We present a study of the internal kinematics of two globular clusters , M10 ( NGC 6254 ) and M71 ( NGC 6838 ) , using individual radial velocity ( RV ) measurements obtained from observations using the Hydra multi-object spectrograph on the WIYN 3.5 m telescope . We measured 120 RVs for stars in M10 , of which 107 were determined to be cluster members . In M71 , we measured 82 RVs and determined 78 of those measurements belonged to cluster members . Using the cluster members , we determine a mean RV of 75.9 \pm 4.0 ( s.d . ) km s ^ { -1 } and -22.9 \pm 2.2 ( s.d . ) km s ^ { -1 } for M10 and M71 , respectively . We combined the Hydra RV measurements with literature samples and performed a line-of-sight rotational analysis on both clusters . Our analysis has not revealed a statistically significant rotation in either of these clusters with the exception of the inner region ( 10 \arcsec - 117 \arcsec ) of M10 for which we find hints of a marginally significant rotation with amplitude V _ { rot } = 1.14 \pm 0.18 km s ^ { -1 } . For M10 , we calculate a central velocity dispersion of \sigma _ { 0 } = 5.44 \pm 0.61 km s ^ { -1 } , which gives a ratio of the amplitude of rotation to the central velocity dispersion V _ { rot } / \sigma _ { 0 } = 0.21 \pm 0.04 . We also explored the rotation of the multiple stellar populations identified in M10 and M71 and found rotation ( or lack thereof ) in each population consistent with each other and the cluster global rotation signatures .