  We consider, in quantum scattering theory, symmetrised time delay defined in
terms of sojourn times in arbitrary spatial regions symmetric with respect to
the origin. For potentials decaying more rapidly than $|x|^{-4}$ at infinity,
we show the existence of symmetrised time delay, and prove that it satisfies an
anisotropic version of Lavine's formula. The importance of an anisotropic
dilations-type operator is revealed in our study.
