The Sea Fairies #548965

First published in 1911, "The Sea Fairies" is a children's fantasy novel written by L. Frank Baum.
As an underwater fantasy, Baum's "The Sea Fairies" can be classed with earlier books with similar themes, like Charles Kingsley's "The Water-Babies", and successors too, like E. Nesbit's "Wet Magic". 

Mayre "Trot" Griffiths is a small girl living on the coast of California, her close friend and companion is Cap'n Bill, formerly her father's employer and now a retired seaman with a wooden leg. As they walk along the beach one day, Trot wishes that she could see a mermaid. Nearby mermaids overhear her, and grant her wish, appearing to her and the Cap'n the next day. The mermaids explain that they are "sea fairies," and offer the girl a chance to experience their world. Trot is eager to go; Bill is not, but is too loyal to let Trot go by herself. Magically transformed, the two embark on an underwater adventure.