, so the identification is certain. (As it happens, the "11th magnitude star to the southeast" is indeed nebulous and is PGC 16720, which is therefore discussed immediately following.)
Physical Information: Based on a recessional velocity relative to the Cosmic Microwave Background of 4110 km/sec (and H₀ = 70 km/sec/Mpc), NGC 1803 is about 205 million light-years away. Given that and its apparent size of about 1.35 by 0.8 arcmin (from the images below), the galaxy is about 80 thousand light-years across. Given their essentially identical distance, NGC 1803 and PGC 16720 may well be a physical pair, which might explain the peculiar appearance of the smaller galaxy.

Historical Identification: As noted in Dreyer's entry for NGC 1803, Herschel suspected that the 11th magnitude star to the southeast was also nebulous. As noted by Steve Gottlieb, the only 11th magnitude object to the southeast of NGC 1803 is PGC 16720, so Herschel was correct in thinking it might be nebulous, and the identification of that "star" with PGC 16720 is certain. Since Herschel wrote "perhaps nebulous", Dreyer did not give it an NGC entry of its own, but it is listed in Corwin's "notngc" notes. (If it had been in the NGC it might have been a little further down on this page, but since it is byproduct of the identification of NGC 1803, it seems best to place its entry here.)
Physical Information: Based on a recessional velocity relative to the Cosmic Microwave Background of 4415 km/sec (and H₀ = 70 km/sec/Mpc), PGC 16720 is about 205 million light-years away. Given that and its apparent size of 0.6 by 0.4 arcmin (from the images below, including the outer ring), it is about 35 thousand light-years across. The nearly stellar appearance of its central region (even resulting in diffraction lines similar to those of foreground stars) suggests that it is a starburst galaxy, and the dust lanes visible in its bright central region are typical of such objects. Given their essentially identical distance, PGC 16720 and NGC 1803 may well be a physical pair, which might explain the peculiar appearance of the lenticular galaxy.

Historical Identification: Per Dreyer, NGC 1804 (= GC 1017 = JH 2742, 1860 RA 05 01 52, NPD 159 16.9) is "faint, small, round, brighter middle".
Physical Information: Apparent size 1.0? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1805 (= GC 1018 = JH 2741, Dunlop 233?, 1860 RA 05 02 02, NPD 156 18.1) is "bright, very small, very suddenly much brighter middle, stars plus nebulosity". The position precesses to RA 05 02 21.3, Dec -66 06 25, on the northern rim of the cluster listed above, the description fits and there is nothing else nearby, so the identification is certain.
Note About PGC Designation: For purposes of completeness LEDA assigns PGC designations to almost all NGC/IC objects, regardless of their nature. However, a search of the database for the designation shown above returns no result, so it is placed in quotes.
Physical Information: Since NGC 1805 is in the Large Magellanic Cloud, it is about 160 to 165 thousand light-years away. Given that and its apparent size of about 2.15 arcmin (from the images below), it spans about 100 to 105 light-years.
Classification Error: NGC 1805 is mistakenly called a globular cluster in the HST press release. However, as is typical for an 'open' cluster, NGC 1805 contains perhaps ten thousand stars formed roughly 25 to 40 million years ago, whereas globular clusters have hundreds of thousands or millions of stars formed billions of years in the past. So though a relatively compact open cluster, it is not a globular cluster.

Historical Identification: Per Dreyer, NGC 1806 (= GC 1019 = JH 2745, 1860 RA 05 02 32, NPD 158 11.3) is "pretty bright, large, gradually brighter middle".
Physical Information: Apparent size 2.2? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1807 (= GC 1020 = JH 348, 1860 RA 05 02 38, NPD 73 39.6) is a "cluster, pretty rich, large and small stars". The position precesses to RA 05 10 41.9, Dec +16 31 11, well within the loose cluster of relatively bright stars listed above, so the identification is certain.
Physical Information: Apparent size 12? arcmin. NGC 1807 is a loose cluster of stars. (Check Gottlieb description)

Historical Identification: Per Dreyer, NGC 1808 (= GC 1021 = JH 2740, Dunlop 549, 1860 RA 05 02 50, NPD 127 41.8) is "bright, large, extended, pretty suddenly bright middle". (Steinicke also lists this as Dunlop 532)
Physical Information: Apparent size 6.5 by 3.9? arcmin.

