(Βυβλίς), a daughter of Miletus and Eidothea (others call her mother Tragasia or Areia), and sister of Caunus. The story about her is related in different ways. One tradition is, that Caunus loved his sister with more than brotherly affection, and as he could not get over this feeling, he quitted his father's home and Miletus, and settled in Lycia. Byblis, deeply grieved at the flight of her brother, went out to seek him, and having wandered about for a long time, hung herself by means of her girdle. Out of her tears arose the well Byblis. (Parthen. Erot. 11; Conon, Narrat. 2.) According to another tradition, Byblis herself was seized with a hopeless passion for her brother, and as in her despair she was on the point of leaping from a rock into the sea, she was kept back by nymphs, who sent her into a profound sleep. In this sleep she was made an immortal Hamadryas; and the little stream which came down that rock was called by the neighboring people the tears of Byblis. (Antonin. Lib. 30.) A third tradition, which likewise represented Byblis in love with her brother, made her reveal to him her passion, whereupon Caunus fled to the country of the Leleges, and Byblis hung herself. (Parthen. l.c.) Ovid (Ov. Met. 9.446-665) in his description combines several features of the different legends; Byblis is in love with Caunus, and as her love grows from day to day, he escapes; but she follows him through Caria, Lycia, &c., until at last she sinks down worn out; and as she is crying perpetually, she is changed into a well. The town of Byblus in Phoenicia is said to have derived its name from her. (Steph. Byz. s. v.)
[L.S]A Dictionary of Greek and Roman biography and mythology
Smith, William
A Dictionary of Greek and Roman biography and mythology. William Smith, LLD, ed. 1890