  We measure and analyse the clustering of the Baryon Oscillation Spectroscopic
Survey (BOSS) relative to the line-of-sight (LOS), for LOWZ and CMASS galaxy
samples drawn from the final Data Release 12 (DR12). The LOWZ sample contains
361\,762 galaxies with an effective redshift of $z_{\rm lowz}=0.32$, and the
CMASS sample 777\,202 galaxies with an effective redshift of $z_{\rm
cmass}=0.57$. From the power spectrum monopole and quadrupole moments around
the LOS, we measure the growth of structure parameter $f$ times the amplitude
of dark matter density fluctuations $\sigma_8$ by modeling the Redshift-Space
Distortion signal. When the geometrical Alcock-Paczynski effect is also
constrained from the same data, we find joint constraints on $f\sigma_8$, the
product of the Hubble constant and the comoving sound horizon at the baryon
drag epoch $H(z)r_s(z_d)$, and the angular distance parameter divided by the
sound horizon $D_A(z)/r_s(z_d)$. We find $f(z_{\rm lowz})\sigma_8(z_{\rm
lowz})=0.394\pm0.062$, $D_A(z_{\rm lowz})/r_s(z_d)=6.35\pm0.19$, $H(z_{\rm
lowz})r_s(z_d)=(11.41\pm 0.56)\,{10^3\rm km}s^{-1}$ for the LOWZ sample, and
$f(z_{\rm cmass})\sigma_8(z_{\rm cmass})=0.444\pm0.038$, $D_A(z_{\rm
cmass})/r_s(z_d)=9.42\pm0.15$, $H(z_{\rm cmass})r_s(z_d)=(13.92 \pm 0.44)\,
{10^3\rm km}s^{-1}$ for the CMASS sample. We find general agreement with
previous BOSS DR11 measurements. Assuming the Hubble parameter and angular
distance parameter are fixed at fiducial $\Lambda$CDM values, we find $f(z_{\rm
lowz})\sigma_8(z_{\rm lowz})=0.485\pm0.044$ and $f(z_{\rm
cmass})\sigma_8(z_{\rm cmass})=0.436\pm0.022$ for the LOWZ and CMASS samples,
respectively.
