Historical Identification: Per Dreyer, NGC 2618 (= GC 1675 = JH 515 = WH III 257, 1860 RA 08 28 49, NPD 88 48.8) is "extremely faint, pretty large, irregular figure". The position precesses to RA 08 36 01.7, Dec +00 42 20, about 2 arcmin east of the galaxy listed above, the description fits and there is nothing else nearby, so the identification is certain.
An Atypical Error By Bigourdan: As for many other NGC objects, Dreyer published a corrected position in the first IC of RA 08 29 01, based on a statement by Bigourdan (Comp. Rend. 112, p. 850) that the object was 12 seconds of time to the east of the NGC position. Usually, such a correction provides a much better fit to the object's position; but in this case, the "corrected" position precesses to RA 08 36 13.7, Dec +00 42 18, which is 3 arcmin further east of the galaxy. This would be an extremely unlikely mistake for as careful an observer as Bigourdan, so I decided to check the measurements recorded in Bigourdan's "big book" of 1904, as shown below.
Bigourdan's Comparison Stars: Bigourdan made six measurements of the position of the nebula, two on Mar 15, 1890 and four on Feb 16, 1896. In each case he measured offsets from BD+1 2137, at (1900) RA 08 31 07.7, Dec +01 06 24, to a 10th magnitude "Anonyme" star, with a resulting position for that star of (1900) RA 08 30 42, Dec +00 55 00. The offsets between the two stars do not exactly agree with the positions Bigourdan listed for them, but are close enough that there should be no difficulty in identifying the stars by precessing their positions to modern coordinates. And there isn't, as precessing the coordinates to the equinox of 2000 gives a position for BD+1 2137 of RA 08 36 16.8, Dec +00 45 38, and for the "Anonyme" star of RA 08 35 50.7, Dec +00 34 17. The former position lies 1 arcmin southwest of 10th magnitude star TYC 210-1534-1 (= BD+1 2137), and the latter position lies 1.3 arcmin southwest of 10th magnitude star TYC 210-1852-1. Given the nearly identical relative positions, those must be the stars that Bigoudan used, and their actual positions, precessed to the equinox of 1900, should provide a proper reference for the position of NGC 2618.
Bigourdan's Actual Position For NGC 2618: The position of Bigourdan's "Anonyme" star is J2000 RA 08 35 54.4, Dec +00 35 11, which precesses to (1900) RA 08 30 45.6, Dec +00 55 54. The average offsets of the six measurements made by Bigourdan are -2.2 seconds of time in right ascension, and +7' 16" in declination. This puts his position for NGC 2618 at (1900) RA 08 30 43.4, Dec +01 03 10, which precesses to J2000 RA 08 35 52.4, Dec +00 42 27, which falls right on the galaxy listed above (to the west of its nucleus, but well within its outline). In other words, although Bigourdan stated that his position for NGC 2618 fell well to the east of the NGC position (which was already to the east of the galaxy), it actually fell right on the galaxy. So although his "corrected" position was well off the mark, it was not due to an error in his measurements, but some kind of blunder in his reductions. This does not affect the identification of NGC 2618, but it does partially resolve an otherwise puzzling error on Bigourdan's part.
Physical Information: Apparent size 2.5 by 2.0 arcmin?

Historical Identification: Per Dreyer, NGC 2619 (= GC 1676 = JH 514 = WH II 319, 1860 RA 08 29 01, NPD 60 49.3) is "faint, pretty small, round, brighter middle, mottled but not resolved". The position precesses to RA 08 37 32.4, Dec +28 41 42, on the southern rim of the galaxy listed above, the description is a reasonable fit and there is nothing else nearby, so the identification is certain.
Physical Information: Apparent size 1.8 by 1.1 arcmin?

