Swans were sacred to the goddess...because the V-formation of their flight was a female symbol, and because, at mid-summer, they flew north to unknown breeding grounds, supposedly taking the dead king's soul with them.
"Tyche and Nemesis"
The Greek Myths: 1, p. 126
Leda and the Swan (16th century)
Paolo Veronese [CORBIS/Bettman source]