Definition of "ineffability"

To him, the spirit lodged within Billy, and looking out from his welkin eyes as from windows, that ineffability it was which made the dimple in his dyed cheek, suppled his joints, and dancing in his yellow curls made him preeminently the Handsome Sailor.

1924, Herman Melville, chapter 11, in Billy Budd‎, London: Constable & Co.

But recently, physiological studies of ritual have suggested that the ineffability of intense emotional, transformative states may be due to the dominance of right brain activity.

1990, Barbara Myerhoff, “The transformation of consciousness in ritual performances: some thoughts and questions”, in Richard Schechner, Willa Appel, editors, By Means of Performance: Intercultural Studies of Theatre and Ritual‎, Cambridge University Press, page 245