We use the Stripe 82 proper motion catalogue of Bramich et al .
( 14 ) to study the kinematics of Galactic disk stars in the solar neighborhood .
We select samples of dwarf stars with reliable spectra and proper motions .
They have cylindrical polar radius between 7 \leqR \leq 9 kpc , heights from the Galactic plane satisfying |z| \leq 2 kpc and span a range of metallicities -1.5 \leq [ { Fe / H } ] \leq 0 .
We develop a method for calculating and correcting for the halo contamination in our sample using the distribution of rotational velocities .
Two Gaussians representing disk and halo populations are used to fit the radial ( { v _ { R } } ) and vertical ( { v _ { z } } ) velocity distributions via maximum likelihood methods .
For the azimuthal velocities ( { v _ { \phi } } ) the same technique is used , except that a skewed non-Gaussian functional form now represents the disk velocity distribution .
This enables us to compute the dispersions \sigma _ { R } , \sigma _ { z } , \sigma _ { \phi } and cross-terms ( the tilt \sigma _ { Rz } and the vertex deviation \sigma _ { R \phi } ) of the velocity ellipsoid as a function of height and metallicity .
We also investigate the rotation lag of the disk , finding that the more metal-poor stars rotate significantly slower than the metal-rich stars .
These samples provide important constraints on heating mechanisms in the Galactic disk and can be used for a variety of applications .
We present one such application , employing the Jeans equations to provide a simple model of the potential close to the disk .
Our model is in excellent agreement with others in the literature and provides an indication the disk , rather than the halo , dominates the circular speed at the solar neighborhood .
We obtain a surface mass density within 1.1 kpc of around 66 \ > { M } _ { \odot } { pc } ^ { -2 } and estimate a local halo density of 0.015 \ > { M } _ { \odot } { pc } ^ { -3 } = 0.57 \ > { GeV cm ^ { -3 } } .