Previous studies have shown that the observed temperature anisotropies of
protons and alpha particles in the solar wind are constrained by theoretical
thresholds for pressure-anisotropy-driven instabilities such as the
Alfv\'en/ion-cyclotron (A/IC) and fast-magnetosonic/whistler (FM/W)
instabilities. In this letter, we use a long period of in-situ measurements
provided by the {\em Wind} spacecraft's Faraday cups to investigate the
combined constraint on the alpha-proton differential flow velocity and the
alpha-particle temperature anisotropy due to A/IC and FM/W instabilities. We
show that the majority of the data are constrained to lie within the region of
parameter space in which A/IC and FM/W waves are either stable or have
extremely low growth rates. In the minority of observed cases in which the
growth rate of the A/IC (FM/W) instability is comparatively large, we find
relatively higher values of $T_{\perp\alpha}/T_{\perp p}$
($T_{\parallel\alpha}/T_{\parallel p}$) when alpha-proton differential flow
velocity is small, where $T_{\perp\alpha}$ and $T_{\perp p}$
($T_{\parallel\alpha}$ and $T_{\parallel p}$) are the perpendicular (parallel)
temperatures of alpha particles and protons. We conjecture that this observed
feature might arise from preferential alpha-particle heating which can drive
the alpha particles beyond the instability thresholds.