Historical Identification: Per Dreyer, NGC 2620 (= GC 5426, Marth #125, Lassell, 1860 RA 08 29 09, NPD 64 35) is "faint, small, extended". The position precesses to RA 08 37 28.2, Dec +24 56 00, about 0.8 arcmin south of the galaxy listed above, the description fits and there is nothing comparable nearby, so the identification is certain.
Discovery Note: The NGC entry is copied from Lassell's 1866 paper about observations at Malta, which included Marth's discoveries. But although Marth discovered most of the objects in the list, the paper states that Lassell was the discoverer of #125 in Marth's list.
Physical Information: Apparent size 2.0 by 0.5 arcmin.

Historical Identification: Per Dreyer, NGC 2621 (= GC 5427, Marth #126, 1860 RA 08 29 18, NPD 64 32) is "very faint, small, round". The position precesses to RA 08 37 37.4, Dec +24 58 58, about 1 arcmin south of the galaxy listed above, the description fits and there is nothing nearby save for NGC 2620, which is accounted for by Marth #125 (and has a similar error in its NGC position), so the identification is certain.
Discovery Note: The NGC entry is copied from Lassell's 1866 paper about observations at Malta, which included Marth's discoveries.
Physical Information: Apparent size 0.8 by 0.4 arcmin.

Historical Identification: Per Dreyer, NGC 2622 (= GC 5428, Marth #127, 1860 RA 08 29 52, NPD 64 37) is "faint, small, round". The position precesses to RA 08 38 11.0, Dec +24 53 53, right on the galaxy listed above, the description fits and there is nothing comparable nearby, so the identification is certain.
Discovery Note: The NGC entry is copied from Lassell's 1866 paper about observations at Malta, which included Marth's discoveries.
Physical Information: The recessional velocity of NGC 2622 is 8580 km/sec, but it is obviously interacting with PGC 24266 (each has extended regions of gas, stars and clusters of stars strewn into intergalactic space by their interaction), so the pair must be at the same distance from us and their average recessional velocity should be used to estimate their Hubble distance. The recessional velocity of PGC 24266 is 8470 km/sec, so the average of their recessional velocities is 8525 km/sec. Based on that (and H₀ = 70 km/sec/Mpc), a straightforward calculation indicates that the pair is about 395 to 400 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 385 million light years away at the time the light by which we see it was emitted, about 390 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 about 0.65 by 0.4 arcmin for the central galaxy and about 1.4 by 1.2 arcmin for its far-flung fragments (from the images below), the central portion of NGC 2622 is about 70 to 75 thousand light years across and the overall structure spans about 155 to 160 thousand light years. One result of their interaction is a starburst in the core of NGC 2622, causing it to be classified as a Seyfert galaxy (type Sy 1.8). The other galaxies in the field of view do not appear to be taking part in the gravitational interaction, and may be foreground or background objects.

Physical Information: Based on a recessional velocity of 8470 km/sec (and H₀ = 70 km/sec/Mpc), a straightforward calculation indicates that PGC 24266 is about 395 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 galaxy was about ? million light years away at the time the light by which we see it was emitted, about ? 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 about ? arcmin, the galaxy is about ? thousand light years across. Based on a recessional velocity of 8470 km/sec, PGC 24266 is about 395 million light years away, but whatever its actual distance, it must be the same as for NGC 2622 (which see for images), based on its obvious gravitational interaction with the larger galaxy. The two galaxies are probably within a few hundred thousand light years of each other, and may be less than 200 thousand light years apart. Given its probable distance and its apparent size of 0.4 by 0.3 arcmin, PGC 24266 is about 45 thousand light years across, but that does not take into account the long tail of gas and stars streaming away to its southwest.

