Historical Identification: Per Dreyer, NGC 1000 (= GC 5257, Stephan list III (#15), 1860 RA 02 29 58, NPD 49 09.0) is "very very faint, pretty small, diffuse". The position precesses to RA 02 38 50.3, Dec +41 27 33, right on the galaxy listed above and there is nothing else nearby, so the identification is certain.
Physical Information: Apparent size 0.8 by 0.7 arcmin?

Historical Identification: Per Dreyer, NGC 1001 (= GC 5258, Stephan list III (#16), 1860 RA 02 30 19, NPD 48 56.2) is "very faint, very small". The position precesses to RA 02 39 12.3, Dec +41 40 18, right on the galaxy listed above and there is nothing else nearby, so the identification is certain.
Physical Information: Apparent size 0.9 by 0.4 arcmin?

Historical Identification: Per Dreyer, NGC 1002 (Stephan list XII (#21), 1860 RA 02 30 25, NPD 55 59.2) is "very faint, very small, irregularly round, brighter middle and nucleus". The position precesses to RA 02 38 55.1, Dec +34 37 19, right on the galaxy listed above and there is nothing else nearby, so the identification is certain. The duplicate listing is due to an error in the position of NGC 983 (which see for a discussion of the problem) which caused that object to remain unidentified for 35 years; so although tradition dictates that the lower number be used in the case of duplicate entries, the galaxy is sometimes called NGC 1002 instead of NGC 983.
Physical Information: Given the duplicate entry, see NGC 983 for anything else.

Historical Identification: Per Dreyer, NGC 1003 (= GC 571 = JH 240 = WH II 238 = WH III 198, 1860 RA 02 30 25, NPD 49 44.2) is "pretty faint, large, extended 90°±, much brighter middle, mottled but not resolved". The position precesses to RA 02 39 15.4, Dec +40 52 18, right on the galaxy listed above, the description fits and there is nothing else nearby, so the identification is certain.
Discovery Notes: A note at the end of the NGC quotes John Herschel, pointing out that his #240 was equivalent to both his father's II 238 and III 198, whence the duplicate identifications listed by Dreyer. Apparently Marth suspected that the two observations were of the same object, and the younger Herschel, going over his father's notes, discovered that his aunt (Caroline Herschel) had overlooked or omitted one of his father's observations of III 198 that "confirms Mr. Marth's surmise that the nebulae are identical".
Physical Information: Apparent size 4.5 by 1.45 arcmin? Used by the de Vaucouleurs Atlas of Galaxies as an example of galaxy type SAB(s:)d.

Historical Identification: Per Dreyer, NGC 1004 (Stephan list IX (#3?), Swift list III (#??), 1860 RA 02 30 29, NPD 88 38.0) is "pretty faint, very small, round, very much brighter middle, 11th magnitude star 2 seconds of time to west". The position precesses to RA 02 37 42.7, Dec +01 58 36, on the eastern rim of the galaxy listed above, there is nothing else nearby and the star to the southwest makes the identification certain.
Physical Information: Apparent size 1.15 by 1.1 arcmin?

Historical Identification: Per Dreyer, NGC 1005 (= GC 5259, Stephan list III (#17), 1860 RA 02 30 35, NPD 49 06.9) is "very faint, very small". The position precesses to RA 02 39 27.8, Dec +41 29 34, right on the galaxy listed above and there is nothing else nearby, so the identification is certain.
Physical Information: Apparent size 1.1 by 0.8 arcmin?

Historical Identification: Per Dreyer, NGC 1006 (Swift list V (#30), 1860 RA 02 30 38, NPD 101 38.4) is "most extremely faint, pretty small, round, a little brighter middle". The position precesses to RA 02 37 24.9, Dec -11 01 48, but the nearest galaxy of note (NGC 1010, whose position is listed above) lies 10 seconds of time to the east. For whatever reason, Dreyer used Swift's V-30 for this entry and that of NGC 1010, and since he used the same observation for both entries, their equality is certain.
Discovery Notes: Per Corwin, of the three galaxies in the region (NGC 1010, 1011 and 1017), Stephan saw only the first two, Stone saw all three but realized that the first two were Stephan's, and Swift saw all three but did not realize the first two had already been discovered, suggesting that he did not have a copy of the GC on hand when he made his observations. When Dreyer prepared the listings, he used all three observations to obtain the position of NGC 1010, but only Swift's observation for NGC 1006, hence the difference in their positions.
Physical Information: Apparent size 0.9 by 0.85 arcmin?

