June 16 falls quite close to the summer solstice (four or five days), as Stephen notes at the end of Proteus: "By the way next when is it Tuesday will be the longest day." Dublin lies north of the 53rd parallel (a line that passes near the southern end of Hudson Bay), meaning that in late June its days are quite long indeed. At the solstice the sun can be seen for nearly 17 hours. It sets in Nausicaa.
Hugh Kenner opens his study Ulysses (2nd ed., 1987) by observing that "In Dublin in 1904, Standard Time and Summer Time still years in the future, local time had the sun rise on 16 June at 3.33 and not set until 8.27. Two or three hours past sunset, on such nights, one can still make out newspaper headlines by skyshine, and at no time between dusk and dawn does the northern sky really darken" (1).
In Nausicaa, which takes place between 8 and 9 PM, we learn at the outset that "the sun was setting." At the end of the chapter, when the sun has set and "the nine o'clock postman" is making his rounds, the narrative reads, "Howth settled for slumber, tired of long days, of yumyum rhododendrons (he was old) and felt gladly the night breeze lift, ruffle his fell of ferns. He lay but opened a red eye unsleeping, deep and slowly breathing, slumberous but awake." Bloom too is slumbrous but awake: "Must be getting on for nine by the light. Go home. Too late for Leah, Lily of Killarney. No. Might be still up. Call to the hospital to see. Hope she's over. Long day I've had." But much of his day remains.