In 1956 metrologists Thompson and Lampard established a new theorem in two-
dimensional electrostatics that gives calculable capacitances for practical
systems possessing a certain symmetry. The theorem is well known among tho
se concerned with electrical standards, but not so well known beyond. This
paper brings the theorem to a wider audience with a pedagogical discussion
of it, first: by treating a simple example by standard methods of electrost
atics, then proving the Riemann mapping theorem on which the theorem is bas
ed. The Thompson-Lampard theorem and its generalization are then proved and
its use in metrology described. Along the way, some curious results about
series and products are exhibited. (C) 1999 American Association of Physics
Teachers.