  We develop a "dual cone" model for millimeter wavelength emission near a
spinning black hole. The model consists of optically thin, luminous cones of
emission, centered on the spin axis, which are meant to represent jet walls.
The resulting image is dominated by a thin ring. We first consider the effect
of black hole's spin on the image, and show that the dominant effect is to
displace the ring perpendicular to the projection of the spin axis on the sky
by $2 a_* \sin i + \mathcal{O}(a_*^3)$. This effect is lower order in $a_*$
than changes in the shape and size of the photon ring itself, but is
undetectable without a positional reference. We then show that the centerline
of the jet can provide a suitable reference: its location is exactly
independent of spin if the observer is outside the cone, and nearly independent
of spin if the observer is inside the cone. If astrophysical uncertainties can
be controlled for, then spin displacement is large enough to be detectable by
future space VLBI missions. Finally, we consider ring substructure in the dual
cone model and show that features in total intensity are not universal and
depend on the cone opening angle.