Historical Identification: Per Dreyer, NGC 1007 (= GC 5260, Marth #66, 1860 RA 02 30 38, NPD 88 29) is "extremely faint, stellar". The position precesses to RA 02 37 52.0, Dec +02 07 35, about 1.8 arcmin south of the galaxy listed above, and the only other suitable candidate (NGC 1008), which lies about 2.8 arcmin south southeast, was separately observed by Marth on the same night and cannot be his #66; so the identification is certain.
Physical Information: Apparent size 0.6 by 0.2 arcmin?

Historical Identification: Per Dreyer, NGC 1008 (= GC 5261, Marth #67, 1860 RA 02 30 41, NPD 88 32) is "very faint, extremely small, stellar".
Physical Information: Apparent size 0.8 by 0.45 arcmin?

Historical Identification: Per Dreyer, NGC 1009 ([Lewis] Swift list III (#15), 1860 RA 02 30 49, NPD 88 18.1) is "most extremely faint, pretty small, round, 9th magnitude star to southeast".
Discovery Notes: Although Dreyer's listing appears to credit Lewis Swift (the author of all of Swift's papers), Swift's paper notes that this object was discovered by his son, Edward.
Physical Information: Apparent size 1.4 by 0.25 arcmin?

Historical Identification: Per Dreyer, NGC 1010 (= GC 5262, Stephan list VIII (#6), Swift list V (#30), 1860 RA 02 30 49, NPD 101 38.1) is "extremely faint, small, round" (described by Swift as 1st of 3, the others being NGC 1011 and and NGC 1017). The position precesses to RA 02 37 35.9, Dec -11 01 31, right on the galaxy, so the identification is certain. Stephan observed this (and NGC 1011 first, and Swift independently rediscovered the objects, not being aware of Stephan's observations. The odd thing is that Swift's single observation of NGC 1010 led to his also being credited with a separate discovery, the duplicate entry NGC 1006 (which see).
Physical Information: Given the duplicate entry, see NGC 1006 for anything else.

Historical Identification: Per Dreyer, NGC 1011 (= GC 5263, Stephan list VIII (#7), Swift list V (#31), 1860 RA 02 30 52, NPD 101 36.9) is "extremely faint, small, round, a little brighter middle" (described by Swift as 2nd of 3, the others being NGC 1010 (which is a duplicate of NGC 1006) and NGC 1017). The position precesses to RA 02 37 38.9, Dec -11 00 19, right on the galaxy, so the identification is certain.
Discovery Notes: cf Corwin
Physical Information: Apparent size 0.65 by 0.6 arcmin?

Historical Identification: Per Dreyer, NGC 1012 (= GC 572 = JH 241 = WH III 152, 1860 RA 02 30 57, NPD 60 27.5) is "faint, pretty small, irregularly round, brighter middle, star involved".
Physical Information: Apparent size 2.85 by 1.25 arcmin?

Historical Identification: Per Dreyer, NGC 1013 (Swift list V (#32), 1860 RA 02 30 58, NPD 102 07.4) is "most extremely faint, very small, round, between two distant double stars".
Physical Information: Apparent size 1.15 by 0.65 arcmin?

Historical Identification: Per Dreyer, NGC 1014 (Muller list II (#342), 1860 RA 02 31 02, NPD 100 07.9) is "extremely faint, extremely small, irregularly round, preceding (western) of 2", the other being NGC 1018. The position precesses to RA 02 37 52.0, Dec -09 31 21, but there is nothing there. Per Corwin, the key to the identification is Muller's statement that NGC 1018 is 0.2 minutes of time east and 1 arcmin north of his #342, and the only thing that fits that statement is the double star 9.4 seconds west and 1.8 arcmin south of NGC 1018; so the identification is essentially certain (or as Corwin puts it, the double star is "positively identified" as the object in question), and the position of the double is the one listed above.
Physical Information: The northern star is at RA 02 38 00.8, Dec -09 34 18; the southern star at RA 02 38 00.9, Dec -09 34 28.

