Le but de cette étude est la recherche des possibilités et des limites de l’emploi des recouvrements de clichés.

Le travail n’est pas terminé. Un travail plus complet sera publié dans quelques mois.

The use of the conditions imposed by the appearance of one star on more than one photographic plate to strengthen the determination of the relationship between the measurement coordinate systems and the system of celestial right ascension and declination, was first advocated by Eichhorn (1960), and since then various reduction procedures have been proposed to incorporate these conditions in the plate-reduction process (Eichhorn, 1963; Henriksen, 1964; Lacroute, 1964; Googe, 1967; Clube, 1967). During the last several years at the Army Map Service the overlap method has been developed and used in several astrometric projects, and the purpose of this paper is to summarize the main features of the algorithm and some of the projects to which it has been applied.

The usual procedure for deriving standard coordinates ξ,η from the measured rectangular coordinates x, y of a star is to adopt a suitable model for the relationship between the measured x, y, magnitude m, color index c and the ξ, η. This relationship may, in general, be written as

From the known standard coordinates ξr, ηr of some reference stars equally distributed over the plate area, the unknown plate constants aijkl, bijkl are found from a least-squares adjustment. After the adjustment the standard coordinates of each field star can be computed. In most cases a statistical criterion for the choice of the proper form of the above relationship between measured and standard coordinates may be useful because the systematic accuracy, obtained from the adjustment, may be seriously affected by the number of unknown parameters included. (Eichhorn et al., 1967). If the same star occurs on two or more plates, i.e. the plates being partly overlapped, one gets the final position by taking the mean of the individual positions on each plate. In this procedure, no direct account is taken of the ‘overlap’ in the equations of condition for the desired plate constants.

An account is given of an investigation to obtain accurate relative star positions from overlapping photographic plates. The method described is quite general, but in the first instance is to be applied to plate material obtained with the new Cape astrometric camera.

The Cape 4-component f/10 20-cm astrometric camera produces a field of 5° square with a scale of 100″ per mm in the focal plane. The telescope is fitted with a yellow filter 12 mm from the focal plane, which in combination with the Ilford-R40 emulsion used, transmits more or less uniformly in the range 5300<λ<6500 and little elsewhere. Within this spectral range, the maximum longitudinal aberration is only 0·75 mm and the images sensibly round out to the edge of the plate. The instrument is currently being used to obtain a complete coverage of the Southern hemisphere down to mv~11·5 such that each plate, effectively 4° square, has overlapping plates centred at each corner and at the middle of each side. In practice, this system of overlapping is applied to a number of zones in declination each about 10° broad. Each plate is taken within 30m of the meridian and is given two 3m exposures above and below the 1950 standard positions, the geometrical plate centre being estimated to be within 20″ of the tangential point. At the time of writing, coverage of the zone −30° to −52° is almost complete, and preparations for the zone 0° to −30° well advanced.

Extragalactic radio sources can be grouped spectroscopically into those that show absorption lines produced by a stellar population (e.g. the nearer radio galaxies, and some more distant ones, usually of D or E type) and those that show only lines (usually in emission) produced by low-density gas (e.g. QSO’s and many N-type galaxies). If absorption lines from stars are present, one can estimate a minimum age from the stellar population, and perhaps a mass for the system from the stellar velocity dispersion. If no spectroscopic evidence on the stellar population is available (and this includes evidence from narrow-band filter photometry), then we have much less hold on the problems of age and evolutionary state. Absence of stellar absorption lines does not necessarily mean that stars are absent, but simply that their light, if present, does not contribute appreciably to the overall optical spectrum.

Complete information about the angular sizes and structures of discrete radio sources would, in principle, require observations in many position angles and at a large number of resolving powers, of which the highest power must resolve the smallest significant features in the sources. Since some sources are known to have components with differing radio spectra, similar amounts of data would be required at each of several wavelengths. One would then be able to examine statistically the relation between fringe visibility and resolving power at two or three wavelengths, and hence search for structural differences between different types of discrete sources.

During the past few years there has been a large increase in the available data on the spectra of radio sources, particularly at short wavelengths, where a number of sources have shown unexpectedly large time variations, with time-scales of 1 year or less.