Historical Identification: Per Dreyer, NGC 1809 (= GC 1022 = JH 2747, 1860 RA 05 03 05, NPD 159 49.2) is "pretty faint, small, round, gradually brighter middle, 2nd of 2", the other presumably being NGC 1801.
Physical Information: Apparent size 3.2 by 0.8? arcmin.

Historical Identification: Per Dreyer, NGC 1810 (= GC 1023 = JH 2746, Dunlop 235, 1860 RA 05 03 09, NPD 156 34.3) is "considerably faint, small, round, a little brighter middle, globular cluster following (to the east)".
Physical Information: Apparent size 1.2 arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1811 (= GC 1024 = JH 2743, 1860 RA 05 03 17, NPD 119 27.9) is "considerably faint, small, a little extended, preceding (western) of 2", theother being NGC 1812.
Physical Information: Apparent size 1.7 by 0.4? arcmin.

Historical Identification: Per Dreyer, NGC 1812 (= GC 1025 = JH 2744, 1860 RA 05 03 27, NPD 119 26.1) is "faint, small, round, gradually a little brighter middle, following (eastern) of 2", the other being NGC 1811.
Physical Information: Apparent size 1.2 by 0.9? arcmin.

Historical Identification: Per Dreyer, NGC 1813 (= GC 1026 = JH 2752, 1860 RA 05 03 55, NPD 160 30.7) is "very faint, small, round, mottled but not resolved".
Physical Information: In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1814 (= GC 1027 = JH 2748, 1860 RA 05 03 55, NPD 157 29.7) is "very faint, round, smaller of 2 in cluster", the other being NGC 1816, and the cluster that contains both of them being NGC 1820.
Physical Information: Apparent size 1.0? arcmin. In the Large Magellanic Cloud. Part of NGC 1820.

Historical Identification: Per Dreyer, NGC 1815 (= GC 1028 = JH 2753, 1860 RA 05 03 56, NPD 160 48.6) is "faint, very small, round, very little brighter middle, among stars".
Physical Information: Apparent size 1.2? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1816 (= GC 1029 = JH 2750, 1860 RA 05 03 59, NPD 157 27.0) is "very faint, round, 2nd nebula in cluster", the other being NGC 1814, and the cluster that contains both of them being NGC 1820.
Physical Information: Apparent size 1.0? arcmin. In the Large Magellanic Cloud. Part of NGC 1820.

Historical Identification: Per Dreyer, NGC 1817 (= GC 1030 = JH 349 = WH VII 4, 1860 RA 05 03 59, NPD 73 28.7) is a "cluster, large, rich, a little compressed, stars from 11th to 14th magnitude".
Physical Information: Apparent size 20? arcmin.

Historical Identification: Per Dreyer, NGC 1818 (= GC 1031 = JH 2749, Dunlop 236, 1860 RA 05 04 02, NPD 156 37.1) is a "globular cluster, very bright, pretty large, round, very much compressed, partially resolved, some stars seen". (Steinicke also lists this as Dunlop 234.)
Physical Information: Apparent size 3.4? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1819 (Swift list III (#36), 1860 RA 05 04 10, NPD 84 58.2) is "very faint, small, round". The second IC lists a corrected RA (per Bigourdan) of 05 04 21.
Physical Information: Apparent size 1.3 by 1.0? arcmin.

Historical Identification: Per Dreyer, NGC 1820 (= GC 1032 = JH 2754, 1860 RA 05 04 22, NPD 157 26.8) is a "cluster, pretty large, rich, compressed, irregular figure".
Physical Information: In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1821 (Leavenworth list I (#147), 1860 RA 05 04 40, NPD 105 17.4) is "very faint, very small, a little extended". The second IC lists a corrected RA (per Howe) of 05 05 25. Physical Information: Apparent size 1.2 by 0.8? arcmin.

