The recent discovery that the parallax star LP701-29 is a white dwarf has firmly extended the degenerate sequence below MV = +16m (Dahn et al. 1978). As the search for white dwarfs extends to cooler and fainter stars, however, it becomes particularly important to develop a plan for selecting candidates among the many thousands of red proper motion stars. We begin by assessing the completeness of the known sample within 10 parsecs in the northern two thirds of the sky. Some color-dependent selection effects must be evaluated, however, since these may preferentially inhibit the discovery of cooler stars. A correction factor for the missing low velocity white dwarfs is estimated. Then, Green's(1977) recent determination of the number density of blue degenerates is used to normalize various theoretical luminosity functions, the benchmarks against which the current sample out to 10 pc can be compared. It is concluded that the sample may be approaching completeness in the northern sky for white dwarfs with tangential velocities (vT) ≥ 40 km/sec (μ ≥ 1″.0/yr.) and Mbol < +15m. The implied luminosity function is thus consistent with that found by Sion and Liebert (1977). Below Mbol = +15m the different theoretical functions predict substantially different numbers.