have obtained long-slit spectroscopic follow-up data for 13 additional candidate binaries to date and all have turned out to be comprised of white dwarfs, confirming the low level of contamination.

System 1 and System 2 are two of these 13 pairings which both appear to harbour a HFMWD. Their components are separated on the sky by only 4.35 arcsec and 5.05 arcsec, respectively. Their $u$, $g$, $r$, $i$ and $z$ magnitudes are listed in Table \[phot\]. To ascertain the likelihood of chance alignments we have used Equation 1 [@struve52], under the assumption of a random on-sky distribution of objects, where $N$ is the number of sources satisfying the photometric selection criteria in area $A$ (square degrees) and $\rho$ is the maximum projected separation (degrees).

$$\begin{aligned}
n(\le\rho)= N (N-1) \pi \rho^{2} / 2 A\end{aligned}$$

We estimate $n$(4 arcsec$<$$\rho$$\le$6 arcsec)$\sim$0.3 for $N$=36231 and $A$=11663 square degrees. In the course of our survey we have unearthed a total of 10 pairs of objects with separations in this range, suggesting that the probability of any one being a mere chance alignment is P$\sim$0.03.

Astrometric follow-up and proper motions
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To probe the reality of the putative associations between the two sources in each of 