Briefly, "Finis" is the story of a new star that is discovered which turns out to be a new, hotter sun. It is a short hard hitting story which shows a man and woman, who stay up the night to watch the expected new star arise. Though written in 1906, it is set in the future of the mid 20th century.
Notes
The Locus database http://www.locusmag.com/index/s591.html spells his name "Pollock", but the latest anthology (1999) uses "Pollack", as do the online texts and other references.