  The problem of determining equilibrium configurations of the free surface of
a conducting liquid is considered with allowance for a finite interelectrode
distance. The analogy is established between this electrostatic problem and
that of finding the profile of a progressive capillary wave on the free surface
of a liquid layer of a finite depth, which was solved by Kinnersley. This
analogy allowed exact solutions to be obtained for the geometry of liquid
electrodes, which expand the existing notions about the possible stationary
states of the system.