Historical Identification: Per Dreyer, NGC 1015 (= GC 5265, Tempel list I (#13 = Tempel list V #1), 1860 RA 02 31 04, NPD 91 55.7) is "very faint, small".
Physical Information: Apparent size 3.2 by 3.1 arcmin? (including the faint outer ring).

Historical Identification: Per Dreyer, NGC 1016 (= GC 5264, Marth #68, Temple list I (#??), 1860 RA 02 31 05, NPD 88 30) is "faint, small, round, pretty suddenly brighter middle".
Discovery Notes: (Discuss Safford's overlooked observation, look up Temple's observation.)
Physical Information: Apparent size 2.8 by 2.8 arcmin?

Historical Identification: Per Dreyer, NGC 1017 (Swift list V (#33), Ormond Stone list I (#??), 1860 RA 02 31 06, NPD 101 35.9) is "most extremely faint, very small, round, very difficult" (described by Swift as 3rd of 3, the others being NGC 1010 (which is a duplicate of NGC 1006) and 1011). The position precesses to RA 02 37 52.9, Dec -10 59 21, about 1.4 arcmin northeast of the appropriate galaxy, but since it is one of three nebulae (NGC 1010, 1011 and 1017) observed on the same night, and Swift's positions have about the correct relative places, the identification is certain.
Discovery Notes: cf Corwin
Physical Information: Apparent size 0.7 by 0.6 arcmin?

Historical Identification: Per Dreyer, NGC 1018 (Muller list II (#343), 1860 RA 02 31 14, NPD 100 06.9) is "extremely faint, very small, extended 180°, following (eastern) of 2", the other being NGC 1014. The position precesses to RA 02 38 04.0, Dec -09 30 22, but there is nothing there. There is, however, a suitable candidate for what Muller saw, both in brightness and orientation (180° corresponding to a north-south extension) less than 3 arcmin to the southeast, and there is no doubt that it is what Muller observed. This is supported by the fact (as discussed at the entry for NGC 1014) that there is a suitable candidate (albeit only a double star) to the southwest of NGC 1018 for the "preceding of 2", or NGC 1014. So despite the error in the individual positions of the two objects, their relative position and the description of NGC 1018 make their identifications certain.
Physical Information: Apparent size 0.95 by 0.65 arcmin?

Historical Identification: Per Dreyer, NGC 1019 (Stephan list IX (= list XI #4?), 1860 RA 02 31 14, NPD 88 42.0) is "very faint, small, a little extended".
Physical Information: Apparent size 1.3 by 1.15 arcmin(?), including fainter outer arms. A Seyfert galaxy (type Sy 1.5).

Historical Identification: Per Dreyer, NGC 1020 (= GC 5266, Marth #69, 1860 RA 02 31 30, NPD 88 23) is "extremely faint, very small".
Physical Information: Apparent size 0.9 by 0.25 arcmin?

Historical Identification: Per Dreyer, NGC 1021 (= GC 5267, Marth #70, 1860 RA 02 31 34, NPD 88 24) is "extremely faint, small".
Physical Information: Apparent size 0.8 by 0.6 arcmin?

Historical Identification: Per Dreyer, NGC 1022 (= GC 574 = JH 244 = WH I 102, 1860 RA 02 31 37, NPD 97 17.1) is "considerably bright, pretty large, round, much brighter middle, 11th magnitude star 2 arcmin to northeast". The position precesses to RA 02 38 32.9, Dec -06 40 38, essetially dead center on the galaxy listed above, the description fits and there is nothing comparable nearby, so the identification is certain.
Physical Information: Based on a recessional velocity of 1455 km/sec (and H₀ = 70 km/sec/Mpc), NGC 1022 is about 65 to 70 million light years away, in reasonable agreement with a pair of redshift-independent distance estimates of about 60 and 85 million light years. Given that and its apparent size of about 2.45 by 2.35 arcmin (from the images below), it is about 45 to 50 thousand light years across. It is used by the de Vaucouleurs Atlas of Galaxies as an example of galaxy type (R)SB(rs)a pec. It is considered to be a starburst galaxy due to the considerable activity observed in its center.

