  Two recently derived integral equations for the Maxwell transmission problem
are compared through numerical tests on simply connected axially symmetric
domains for non-magnetic materials. The winning integral equation turns out to
be entirely free from false eigenwavenumbers for any passive materials, also
for purely negative permittivity ratios and in the static limit, as well as
free from false essential spectrum on non-smooth surfaces. It also appears to
be numerically competitive to all other available integral equation
reformulations of the Maxwell transmission problem, despite using eight scalar
surface densities.