Note About Designation: NED does not recognize the LEDA designation for this object; instead, it lists it as 2MASXJ08380492+2453267.
Physical Information:

Historical Identification: Per Dreyer, NGC 2623 (Stephan list XIII (#41), 1860 RA 08 30 03, NPD 63 45.6) is "very faint, very small, round, brighter middle, mottled but not resolved".
Physical Information: Two galaxies must have recently collided and merged to form this galaxy, which is in the late stages of its merger, having developed a nearly common (though very distorted and spectacularly bright) core, but still showing the aftereffects of its merger in two spectacularly long arms of stars, star clusters and gases thrown out into intergalactic space and now filled with hot, bright young clusters of stars that heat and light up the gases surrounding them. Based on its recessional velocity of 5550 km/sec, NGC 2623 is about 260 million light years away, in reasonable agreement with redshift-independent distance estimates of 250 to 350 million light years. Given that and its apparent size of 2.4 by 0.7 arcmin, it is about 180 thousand light years across. The core of the galaxy, filled with exceptionally large numbers of bright young stars, causes it to be classified as a Seyfert galaxy (type Sy 2).

Historical Identification: Per Dreyer, NGC 2624 (= GC 5429, Marth #128, 1860 RA 08 30 06, NPD 69 48) is "extremely faint".
Discovery Note: The NGC entry is copied from Lassell's 1866 paper about observations at Malta, which included Marth's discoveries.
Physical Information: Apparent size 0.6 by 0.5 arcmin. (Note: Within the western boundary of open cluster M44, but a completely insignificant and unnoticeable speck in images showing the cluster as a whole, and of course as a distant galaxy, completely unrelated to the cluster, save for being in approximately the same direction.)

Historical Identification: Per Dreyer, NGC 2625 (= GC 5430, Marth #129, 1860 RA 08 30 19, NPD 69 48) is "extremely faint, very small".
Discovery Note: The NGC entry is copied from Lassell's 1866 paper about observations at Malta, which included Marth's discoveries.
Physical Information: Apparent size 0.7 by 0.6 arcmin. (Note: Within the western boundary of open cluster M44, but a completely insignificant and unnoticeable speck in images showing the cluster as a whole, and of course as a distant galaxy, completely unrelated to the cluster, save for being in approximately the same direction.) Classification Note: This galaxy is listed as an elliptical in some references, but as shown in the images below, it is actually a spiral.

Historical Identification: Per Dreyer, NGC 2626 (= GC 1677 = JH 3131, 1860 RA 08 30 28, NPD 130 11.1) is "a 9th magnitude star involved in a pretty bright, pretty large, round nebula".
Physical Information: Apparent size 5.0 by 5.0 arcmin

Historical Identification: Per Dreyer, NGC 2627 (= GC 1678 = JH 516 = JH 3132 = WH VII 63, 1860 RA 08 31 28, NPD 119 28.0) is "a cluster, considerably large, pretty rich, pretty compressed, stars from 11th to 13th magnitude".
Physical Information: Apparent size 9.0 arcmin

Historical Identification: Per Dreyer, NGC 2628 (= GC 1680 = WH III 235, 1860 RA 08 31 51, NPD 65 57.3) is "extremely faint, small".
Physical Information: Apparent size 1.1 by 1.1 arcmin

Historical Identification: Per Dreyer, NGC 2629 (= GC 1679 = WH III 982, H O N, d'Arrest, 1860 RA 08 32 00, NPD 16 31.5) is "very faint, small, stellar".
Note About "H O N": In John Herschel's treatise on observations made at the Cape of Good Hope in the 1830's he lists eight nebulae discovered by his father, but not previously published. WH III 982 and WH III 983 (= NGC 2641) are among those eight nebulae; and "H O N" alerts the reader of the GC and NGC to the fact that they will not find those objects in William Herschel's catalogs, but in the Cape catalog.
Apparent size 1.5 by 1.3 arcmin

2630/2631 are presumably (per Corwin) the two overlooked nebulae in this note at the end of T IX:
"The 4 new nebulae of the 27th of July are 1 degree north of GC 1679 (NGC 2629) & 1682 (NGC 2641), as well as a new mists of d'Arrest, which I saw earlier when I sketched 1679, where I found two new fine nebulae near 1679. It is, however, very striking that d'Arrest, the new mist found south and north of this group, also measured above 1679 and 82, has overlooked my two new nebulae, which are much brighter than his own and Herschelian ones. Since I described years ago as two pretty little nebulae, and I found them so bright in 1883, I might raise the question whether they are perhaps mutable. I would put less emphasis on my own observations, if not this stellar part of Will and John Herschel and d'Arrest were so well studied."