Historical Identification: Per Dreyer, NGC 1023 (= GC 575 = JH 242 = WH I 156, 1860 RA 02 31 39, NPD 51 32.5) is "very bright, very large, very much extended, very very much brighter middle".
Physical Information: Apparent size 7.3 by 2.5 arcmin? One of the nearest 'early-type' galaxies, with an almost unnoticeable low-surface brightness irregular companion on its eastern side, leading to its designation as Arp 135. Used by the Arp Atlas as an example of an elliptical galaxy (NGC 1023) with a nearby fragment (PGC 10139). Used by the de Vaucouleurs Atlas of Galaxies as an example of galaxy type SB0^-.

Physical Information: Apparent size 1.7 by 1.0 arcmin? A very low-surface brightness apparent companion of NGC 1023. Used by the Arp Atlas as an example of an elliptical galaxy (NGC 1023) with a nearby fragment (PGC 10139).

Historical Identification: Per Dreyer, NGC 1024 (= GC 576 = JH 243 = WH II 592, 1860 RA 02 31 41, NPD 79 45.6) is "pretty faint, small, a little extended, brighter middle, 11th magnitude star 1 arcmin to northeast".
Physical Information: Apparent size 4.0 by 1.25 arcmin? Used by the Arp Atlas as an example of a "miscellaneous" galaxy type.

Historical Identification: Per Dreyer, NGC 1025 (= GC 577 = JH 2488, 1860 RA 02 31 43, NPD 145 28.8) is "extremely faint, small, round, preceding (western) of 2", the other being NGC 1031.
Physical Information: Apparent size 0.9 by 0.5 arcmin?

Historical Identification: Per Dreyer, NGC 1026 (= GC 5268, Marth #71, 1860 RA 02 31 57, NPD 84 03) is "pretty faint, small, round, pretty suddenly brighter middle".
Physical Information: Apparent size 2.1 by 1.3 arcmin?

Historical Identification: Per Dreyer, NGC 1027 (= GC 578 = WH III 66, 1860 RA 02 32 00, NPD 29 03.4) is "a cluster, large, scattered stars, one 10th magnitude", the "10th-magnitude star" actually being 7th-magnitude HD 16626 (which is a foreground star, so although it lies near the center of the cluster, that is merely a coincidence). The position precesses to RA 02 42 46.4, Dec +61 32 46, a bit south of the center of the cluster but well within its boundary, so the identification is certain. (See IC 1824 for a discussion of the duplicate listing.)
Physical Information: Apparent size about 15 arcmin?

Historical Identification: Per Dreyer, NGC 1028 (= GC 5269, Marth #72, 1860 RA 02 32 00, NPD 79 46) is "extremely faint".
Physical Information: Apparent size 0.85 by 0.4 arcmin?

Historical Identification: Per Dreyer, NGC 1029 (= GC 5270, Marth #73, 1860 RA 02 32 02, NPD 79 49) is "faint, small, much extended".
Physical Information: Apparent size 1.5 by 0.4 arcmin?

Historical Identification: Per Dreyer, NGC 1030 (= GC 579 = JH 245 = WH III 581, 1860 RA 02 32 02, NPD 72 34.6) is "very faint, irregularly extended".
Physical Information: Apparent size 1.8 by 0.65 arcmin?

Historical Identification: Per Dreyer, NGC 1031 (= GC 580 = JH 2490, 1860 RA 02 32 08, NPD 145 28.3) is "faint, small, round, gradually brighter middle, 11th magnitude star 2 arcmin to south".
Physical Information: Apparent size 2.3 by 1.0 arcmin?

Historical Identification: Per Dreyer, NGC 1032 (= GC 581 = JH 246 = WH II 5, 1860 RA 02 32 11, NPD 89 30.8) is "pretty bright, small, very little extended, brighter middle, 3 star trapezoid".
Physical Information: Apparent size 4.0 by 0.95 arcmin?

Historical Identification: Per Dreyer, NGC 1033 (Leavenworth list II (#344), 1860 RA 02 32 14, NPD 99 23.9) is "extremely faint, pretty large, irregularly extended 190°, suddenly brighter middle and nucleus".
Physical Information: Apparent size 1.4 by 1.2 arcmin?

Historical Identification: Per Dreyer, NGC 1034 (Leavenworth list I (#55), 1860 RA 02 32 35, NPD 106 24.9) is "very faint, very small, a little extended, a little brighter middle, 2 bright stars 20 seconds of time to the west". The second Index Catalog lists a corrected RA (per Howe) of (1860) 02 31 37 and adds "the 2 stars to the west are of only 11th to 12th magnitude". The corrected position precesses to RA 02 38 13.4, Dec -15 48 24, right on the galaxy, so the identification is certain.
Physical Information: Apparent size 0.7 by 0.65 arcmin?