Historical Identification: Per Dreyer, NGC 1822 (= GC 1033 = JH 2756, 1860 RA 05 04 48, NPD 156 23.8) is "very faint, small, preceding (western) of 2", the other being NGC 1826.
Physical Information: Apparent size 0.8? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1823 (= GC 1034 = JH 2758, 1860 RA 05 04 52, NPD 160 31.9) is a "cluster, pretty faint, large, irregular figure, stars from 12th to 15th magnitude".
Physical Information: Apparent size 0.9? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1824 (= GC 1035 = JH 2755, 1860 RA 05 04 53, NPD 149 54.2) is "very faint, pretty large, very much extended 162°".
Physical Information: Apparent size 3.2 by 0.8? arcmin.

Historical Identification: Per Dreyer, NGC 1825 (= GC 1036 = JH (199), 1860 RA 05 05 02, NPD 159 07.9) has "no description, in Nubecula major", "JH (199)" referring to the object's inclusion in a supplementary catalog of objects observed by Herschel in the Large Magellanic Cloud.
Physical Information: Apparent size 0.5? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1826 (= GC 1037 = JH 2757, (Dunlop 235), 1860 RA 05 05 11, NPD 156 25.0) is "very faint, small, following (eastern) of 2", the other being NGC 1822.
Physical Information: Apparent size 0.9? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1827 (= GC 1038 = JH 2751, 1860 RA 05 05 13, NPD 127 09.3) is "very faint, very much extended, long ray, 11th magnitude star involved".
Physical Information: Apparent size 3.0 by 0.7? arcmin.

Historical Identification: Per Dreyer, NGC 1828 (= GC 1039 = JH 2761, 1860 RA 05 05 17, NPD 159 34.6) is "faint, small, round, 1st of 3", the others being NGC 1830 and 1835.
Physical Information: Apparent size 0.7? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1829 (= GC 1040 = JH 2760, 1860 RA 05 05 23, NPD 158 14.2) is "faint, pretty large, round, mottled but not resolved".
Physical Information: Apparent size 2.1? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1830 (= GC 1041 = JH 2762, 1860 RA 05 05 34, NPD 159 31.8) is "faint, pretty small, round, 2nd of 3", the others being NGC 1828 and 1835.
Physical Information: Apparent size 0.7? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1831 (= GC 1042 = JH 2759, Dunlop 246, 1860 RA 05 05 36, NPD 155 06.7) is "bright, large, round, gradually a little brighter middle, mottled but not resolved".
Physical Information: Apparent size 3.9? arcmin.

Historical Identification: Per Dreyer, NGC 1832 (= GC 1043 = WH II 292, 1860 RA 05 05 53, NPD 105 53.2) is "pretty bright, irregularly round, much brighter middle, considerable star 1 arcmin to northeast".
Physical Information: Apparent size 2.6 by 1.7? arcmin.

