  We are interested in cell properties of translations in affine Weyl groups.
We find out some translations in the second lowest two-sided cell of an affine
Weyl group and use the translations to formulate a refinement of Jianyi Shi's
conjecture on the number of left cells in the second lowest two-sided cell. We
verify the refinement for an affine Weyl group of type $\tilde A_{n-1}$ and
type $\tilde G_2$.