Historical Identification: Per Dreyer, NGC 1035 (= GC 582 = JH 249 = JH 2489 = WH II 284, 1860 RA 02 32 35, NPD 98 44.5) is "pretty faint, large, much extended, mottled but not resolved, 17th magnitude star attached on southeast".
Physical Information: Apparent size 2.2 by 0.65 arcmin?

Historical Identification: Per Dreyer, NGC 1036 (= GC 583 = JH 247 = WH III 475, 1860 RA 02 32 40, NPD 71 19.3) is "faint, small, round, a little brighter middle". The position precesses to RA 02 40 30.9, Dec +19 16 59, less than an arcmin to the southeast of the galaxy, so the identification is certain.
Physical Information: Apparent size 1.45 by 1.3 arcmin?

Historical Identification: Per Dreyer, NGC 1037 (Swift list V (#35), RA 02 32 52, NPD 92 20.3) is "most extremely faint, very small, much extended, very difficult". The position precesses to RA 02 39 58.1, Dec -01 44 00 (whence the position above), but there is nothing there. Per Corwin, Swift's original notes include the statement "(GC) 581 (= NGC 1032) in the field", which given the half-degree wide field of view for Swift's instrument would mean that NGC 1037 was within 1/2 degree and more likely within 1/4 degree of NGC 1032; but there is nothing within that distance of NGC 1032 that Swift could have seen, and his position for NGC 1037 is nearly 3 degrees to the south of NGC 1032, so whatever "nearby" object Swift observed was certainly not NGC 1032. Given this, Corwin's original opinion was that NGC 1037 was lost or nonexistent. However, in a more recent post he notes that others have suggested that PGC 9973, a couple of minutes west and not quite 7 arcmin to the south of Swift's position might be what Swift saw, and there is a faint galaxy to its west (PGC 9936) that Swift could have confused with NGC 1032, though only if he had no idea how much brighter that galaxy is than either of the PGC objects. But although Corwin mentioned this suggestion, he still felt that NGC 1037 is a lost or nonexistent object, and most of those who suggested or adopted its identification with PGC 9973 have abandoned that position and now agree with Corwin; so although some references still identify PGC 9973 as NGC 1037 (hence the need for the entry below), they represent a dwindling minority.
Additional Note: Although PGC 135657 is not far from Swift's position (and therefore appears in the first image below), it is too faint for him to have seen, and there is nothing within a degree of it, so even if he could have seen it he would not have noted the presence of another galaxy in its field, and it cannot be what he observed.
Perhaps NGC 1037 = IC 243: As noted in the title for this entry, I think it possible that NGC 1037 is a badly misrecorded observation of IC 243 (in which case Swift would be the original observer of that object). His list V contains a large number of objects observed on the same night as NGC 1037. All the others have (1900) declinations ranging from -8 to -16 degrees, and it seems odd that this object has a declination 6 degrees beyond the northern edge of that range. Usually, those looking for one of Swift's misrecorded objects assume that his declination is reasonable and his right ascension is off, but it appears likely that in this case the error is in his declination. Suppose that he made an error of five degrees in recording his observation, so that his published (1900) position should be read as RA 02 34 08, Dec -07 13 47, instead of Dec -02 13 47. This could have been caused by misreading his declination circle, or by writing such a sloppy "7" that he misread it as a "2" (either error is easy to make, and Swift's observations are riddled with similar mistakes). If this suggestion is correct, Swift's (corrected) position would precess to RA 02 39 05.0, Dec -06 47 53. This lies half a minute of time to the east and six arcmin to the north of IC 243, which is a positional error more typical of Swift's measurements, and NGC 1022 lies less than a quarter degree to the north of IC 243, which fits Swift's statement that a (much brighter) GC object was in his field of view. If the correction suggested here were only a degree or two, there would probably be general agreement that the identification of NGC 1037 as IC 243 is "reasonably certain". Given the much larger error required, whether this suggestion will become accepted is less certain; but Corwin agrees that it deserves mention, hence my decision to post this discussion and a corresponding image (namely, the second below).
Physical Information: If NGC 1037 is lost or nonexistent, there is nothing else to say. If it is a duplication of IC 243, see that entry for anything else.