The simple power-law spectrum, which is a straight line on a log-log plot of flux density against frequency, is shown by about 30% of sources. Most sources have a spectrum with negative curvature, which steepens at high frequencies. Many have a sharp cut-off, which is almost certainly due to synchrotron self-absorption, at low frequencies. In several of these sources, such as 3C 48, 3C 147 and 3C 295, the spectrum begins to flatten at a considerably higher frequency than the cut-off frequency. This flattening is too sharp to be caused by a change in the energy distribution of the electrons and is probably due to parts of the source becoming optically thick at higher frequencies. Some sources have components which are optically thick even at centimetre wavelengths. These must have angular sizes of 10−3″ or less. The energy density in relativistic electrons in these compact sources is much larger than the magnetic-energy density, so that the source cannot be stable and variations in the flux density are to be expected.

In this paper I shall consider briefly two major questions. The first is concerned with whether the QSO’s are at cosmological distances or not. The second is concerned with the theoretical models proposed to explain the observed properties of radio galaxies and quasi-stellar objects.

In the Invited Discourses Dr. Sandage and Sir Martin Ryle gave arguments which lead them to believe that the QSO’s lie at cosmological distances. They both have strong convictions in this matter. However, Dr. Sandage did remark that he was only giving one side of a ‘great debate’. It is presumably up to me to give the other side of this argument. I have no strong beliefs in this matter but it appears that on the basis of the evidence as it is today we cannot reasonably assert that the QSO’s are at cosmological distances.

There seem to be two promising ways of investigating the evolution of radio sources: (a) the collection of data on a large number of sources so that attempts may be made to arrange them in an evolutionary sequence, (b) the study of a few sources, for which really detailed information is obtainable, to gain insight into the physical mechanisms occurring.

It is important to distinguish between the most powerful radio sources, the majority of which appear to have a simple double structure at the resolutions now attainable, and the more complex sources. The structure of the latter suggests that energetic particles have been accelerated in multiple ‘events’, each being of smaller magnitude than the events which give rise to the double sources; the total energy released may, however, be comparable.

Although the energy problem is one of the main difficulties of the cosmological interpretation of quasar red-shifts, there is no need to go beyond conventional physical laws in seeking an explanation. Various proposals have been made which differ in important details. I believe a suitable basis for a theory of quasars to be a supermassive plasma configuration, the matter of which is in mostly regular motion in a magnetic field. Such a magnetodynamic configuration I shall call a ‘magnetoid’. On this model a quasar is a galaxy with a dense non-stellar nucleus, the magnetoid, which gives rise to the characteristic non-thermal luminosity. The mass of the quasar is determined by its stars while the parameters of the magnetoid depend on the stage of evolution or conditions of formation in a similar way to those of radiogalaxies or active nuclei of galaxies.

It has often been suggested that the energy supply of a quasar is derived from a central body with a mass of 109−1010M⊙. However, it is known that such bodies have no stable and static equilibrium configurations beyond a relatively low degree of condensation. Only a very limited amount of energy can be extracted before instability sets in. Basically the instability is due to the dominance of radiation pressure in supporting the mass against its self-gravitation.

But if a massive object is in rapid rotation, then it is partly supported by centrifugal force, and is much less liable to an instability of this kind. It is therefore interesting to investigate the properties of a rotating disk-like object with a mass of the order of 109−1010M⊙, and to see whether its overall properties match those of any quasar. The most important parameters are 2σ0, the mass per unit area of the disk, and Z, its half-thickness. In the case of the quasar 3C 273 B, assumed to be at a distance of 450 Mpc, the most suitable pair of values are σ0 = 107 gm/cm2 and Z = 1016 cm.

The 4th edition of the Finding List for Observers of Eclipsing Variables (Koch et al, 1963) contains 145 sufficiently well-observed eclipsing binaries brighter than 8·5m at maximum light. Among them, 59 binaries, or 41%, are systems with both components on the main sequence. The second largest group, 52 binaries or 36% of all systems, are systems similar to Algol. These can be characterized as follows:

1. (1) The primary (more massive) components are main-sequence stars, fitting well into the mass-luminosity relation defined by visual binaries and by eclipsing binaries with both components on the main sequence (detached systems).

2. (2) The secondary components are of later spectral type than the primaries, and can be best characterized as subgiants. They are overluminous for their mass as well as for their spectral class.

3. (3) As a rule, the secondary components fill their respective critical Roche lobes (innermost Lagrangian surfaces).

I shall discuss here the evolution of massive binaries in the case B. In this case the initially more massive component fills up the Roche lobe after the exhaustion of hydrogen in the core. By a massive binary I understand the binary in which the phase of a rapid mass exchange is terminated by helium ignition in the core of the initially more massive star. The helium ignition stops the contraction of the core and the expansion of the envelope of that component. In a small mass star the degeneracy plays the role of helium ignition in this respect. The last case will be discussed by Dr. A. Weigert in his lecture.