Historical Identification: Per Dreyer, NGC 2630 and 2631 (Tempel list IX (note), 1860 RA 08 32, NPD 16 30±) are "2 very faint, very small, very near III 982", (WH) III 982 being NGC 2629. Dreyer's 1860 positions are 1.5 arcmin due north of NGC 2629, but there is nothing located there or at the corresponding precessed position of RA 08 47 07.2, Dec +73 00 00 (whence the position listed above), so the two entries are listed as nonexistent or lost.
However, per Corwin, Temple stated that the two galaxies were brighter than the comparison galaxy, so they presumably do exist, and their positions are simply wrong. He suggests that Temple may have mistaken NGC 2633 for NGC 2629, in which case NGC 2630 and 2631 might be NGC 2634 and PGC 24760 (or "NGC 2634A"); but even if that should prove correct, this entry will contain only historical information.

Historical Identification: Per Dreyer, NGC 2630 and 2631 (Tempel list IX (note), 1860 RA 08 32, NPD 16 30±) are "2 very faint, very small, very near III 982", (WH) III 982 being NGC 2629. Dreyer's 1860 positions are 1.5 arcmin due north of NGC 2629, but there is nothing located there or at the corresponding precessed position of RA 08 47 07.2, Dec +73 00 00 (whence the position listed above), so the two entries are listed as nonexistent or lost.
Listed by Dreyer as a pair with NGC 2630, which see for historical information, and has been suggested (per Corwin) as possibly being PGC 24760, or "NGC 2634A"; but even if that should prove correct, this entry will remain essentially as-is.

"Ancient" History: Praesepe, or the Beehive Cluster, is easily visible as a "little cloud" of stars in dark skies, and was already known in ancient times, when truly dark night skies were common. The first known mention of its existence is by Aratos, as part of a poem meant to reproduce the now lost prose of Eudoxus of Cnidus. Eudoxus was the first to propose a system of turning spheres as an explanation of the motions of heavenly bodies, and apparently as part of that work he discussed the rising and setting of various constellations. A review of Aratos' work by Hipparchus shows that Eudoxus' work was still extant at the time of Hipparchus, who pointed out errors in both the original prose and (more critically) its poetic transformation. Although practically all of Hipparchus' astronomical works have been lost, we know through Ptolemy that Hipparchus made thousands of relatively accurate observations of celestial objects, and on that basis can be confidently assigned the place of honor as the first person to estimate a reasonably accurate position for the cluster; but the existence of the "little cloud" must have been known no later than the time of Eudoxus and more likely, as early as the time of Eudoxus' father, Aeschines of Cnidus, who was an avid observer of the skies. The cluster was first resolved into "more than 40 small stars" by Galileo, and not long after by some of his contemporaries (probably resoved by Peiresc, definitely resolved by Marius, and Hodierna had it as #1 in his list of objects which were nebulous to the naked eye, but resolved into stars by a telescope); so it had a long history before Messier added it to his catalog.
Historical Identification: Per Dreyer, NGC 2632 (= GC 1681 = JH 517, Hipparchus, M 44, 1860 RA 08 32, NPD 69 32) is "Praesepe Cancri". The position precesses to RA 08 40 03.8, Dec +19 58 33, well within the 95 arcmin diameter of the cluster, so even without the millennia of historical precedence the identification would be certain.
Physical Information: Praesepe is one of the nearest clusters to the Sun, being only about 575 light years away. Given its distance and apparent size, it is about 15 light years across. Studies of the proper motion of objects in the region of the cluster show that about 200 stars share the same motion, and must be cluster members. The nature of the brightest stars in the cluster suggests an age of 730 million years, which is not much less than the 790 million years estimated for the Hyades, and both clusters have similar proper motions, so it is possible that they originated in the same (unknown) star-forming region, at about the same time.

