The attainable accuracy of photographic trigonometric parallaxes may be improved by the use of modern measuring engines, larger number of exposures, facilitated by increased speed of emulsions, more refined knowledge of reduction to absolute parallax. Systematic errors remain an obstacle both in trigonometric and statistical parallaxes.

With an attainable goal of ±0″.002 for the probable error of a parallax it appears difficult to obtain absolute magnitudes with a probable error less than 0.2 mag. for stars beyond 20 pc.

A brief review is given of the several ways in which stellar motions may be used statistically. In the case where the motions of all stars shown on plates of certain regions are measured these are generally used to determine kinematical relations in the Galaxy and only secondarily for the estimation of luminosities; when motions are measured for special groups of stars the solar motion is first determined and then used for the calculation of distances and luminosities.

The importance of red and infrared magnitudes for late dwarf M-type stars is stressed. The absolute magnitudes for the nearest stars with (R − I) ⩾ 1.20 is re-assessed.

By a method based on the principle of maximum likelihood, we obtained for a sample of 102 RR Lyrae stars and σMpg = 0.5 ± 0.2. We could not confirm the results of Clube and Jones (1971). The study of the correlations between , the period, the abundance parameter ΔS and the light variation amplitude showed that on ground of the present data, no significant correlation can be established.

A list is presented of very probable Hyades cluster members that are suitable for an accurate determination of the cluster's trigonometric parallax.

A photometric method, using the U B V B1B2V1G system, is suggested to determine the distance of clusters. This method based on the assumption that stars with same seven colours have also same absolute visual magnitude is applied, as an example, to Hyades and Praesepe.

Four ultraviolet fluxes measured in U2 (centered at λeff 2300 Å) by the Celescope experiment aboard OAO 2, reveal an important flux difference between Pleiades and Hyades stars. Available blanketed stellar models show that the difference is too large to be understood as a blocking effect for admissible metal overabundance in Hyades stars. Known rotation and presence of Ap and Am stars in the Hyades and Pleiades apparently cannot account for the discrepancy.

Photo-electric measures of Hα and Hβ have been made in an attempt to confirm the scatter in the Luminosity-Balmer line relation predicted by Hardorp and Strittmatter as an effect of Stellar rotation.

The effects of rotation on the determinations of absolute magnitudes by means of the c1 vs (b – y) and d vs (B2 – V1) diagrams are discussed.

Attention is drawn to important systematic effects in the calibration procedure due to the accidental errors in the measured luminosity criteria. The present state of the luminosity calibrations in the MK system is reviewed with reference to recent work based on proper motions and radial velocities, and on trigonometric parallaxes, resulting in evidence for corrections of about −0.4 mag. for the K0–K5, III stars. Brief reference is made to the developments with regard to the Mv(K) system.

The present report summarizes the principal elements of the review presented at the symposium.

Concerning the absolute magnitudes of the giant stars contained in the Mt. Wilson catalogue of Adams et al., the following facts are pointed out:

1. (1) There is a linear relation between the Mt. Wilson magnitudes and the absolute magnitudes derived on account of the Wilson-Bappu effect (Figure 1). The scale factor is 2.3.

2. (2) The accuracy of the properly scaled Mt. Wilson magnitudes follows from the scatter in relation (1) and the accuracy of the Wilson-Bappu magnitudes (± 0.6). It is ± 0m.6 (mean error).

3. (3) The assured reliability of the corrected Mt. Wilson magnitudes allows a subdivision into bright, intermediate and faint giants (Figure 2). The 3 subgroups exhibit different 2-colour relations (Figures 3, 4, 5).

4. (4) The large number of giant stars present in the Mt. Wilson catalogue allows a trustworthy derivation of the mean absolute magnitudes of giant branch stars (Figure 6) and an estimate of its dispersion as well (Figure 7).

Bright fine mottles seen on the solar disk are identified as the agency that locates the Sun on the K-line width-absolute magnitude relation of Wilson and Bappu. The contribution of the supergranular network emission and the plage emission from centres of activity tends to upset the uniqueness of the relation. The line width-absolute magnitude relation is thus a characteristic of the convection zone underlying the stellar atmosphere.

Calibration curves giving Mv for stars of luminosity classes III, II, Ib, Iab and 0 are derived and shown graphically in the HR diagram. There are serious gaps in which the calibration needs to be improved.

The calibration of the BCD stellar classification in absolute magnitudes (classification in three parameters λ1, D, Φb) was used to determine the distance modulus of the Large Magellanic Cloud. The described method makes use of the spectrophotometric parameters of B and A supergiants of the Large Cloud and gives a value of the distance modulus which is independent from other determinations, in particular from those which are based on the RR Lyrae and the Cepheid variables. The value found for the distance is slightly smaller than those generally admitted. The results are still based only on a limited number of measurements and new observations are in process; however, it seems doubtful that one will obtain much larger values. In other respects, the observations have shown that the parameter λ1 was still sensitive to luminosity for the B and A stars brighter than M = −8 and that the calibration of the λ1D diagram in absolute magnitudes can be extended up to M = −9.

Spectroscopic and photometric parallaxes are based on the assumption that to each point in the relevant region of (g, Teff, a)-space there corresponds a unique mass. The implications of a breakdown in this assumption are discussed briefly and an alternative approach to problems that traditionally have required spectroscopic or photometric parallaxes is presented. This alternative approach involves the use of the (log g, log Teff)-diagram as an HR-diagram.

The history and status of Balmer hydrogen-line photometry are briefly reviewed, and problems associated with calibrations in general are commented on.

The calibration work at Kitt Peak is described in some detail for B, A, and F type stars. The data used, the determination of intrinsic colours and colour excesses, photometric classification, and the relation of our indices to other people's are reviewed. With this background, the procedure used in establishing the absolute magnitude — Hβ calibration is given, and the preliminary calibration is presented. Finally, the work remaining to be done before the calibration is final is noted, and a comparison is given to Blaauw's zero-age main sequence calibration.

The dependency of the Hβ-index on two physical parameters is briefly discussed. The previous calibration of Mv(β) (Fernie, 1965 or Crawford, 1971) is confirmed for main sequence O and B stars; however, the β-values of the later B-supergiants tend to be too large for their absolute magnitudes. The problem of filtering out stars with marginal emission is emphasized.

It is possible to obtain for the stars of the spectral type included between A0 and G5 three parameters respectively correlated with the effective temperature, the luminosity and the blanketing. A method to determine the absolute magnitude is given.