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IC 5204 is probably NGC 7300. Swift found it the same night that he found I5228 = N7302, and describes it as "vF, eE, a ray; p of 2." There is nothing within a degree of Swift's position that matches this description.
However, we know that IC 5228 is certainly NGC 7302; the positions match to within 10 seconds of time, and there is nothing else nearby that could be Swift's object. His description reads, "pB, pS, R; B * nr s; f of 2." The bright star is there, and this galaxy is the "f of 2" with the preceding object being NGC 7300.
Looking at Swift's position for I5204 (22 18 00, -14 39.1 for B1950.0), we see that it is about 10 minutes west and 20 arcmin south of N7300. Given that Swift's description could well apply to the bright inner part of N7300, I'm going to suggest simple digit errors in Swift's position.
Lacaille's catalogue
The Messier objects
Dunlop's catalogue
The Bennett objects
The Caldwell list
Named DSOs
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