Historical Identification: Per Dreyer, NGC 1833 (= GC 1044 = JH 2765, 1860 RA 05 05 56, NPD 160 55.1) is "very faint, pretty large, 1st of several".
Physical Information: Apparent size 2.1? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1834 (= GC 1045 = JH 2764, 1860 RA 05 06 03, NPD 159 23.9) is a "planetary?, bright, extremely small, a little extended".
Physical Information: In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1835 (= GC 1046 = JH 2763, (Dunlop 116), 1860 RA 05 06 04, NPD 159 35.2) is "considerably bright, small, round, gradually much brighter middle, 3rd of 3", the others being NGC 1828 and 1830.
Physical Information: Apparent size 1.2? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1836 (= GC 1047 = JH 2766, (Dunlop 170), 1860 RA 05 06 13, NPD 158 48.7) is a "star plus nebula, 1st of several".
Physical Information: Apparent size 0.8? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1837 (= GC 1048 = JH 2769, 1860 RA 05 06 28, NPD 160 53.9) is a "cluster, large, rich, scattered stars".
Physical Information: Apparent size 1.3? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1838 (= GC 1049 = JH 2767, Brisbane 895, 1860 RA 05 06 33, NPD 158 37.5) is a "cluster, large, very little compressed".
Discovery Notes: Brisbane 895 is HD 33617, an 8th magnitude star on the western side of the cluster, and one of 7385 primarily southern stars observed by Thomas Brisbane and his assistants from 1822 to 1826; however, Brisbane states that to ensure consistency in the resulting catalog, almost all the observations were done by a single observer (Dunlop), so he is presumably the first observer of the star, and thanks to Herschel's reference to Brisbane 895, was given some credit for discovering the cluster, whether he realized its nature or not.
Physical Information: Apparent size 0.7? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1839 (= GC 1050 = JH 2768, Dunlop 170?, 1860 RA 05 06 38, NPD 158 48.6) is "stars plus nebula, pretty bright, irregular figure, 2nd of several", the first being NGC 1836.
Physical Information: In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1840 (= GC 1051 = JH 2771, 1860 RA 05 06 46, NPD 161 56.1) is "faint, round, brighter middle, mottled but not resolved (min of RA questionable?)".
Physical Information: Apparent size 0.6? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1841 (= GC 1052 = JH 2788, 1860 RA 05 07 02, NPD 174 12.6) is "pretty faint, large, irregularly round, very suddenly brighter middle, mottled but not resolved".
Physical Information: Apparent size 2.4? arcmin. Although 15 degrees away from the Large Magellanic Cloud, NGC 1841 is at about the same 160 thousand light-year distance from us, and is about four times closer to the LMC than to the Milky Way, so it may be a distant member of that galaxy, rather than our own.

Historical Identification: Per Dreyer, NGC 1842 (= GC 1053 = JH 2772, 1860 RA 05 07 21, NPD 157 27.3) is "very very faint, round, preceding (western) of 2", the other being NGC 1844.
Physical Information: Apparent size 0.8? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1843 (= GC 5350, Stephan list VIII (#17), 1860 RA 05 07 30, NPD 100 47.5) is "faint, small, round, a little brighter middle".
Physical Information: Apparent size 2.1 by 1.7? arcmin.

Historical Identification: Per Dreyer, NGC 1844 (= GC 1054 = JH 2773, 1860 RA 05 07 37, NPD 157 29.9) is "pretty faint, pretty large, round, gradually brighter middle, following (eastern) of 2", the other being NGC 1842.
Physical Information: Apparent size 1.3? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1845 (= GC 1055 = JH 2770, 1860 RA 05 07 38, NPD 160 44.7) is a "cluster, very little compressed middle, stars of 9th and 11th through 16th magnitude".
Physical Information: Apparent size 20? arcmin. (Note to self: Check to see if this could be a foreground object in our galaxy.)

Historical Identification: Per Dreyer, NGC 1846 (= GC 1056 = JH 2774, (Dunlop 209), 1860 RA 05 07 45, NPD 157 38.0) is "pretty bright, considerably large, round, very gradually a little brighter middle, mottled but not resolved".
Physical Information: Apparent size 2.8? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1847 (= GC 1057 = JH 2775, 1860 RA 05 07 56, NPD 159 08.9) is "bright, small, a little extended, double star in middle".
Physical Information: Apparent size 1.0? arcmin. In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1848 (= GC 1058 = JH 2776, 1860 RA 05 08 06, NPD 161 21.9) is a "cluster, very little compressed, stars from 9th magnitude".
Physical Information: In the Large Magellanic Cloud.

Historical Identification: Per Dreyer, NGC 1849 (= GC 1059 = JH 2778, 1860 RA 05 09 21, NPD 156 28.7) is "very faint, small, a little extended, gradually a little brighter middle".
Physical Information: Apparent size 1.3? arcmin. In the Large Magellanic Cloud.