Historical Identification: Per Dreyer, NGC 2633 (Tempel list VI (#4), list IX (#6), 1860 RA 08 32 22, NPD 15 23.2) is "faint, small, a little extended". The position precesses to RA 08 48 03.9, Dec +74 06 42, on the northern rim of the galaxy listed above, the description fits and there is nothing else nearby, so the identification is certain. (It is further confirmed by the accurate position of NGC 2634, observed by Tempel on the same nights.)
Discovery Notes: The date of discovery is for Tempel's list VI #4, but Dreyer's position is essentially the same as Tempel's list IX #6. (Dreyer maintained a regular correspondence with Tempel, and presumably confirmed the best position through that correspondence prior to publishing the NGC.)
Physical Information: Based on a recessional velocity of 2160 km/sec, NGC 2633 is about 100 million light years away, in good agreement with redshift-independent distance measurements of 90 to 110 million light years. Given that and its apparent size of 2.3 by 1.5 arcmin, it is about 65 thousand light years across. As in the case of Arp 79, NGC 2633's listing as Arp 80 is supposed to mean it is a spiral galaxy with a large high surface brightness companion, but there is no sign of such a companion on the corresponding Arp Atlas plate, and the assignment was presumably made merely on the basis of the increased brightness in the star-forming regions on the southern side of the galaxy.

Historical Identification: Per Dreyer, NGC 2634 (Tempel list VI (#5), list IX (#7), 1860 RA 08 32 34, NPD 15 31.2) is "faint, small, a little extended". The position precesses to RA 08 48 11.0, Dec +73 58 40, about 1.1 arcmin northwest of the center of the galaxy, and just off its northwestern rim and there is nothing comparable nearby, so the identification is certain. (It is further confirmed by the accurate position of NGC 2633, observed by Tempel on the same nights.)
Discovery Notes: Both Dreyer's position and the date of discovery are for Tempel's list VI #5. (Dreyer maintained a regular correspondence with Tempel, and presumably confirmed the best position through that correspondence prior to publishing the NGC.)
Physical Information: Apparent size 1.7 by 1.6 arcmin. Possibly the lost or otherwise nonexistent NGC 2630.

Physical Information: Possibly two or three interacting galaxies. Apparent size 1.8 by 0.4 arcmin

Historical Identification: Per Dreyer, NGC 2635 (= GC 1683 = JH 3133, 1860 RA 08 32 58, NPD 124 16.2) is "a cluster, pretty much compressed, irregular triangle, stars from 13th magnitude".
Physical Information: Apparent size 3.0 arcmin

Historical Identification: Per Dreyer, NGC 2636 (Tempel list IX (#8), 1860 RA 08 33 00, NPD 15 51) is "very faint, small, 2 stars of 11th or 12th magnitude to east". The position precesses to RA 08 48 25.4, Dec +73 38 49, about 1.4 arcmin south of the galaxy listed above, there is nothing else in the region and the two stars about 6 arcmin to the east make the identification certain.
Discovery Note: Tempel's position for his list IX #8 is a rough value based on Bonner Durchmusterung charts for equinox 1855; Dreyer's 1860 right ascension for NGC 2636 is exactly the same as Tempel's right ascension (precessed for the 5 year difference in equinoxes), but his declination is a degree to the south; however, he maintained a regular correspondence with Tempel, and presumably obtained a more accurate position from him prior to publishing the NGC.
Physical Information: Apparent size of about 0.55 by 0.55 arcmin (from the images below).