Today we know accurate masses, radii, surface gravities and luminosities or effective temperatures of a very small number of stars. There are several reasons for deriving accurate parameters of stars. I shall mention only four problems:

1. (i) checking stellar evolution calculations, particularly calculations of isochrones, using binaries,

2. (ii) derivation of helium content in stars of different age,

3. (iii) checking log g derived from photometry and stellar atmosphere calculations,

4. (iv) determination of accurate positions in the HR diagram to get an independent check on calibrations of photometric systems.

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.

There has existed for some years a generally accepted conceptual scheme of stellar evolution as reflected in HR diagrams. Such evolutionary sequences are normally only apparent in stellar clustering where, in the first order at least, coeval formation is assumed. Such observational evidence of evolutionary sequences is directly dependent upon the identification of cluster membership. Only in very recent years have the necessary high precision and full membership based independently upon proper motion become available for a significant sample of clusters. The result of these studies for some sample cluster C-M diagrams are discussed and some possible difficulties with our evolutionary scheme are evidenced.

Strömgren (1966) set up the four-color system of photometry as a means of studying early-type stars in the spectral range 0 through F. In this spectral range one of the important measures that can be made of a stellar spectrum is the magnitude of the Balmer jump. For stars of a given (b-y) color the discontinuity is very large for stars of high luminosity and small for low luminosity stars. For very hot stars (0 and B stars) this luminosity effect becomes too small to be used as a luminosity indicator, but because of this insensitivity to luminosity changes the magnitude of the Balmer discontinuity becomes a temperature indicator (see Philip and Newell 1974 and Davis and Shobbrook 1977). Photoelectric measures of the strength of the Hß line can be used in a similar, but reverse, manner. For the B and O stars the index is a measure of luminosity; for late A and F stars the index is a good temperature index. In the spectral range A0-A3 both the Balmer jump and the Beta index are functions of temperature and luminosity. For a bibliography of the many uses of Strömgren four-color and Hß photometry see the paper prepared by Philip and Perry (1977).

Given the angular diameter and total energy flux of a star, its effective temperature can be determined. Until recently, there were few well-determined angular diameters of cool stars, and effective temperature calibrations rested on angular diameter measurements of several not necessarily “normal” stars. The number of measured angular diameters of stars cooler than about spectral type G is steadily being increased by using the method of photoelectric observations of lunar occultations.

To place a star on the HR diagram by means of spectroscopic data alone-i.e., without knowledge of the parallax-one must separate the spectroscopic effects of temperature and luminosity as cleanly as possible. Here we discuss the use of the red and near-infrared bands of TiO, VO, CN, and CaH as classification criteria for M stars. Our eight-color system of filter photometry (Wing 1971; White 1971a) has provided data on the first three molecules.