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The reduced proper motion diagram (RPMD) for a complete sample of faint starswith high accuracy proper motions in the North Galactic Pole field SA57 isinvestigated. Eight stars with very large reduced proper motions are identifiedas faint white dwarf candidates. We discriminate these white dwarf candidatesfrom the several times more numerous QSOs based on proper motion andvariability.  We discuss the implausibility that these stars could be any kind of surveycontaminant. If {\it bona fide} white dwarfs, the eight candidates found hererepresent a portion of the white dwarf population hitherto uninvestigated byprevious surveys by virtue of the faint magnitudes and low proper motions. Thenewly discovered stars suggest a disk white dwarf scaleheight larger than thevalues of 250-350 pc typically assumed in assessments of the local white dwarfdensity. Both a <V/V_{max}> and a more complex maximum likelihood analysis ofthe spatial distribution of our likely thin disk white dwarfs yieldscaleheights of 400-600 pc while at the same time give a reasonable match tothe local white dwarf volume density found in other surveys.  Our results could have interesting implications for white dwarfs as potentialMACHO objects. We can place some direct constraints (albeit weak ones) on thecontribution of halo white dwarfs to the dark matter of the Galaxy. Moreover,the elevated scale height that we measure for the thin disk could alter theinterpretation of microlensing results to the extent of making white dwarfsuntenable as the dominant MACHO contributor. (Abridged)Comment: 38 pages, 5 figures, to appear in April Ap

Absolute Proper Motions toB ∼ 22.5. IV. Faint, Low‐Velocity White Dwarfs and the White Dwarf Population Density Law