  Exact solutions are presented for a doubly-periodic array of steadily moving
bubbles in a Hele-Shaw cell when surface tension is neglected. It is assumed
that the bubbles either are symmetrical with respect to the channel centreline
or have fore-and-aft symmetry, or both, so that the relevant flow domain can be
reduced to a simply connected region. By using conformal mapping techniques, a
general solution with any number of bubbles per unit cell is obtained in
integral form. Several examples are given, including solutions for multi-file
arrays of bubbles in the channel geometry and doubly-periodic solutions in an
unbounded cell.
