Crystal ball
From The Heretic Knowledge Vault
Standard fantasy magic-user paraphernalia, presumably used for scrying (seeing at a distance). According to Bani's flashback, crystal balls are status symbols among the girls at the Sashi Mu Academy of Thaumaturgy and Conjuration. Size matters: the smaller the crystal ball, the higher the status of the owner. (Bani, of course, resents this, as she resents just about everything else about most of her classmates.)
Neither Meji, Bani nor Sarine have ever been seen to use, or necessarily to own, a crystal ball. Sarine, at least, seems to have an uncanny ability to find interesting things (notably Jon Amraphel) at a distance, so perhaps she doesn't need one.
According to Meji, the modern library uses a crystal ball-looking thingy as a directory to keep track of their holdings. The Heretic Knowledge Vault, not being particularly modern, settles for an old-fashioned card catalog instead, to Meji's contempt.
Whether there is a difference between a crystal ball and a Tsuiraku Crystal Doohickey is not clear.