  We use radial velocities from spectra of giants obtained with the WIYN
telescope, coupled with existing chemical abundance measurements of Na and O
for the same stars, to probe the presence of kinematic differences among the
multiple populations of the globular cluster (GC) M13. To characterise the
kinematics of various chemical subsamples, we introduce a method using Bayesian
inference along with an MCMC algorithm to fit a six-parameter kinematic model
(including rotation) to these subsamples. We find that the so-called "extreme"
population (Na-enhanced and extremely O-depleted) exhibits faster rotation
around the centre of the cluster than the other cluster stars, in particular
when compared to the dominant "intermediate" population (moderately Na-enhanced
and O-depleted). The most likely difference between the rotational amplitude of
this extreme population and that of the intermediate population is found to be
$\sim$4 km s$^{-1}$, with a 98.4% probability that the rotational amplitude of
the extreme population is larger than that of the intermediate population. We
argue that the observed difference in rotational amplitudes, obtained when
splitting subsamples according to their chemistry, is not a product of the
long-term dynamical evolution of the cluster, but more likely a surviving
feature imprinted early in the formation history of this GC and its multiple
populations. We also find an agreement (within uncertainties) in the inferred
position angle of the rotation axis of the different subpopulations considered.
We discuss the constraints that these results may place on various formation
scenarios.
