Thepotential problem of two nearby holes in an infinitely thin perfectly conducting screen immersed in a homogeneous normal electrostatic field is considered. Expressions are derived for the double layer of charge arising in the plane of the hole, the centre of gravity of this distribution and the total amount of polarization induced by a nearby point dipole. In the derivation a set of integrals are used that connect the terms of a series expansion of the potential in the oblate spheroidal system of co-ordinates with sources on the focal disk. The results are applied to solve the excess polarization and centre of the dipole distributions for two similar as well as two dissimilar holes.