stars[@carlin12; @koposov13; @sohn15], and hence we can provide a further test of our SDSS-*Gaia* proper motions. Note that we use RRL stars (rather than BHBs or K giants) in Sgr as these stars have the most accurate distance measurements, and thus Sgr members can be identified relatively cleanly. We identify Sgr stars according to position on the sky $(\alpha,\delta)$ and heliocentric distance using the approximate stream coordinates used by [@deason12b] and [@belokurov14]. The top panel of Fig. \[fig:sgr\_pms\] shows that our distance selection of Sgr stars agrees well with the [@law10] model. Our selection procedure identifies $N=830$ candidate Sgr associations, which corresponds to roughly 10% of our RRL sample.

In Fig. \[fig:sgr\_pms\] we show proper motions in Galactic coordinates ($\mu_\ell, \mu_b$) as a function of longitude in the Sgr coordinate system (see @majewski03). The red and blue points show the leading and trailing arms of the [@law10] model of the Sgr stream. Note that we only show material stripped within the last 3 pericentric passages of the model orbit. The black filled squares show the median SDSS-*Gaia* proper motions for RRL stars associated with the Sgr stream in bins of Sgr longitude, and the error bars indicate $1.48 \, \mathrm{MAD}/\sqrt{N}$, 