  Previous studies of the rotation law in the outer Galactic disc have mainly
used gas tracers or clump giants. Here, we explore A and F stars as
alternatives: these provide a much denser sampling in the outer disc than gas
tracers and have experienced significantly less velocity scattering than older
clump giants. This first investigation confirms the suitability of A stars in
this role. Our work is based on spectroscopy of $\sim$ 1300
photometrically-selected stars in the red calcium-triplet region, chosen to
mitigate against the effects of interstellar extinction. The stars are located
in two low Galactic latitude sightlines, at longitudes $\ell = 118^{\circ}$,
sampling strong Galactic rotation shear, and $\ell = 178^{\circ}$, near the
Anticentre. With the use of Markov Chain Monte Carlo parameter fitting, stellar
parameters and radial velocities are measured, and distances computed. The
obtained trend of radial velocity with distance is inconsistent with existing
flat or slowly rising rotation laws from gas tracers (Brand & Blitz 1993; Reid
et al. 2014). Instead, our results fit in with those obtained by Huang et al.
(2016) from disc clump giants that favoured rising circular speeds. An
alternative interpretation in terms of spiral arm perturbation is not straight
forward. We assess the role that undetected binaries in the sample and distance
error may have in introducing bias, and show that the former is a minor factor.
The random errors in our trend of circular velocity are within $\pm 5$ km
s$^{-1}$.