Physical Information: Apparent size 2.1 by 1.0 arcmin?

Historical Identification: Per Dreyer, NGC 1038 (Swift list III (#16) and list V (#??), 1860 RA 02 32 55, NPD 89 05.5) is "extremely faint, pretty small, round, a little brighter middle".
Physical Information: Apparent size 1.2 by 0.35 arcmin?

Historical Identification: Per Dreyer, NGC 1039 (= GC 584 = JH 248, Messier 34, 1860 RA 02 33 02, NPD 47 49.4) is "a cluster, bright, very large, a little compressed, scattered 9th magnitude stars". (Note: See the discussion of Hodierna for an explanation of why he was not credited with the discovery of this object.) The position precesses to RA 02 42 01.0, Dec +42 46 45, about 2 arcmin southwest of the center of the cluster, but essentially dead center in comparison to its apparent size of 30 or so arcmin, so the identification is certain.
Physical Information: M34 consists of a hundred or so stars formed at the same time, about 200 million years ago. At its distance of about 1400 light years, its apparent size corresponds to a 15 light year diameter. An easy object to observe with binoculars or a small telescope, M34 will gradually disintegrate as it moves around the galaxy due to the gravitational effects of passing stars and star clusters. More massive clusters can survive such interactions for long periods of time, but small ones like M34 don't remain a cluster for more than a few hundred million years. However, even after the cluster's stars have been completely scattered they will continue to live out their lives, essentially unaffected by the loss of their siblings.

Historical Identification: Per Dreyer, NGC 1040 (= GC 5271, Stephan list III (#18), 1860 RA 02 33 18, NPD 49 06.0) is "faint, small, brighter middle". The position precesses to RA 02 42 12.3, Dec +41 30 08, but there is nothing there. There is, however, a suitable candidate (namely NGC 1053, which see for anything other than historical information) exactly 1 minute of time to the east, which (per Corwin) was suggested by Reinmuth as being the object Stephan observed. As Corwin notes it is ironic that Stephan, who usually made very accurate measurements, was in this case outdone by Swift, who often made poor measurements; but an examination of Stephan's original notes suggests that he made a careless error in subtracting the RA offset from his comparison star, leading to a single-digit error in the position (namely, 1 minute of time). As a result, although Stephan's error led to a double listing and to Swift's observation taking precedence for several decades, the equivalence of the two listings is certain. Note: This object was initially known only as NGC 1053, because NGC 1040 appeared to be "lost" (as discussed above); but since Reinmuth noted the equivalence of the two entries nearly a century ago, it is now referred to as NGC 1040 almost as often as NGC 1053.
Physical Information: Apparent size 1.25 by 0.45 arcmin (per images below). Vr 4815 km/sec. Previously thought to be S0+ but the PanSTARRS image (added Apr 13, 2019) shows that it is more complex than that, as indicated by the new classification.

Physical Information: Apparent size of about 0.5 by 0.25 arcmin (from image below). Vr unknown, so whether this is in any way connected to NGC 1040 is also unknown; and since neither galaxy shows any obvious signs of interaction, they are probably merely an optical double.

Historical Identification: Per Dreyer, NGC 1041 (Stephan list XII (#22), 1860 RA 02 33 27, NPD 96 02.5) is "pretty faint, pretty small, irregularly round, brighter middle".
Physical Information: Apparent size 1.9 by 1.5 arcmin?

Historical Identification: Per Dreyer, NGC 1042 (Swift list III (#17), 1860 RA 02 33 35, NPD 99 03.0) is "most extremely faint, large, round, northwestern of 2", the other being NGC 1048.
Physical Information: Apparent size 5.9 by 4.8 arcmin? Used by the de Vaucouleurs Atlas of Galaxies as an example of galaxy type SAB(s)c.

Historical Identification: Per Dreyer, NGC 1043 (Swift list V (#36), 1860 RA 02 33 38, NPD 89 16.2) is "most extremely faint, small, round, very difficult".
Physical Information: Apparent size 0.9 by 0.2 arcmin?

