Per Dreyer, NGC 558 = GC 5180 d'Arrest (1860 RA 01 20 07, NPD 92 41.9), "extremely faint, small, extended, 10th-magnitude star to west". The position precesses to within 0.4 arcmin of the correct position, and there is a star just off to the west (although only 11.5 magnitude), so the identification is certain. Listed as part of Abell 194. Based on recessional velocity of 4955 km/sec, about 220 million light years away. Given that and apparent size of 0.4 by 0.2 arcmin, about 25 thousand light years across.

Per Dreyer, NGC 560 = William Herschel (list III, #441) (1860 RA 01 20 19, NPD 92 38.8), "very faint, very small, irregularly extended, western of 2". (The other, or "eastern of 2", being William Herschel list III #442, = NGC 564.) The position precesses to within 0.5 arcmin of the correct position, so the identification is certain (and would be nailed down by the relative positions of NGC 560 and 564, even if the position were slightly in error). Listed as part of Abell 194. Based on recessional velocity of 5510 km/sec, about 245 million light years away. Given that and apparent size of 2.0 by 0.5 arcmin, about 145 thousand light years across.

Per Dreyer, NGC 564 = William Herschel (list III, #442) (1860 RA 01 20 40, NPD 92 36.9), "very faint, very small, irregular figure, eastern of 2". (The other, or "western of 2", being William Herschel list III #441, = NGC 560.) The position precesses to within 0.5 arcmin of the correct position, so the identification is certain (and would be nailed down by the relative positions of NGC 560 and 564, even if the position were slightly in error). Listed as part of Abell 194. Based on recessional velocity of 5835 km/sec, about 260 million light years away, in fair agreement with redshift-independent distance estimates of about 200 million light years. Given that and apparent size of 1.4 by 1.2 arcmin, about 100 thousand light years across.

Per Dreyer, NGC 577 (= Tempel I (#8), II, 1860 RA 01 23 34, NPD 92 43.1), "faint". Skinner discovered the object in 1867, but his observation was not published until 1886, and even then only in a footnote to another paper, so Dreyer had little chance to note the error, so Tempel's "rediscovery" was an independent observation (although as noted in the discussion of the double listing at NGC 580, muddled by an apparently fatal error in another "observation" of the same night). In any event, the position precesses to exactly the correct position, so the current identification is certain. Listed as possible member of Abell 194. Based on recessional velocity of 5935 km/sec, about 265 million light years away. Given that and apparent size of 1.8 by 1.4 arcmin, about 140 thousand light years across.

Per Dreyer, NGC 598 (= Messier 33, 1860 RA 01 25 58, NPD 60 03.8) is "remarkable object, extremely bright, extremely large, round, very gradually much bright middle and nucleus". The position precesses to RA 01 33 50.1, Dec +30 39 25, right on the nucleus of the galaxy, so the identification is certain. (Note: See the discussion of Hodierna for an explanation of why he was not credited with the discovery of any NGC object.) M33 is a member of the Local Group of Galaxies, and as such, its recessional velocity of -180 km/sec represents its random motion relative to our galaxy, and has nothing to do with the Universal expansion; so it cannot be used to estimate the distance of the galaxy. However, dozens of redshift-independent distance estimates indicate that the galaxy is between 2 and 4 million light years away. Given that and its apparent size of 60 by 35 arcmin, it is about 50 thousand light years across.