  We report the first measurements of the inelastic spin exchange collision
rate between the Hyperfine (HF) levels of antiprotonic helium. We measure the
time dependent evolution of the (37, 35) substates to obtain an inelastic
collision rate which qualitatively agrees with recent theoretical calculations.
We evaluate these results by using the obtained rate as a parameter in a
rigorous simulation which we then compare to to previously measured data. We
find that our measurement slightly underestimates the collision rate and
therefore conclude that the actual value most probably falls within the upper,
rather than lower, limit of the error.