Historical Identification: Per Dreyer, NGC 1044 (= GC 585 = JH 251 = WH III 228, 1860 RA 02 33 38, NPD 81 52.1) is "very faint, very small, preceding (western) of 2, 10th magnitude star to west", the "following" (eastern) of 2 being NGC 1046.
Physical Information: NGC 1044 is almost certainly part of a physical pair with PGC 3080165, with which it appears to be interacting, and the pair is probably associated with NGC 1046. The recessional velocity of the pair is listed as 6360 km/sec. Based on that, the pair is about 295 million light years away. Given that and its apparent size of 1.1 by 1.0 arcmin, NGC 1044 is about 95 thousand light years across.

Physical Information: PGC 3080165 is almost certainly part of a physical pair with NGC 1044 (which see for images), with which it appears to be interacting, and the pair is probably associated with NGC 1046. The recessional velocity of the pair is listed as 6360 km/sec. Based on that, the pair is about 295 million light years away. Given that and its apparent size of 0.4 by 0.3 arcmin, PGC 3080165 is about 35 thousand light years across.

Historical Identification: Per Dreyer, NGC 1045 (= GC 586 = JH 253 = JH 2491 = WH II 488, 1860 RA 02 33 43, NPD 101 53.5) is "faint, small, round, brighter middle".
Physical Information: Apparent size 1.8 by 1.2 arcmin?

Historical Identification: Per Dreyer, NGC 1046 (= GC 587 = JH 252 = WH III 229, 1860 RA 02 33 46, NPD 81 53.4) is "extremely faint, very small, following (eastern) of 2", the other being NGC 1044.
Physical Information: Based on a recessional velocity of 6045 km/sec, NGC 1046 is about 280 million light years away. If so, it would be about 15 million light years closer than NGC 1044, but it is generally thought that the difference in recessional velocity between the objects is at least partly a "peculiar" (non-Hubble expansion) velocity, and that they are more likely to be companions than not. If so, their distances are probably in between those calculated directly from their recessional velocities; but since that cannot be independently confirmed, the 280 million light year distance is the best estimate available. Given that and its apparent size of 1.1 by 1.1 arcmin, NGC 1046 is about 90 thousand light years across.

Historical Identification: Per Dreyer, NGC 1047 (Swift list III (#18), 1860 RA 02 33 47, NPD 98 46.0) is "most extremely faint, pretty small, round, very difficult". The position precesses to RA 02 40 39.6, Dec -08 09 48, about 2 arcmin southeast of the galaxy listed above, and there is nothing else nearby, so the identification is certain.
Physical Information: Based on a recessional velocity of 1340 km/sec, NGC 1047 is about 60 million light years away. Given that and its apparent size of 1.6 by 1.3 arcmin (counting its apparent halo), it is about 30 thousand light years across.

Historical Identification: Per Dreyer, NGC 1048 (Swift list III (#19), 1860 RA 02 33 47, NPD 99 08.9) is "most extremely faint, pretty small, round, southeastern of 2", the other being NGC 1042. The position precesses to RA 02 40 38.8, Dec -08 32 42, almost exactly on the pair of galaxies listed above, and the relative position of NGC 1042 helps make the identification certain. Swift almost certainly observed the combined light of the pair rather than either of them individually (in which case he would presumably have stated that the object was "double"), so it seems most appropriate to treat the pair as the NGC object and each of the galaxies as individual components of the pair, and that is the usual practice; but sometimes the northern one is listed as NGC 1048 and the other as merely a companion.
Physical Information: Based on a mutual recessional velocity of 11625 km/sec, a straightforward calculation indicates that NGC 1048 is about 540 million light years away. However, for objects at such distances we should take into account the expansion of the Universe during the time it took their light to reach us. Doing that shows that the pair was about 515 million light years away at the time the light by which we see it was emitted, about 525 million years ago (the difference between the two numbers being due to the expansion of the intervening space during the light-travel time). Given that and its apparent size of 0.95 by 0.35 arcmin, PGC 10140 is about 145 thousand light years across, while the 0.7 by 0.3 arcmin apparent size of PGC 10137 makes it about 105 thousand light years. (Note: PGC 10137 is a Seyfert galaxy (type Sy 2).)

Historical Identification: Per Dreyer, NGC 1049 (= GC 588 = JH 2492, 1860 RA 02 33 58, NPD 124 52.3) is "pretty bright, small, round, stellar".
Physical Information: Apparent size 0.85 arcmin? NGC 1049 is the brightest of six known globular clusters in the Fornax dwarf galaxy, a satellite of our Milky Way galaxy.