  A new gyroscopic interference effect stemming from the Galilean translational
factor in the matter wave function is pointed out. In contrast to the
well-known Sagnac effect that stems from the geometric phase and leads to a
shift of interference fringes, this effect causes slanting of the fringes. We
illustrate it by calculations for two split cigar-shaped Bose-Einstein
condensates under the conditions of a recent experiment, see Y.Shin et al.,
Phys. Rev. Lett. 92, 050405 (2004). Importantly, the measurement of slanting
obviates the need of a third reference cloud.
