Context : NGC 4372 is a poorly studied old , very metal-poor Globular Cluster ( GC ) located in the inner Milky Way halo .

Aims : We present the first in-depth study of the kinematic properties and derive the structural parameters of NGC 4372 based on the fit of a Plummer profile and a rotating , physical model .
We explore the link between internal rotation to different cluster properties and together with similar studies of more GCs , we put these in the context of globular cluster formation and evolution .

Methods : We present radial velocities for 131 cluster member stars measured from high-resolution FLAMES/GIRAFFE observations .
Their membership to the GC is additionally confirmed from precise metallicity estimates .
Using this kinematic data set we build a velocity dispersion profile and a systemic rotation curve .
Additionally , we obtain an elliptical number density profile of NGC 4372 based on optical images using a MCMC fitting algorithm .
From this we derive the cluster ’ s half-light radius and ellipticity as r _ { h } = 3.44 \arcmin \pm 0.04 \arcmin and \epsilon = 0.08 \pm 0.01 .
Finally , we give a physical interpretation of the observed morphological and kinematic properties of this GC by fitting an axisymmetric , differentially rotating , dynamical model .

Results : Our results show that NGC 4372 has an unusually high ratio of rotation amplitude to velocity dispersion ( 1.2 vs . 4.5 km s ^ { -1 } ) for its metallicity .
This , however , puts it in line with two other exceptional , very metal-poor GCs - M 15 and NGC 4590 .
We also find a mild flattening of NGC 4372 in the direction of its rotation .
Given its old age , this suggests that the flattening is indeed caused by the systemic rotation rather than tidal interactions with the Galaxy .
Additionally , we estimate the dynamical mass of the GC M _ { dyn } = 2.0 \pm 0.5 \times 10 ^ { 5 } ~ { } \mathrm { M _ { \odot } } based on the dynamical model , which constrains the mass-to-light ratio of NGC 4372 between 1.4 and 2.3 ~ { } \mathrm { M _ { \odot } / L _ { \odot } } , representative of an old , purely stellar population .

Conclusions :