A number of recent investigations have demonstrated that the heavy element abundance in galactic disks decreases with increasing distance from the center. Although there is little question that the composition in the outermost parts of galactic disks differs from that in the inner regions, the precise nature of the presumed gradient in our own galaxy remains undetermined. At the present time, the most specific evidence for a gradient is based either on kinematics of stars in the solar vicinity (e.g., Janes, 1975 or Mayor, 1976) or on observations of distant H II regions (Hawley, 1977) and planetary nebulae (Peimbert, et al, 1977). Little is known about the variation of abundance ratios with position or the relation between stellar ages and the composition gradient. However, all three of these quantities (that is, the overall metallicity gradient, variation of abundance ratios and stellar age effects) can now be estimated from theoretical models of galactic evolution (for example, see Tinsley and Larson, 1977).

The published data on chemical abundances derived from fine analysis for about 80 G, F and A main sequence stars are analysed. The following conclusions are drawn :

Extensive recent infrared observations of carbon stars (Gillet et al. 1971, Hackwell 1972, Morrison and Simon 1973) have shown that spectra of some cool variable carbon stars reveal infrared excesses, which are believed to be due to thermal radiation of the dust envelopes surrounding these stars. Observations of the visual intrinsic polarization made by Dyck et al. (1971) have confirmed this discovery. The relation existing between stars loosing their mass and those revealing the infrared excess (Geisel 1970) gives evidence for the reality of mass loss from cool variable carbon stars. On the other hand, several investigations (Kamijo 1967, Donn et al. 1968, Salpeter 1974), although differing considerably in details, do agree that conditions in the atmospheres of cool carbon stars are appropriate for the condensation of carbon grains. Hence, it is believed that evolutionary advanced cool variable carbon stars supply carbonaceous material, mainly graphite, into the interstellar matter, in which carbon seems to be the major constituent (Donn et al. 1968).

All stars in the mass interval 1-4Mʘ probably evolve through a double shell source phase before losing their entire envelopes through stellar wind and the ejection of planetary nebula shells. The remnant carbon-oxygen core rapidly evolves to a blue nucleus, illuminates the surrounding nebula for a few tens of thousands of years and finally cools off as a white dwarf (Paczynski, 1970, Harm and Schwarzschild 1975). A large fraction of the mass contained in the main-sequence stars of mass 1-4Mʘ thus returns to the interstellar medium. A common feature of the double shell source (DSS) evolution of stars is the occurrence of He shell flashes. Evolutionary studies by Schwarzschild and Harm (1967), Iben (1975) and others show that the flash-driven convection zone carries helium burning products towards the hydrogen-rich layers. The consequences of mixing between the outer convective envelope and the intershell region have received a great deal of attention in recent years particularly in connection with the interpretation of carbon stars. If a deep temporary convection zone exists extending from the surface of the star to a point near the helium burning shell and mixing is allowed to take place for sufficiently long time Sackmann, Smith, and Despain (1974) found that the flash-produced 12C underwent further ON0 processing enriching the surface of the star in 12N. Iben (1976) has also speculated on the possibility of surface enrichment of 14N during the DSS evolution of intermediate-mass stars. The subsequent loss of this envelope as a planetary nebula shell can thus cause nitrogen enrichment of the interstellar gas. In the present work we have evaluated the extent of this enrichment and have also derived the gradient of nitrogen abundance in the disc of the Galaxy based on the simple model of galactic evolution due to Talbot and Arnett (1973, hereinafter TA).

Larson has emphasized at this meeting that one relation which is valuable in determining the correct model for the formation of the Galactic disk is the dependence of stellar abundances on the time of formation of the disk stars. While Mayor has demonstrated that correlations exist between metal abundance and both kinematics and positions of stars in the disk, Larson has suggested that it is possible in an extreme infall model to have such trends and still have no age dependence.

Among the observations of heavy s-process elements at the surface of very metal poor stars (population II stars), Peterson 1976 and Spite and Spite 1977 recently showed that the ratio of the abundances of these elements against that of Fe increases with increasing [Fe/H].

A new study of carbon and nitrogen abundances has been carried out for a sample of halo dwarf stars. This sample was limited to relatively bright high velocity stars with substantial metal deficiencies (-0.65≥[Fe/H]≥ −2.00). Synthesis of CH molecular bands for nine program stars indicates that [c/Fe] = −0.1±0.2 in halo stars. Preliminary results of the NH synthesis in two stars shows discrepant results: a moderate velocity star has [N/Fe]≲ −1.0 while a very high velocity star has [N/Fe]⋍ +0.0. Implications of these abundances for galactic chemical evolution are discussed.

It is obviously interesting to study in detail the chemical composition of extreme Population II stars since they may give indications about the processes which took place in the very first ages of the Galaxy.

It is well known that de abundance of metals in the stars of extreme Population II are smaller than in Population I stars, but it is not yet clear from the literature if all the metals, in all the metal deficient stars, are deficient by the same factor or not. However some anomalies were shown in some halo stars : over-deficiency of barium, “s process” element (Pagel 1965), over-deficiency of odd elements (Arnett 1971, Peterson 1976). These differences are however difficult to measure and are not very much larger than the possible errors of the analysis, so that according to Trimble 1975 they are “not proven”.

Many recent observations have indicated variations of metallicity within our Galaxy. Apart from a general negative radial abundance gradient indirect evidences suggest the existence of spatial chemical inhomo-geneities in different regions of the galactic disk. Since this problem is of great importance in providing clues to processes of nucleosynthesis and galactic structure and evolution, it seems to be interesting to examine if these spatial inhomogeneities have any systematic character and if they are correlated with position of spiral arms.

A large amount of work has been devoted to correlations between kinematic properties and spectral types in order to improve our knowledge of stellar populations in our Galaxy and hence to deduce its structure and evolution. The classical results will not be repeated in the present review paper. However, emphasis will be laid on the sometimes contested correlations between age, abundance, kinematic properties and position in the Galaxy.

The main steps of the non-linear theory of spiral structure are described. Near each of the main resonances the basic periodic orbits are calculated, and the sets of non-periodic orbits that follow them are found. A different integral of motion is applicable for each set, besides the Jacobi integral. Then the initial distribution function, f, is expressed as a function of the two integrals and the corresponding angles. The final distribution function is found by averaging over the angles: Then by integrating over all velocities we find the response density σresp. In order that σresp should be equal to the imposed density, σimp we must adjust the parameters of the imposed spiral field. The form of σresp away from resonances can be derived explicitely for tight ana open spirals or bars; however near the resonances σresp can be only calculated numerically. If the imposed field has almost constant amplitude, then the amplitude of the response is very large near the Inner Lindblad Resonance. In the case of a tight spiral the azimuth of the response density maximum with respect to the imposed density maximum tends to zero outside the ILR, while it tends to -90° inside the ILR. One possible self-consistent solution has zero amplitude inside the ILR both in the case of tight spirals and of bars. Finally an important quadrupole term was found near the ILR.

At least three component parts of the galaxy must be recognized. The Disk Component of the galaxy might be defined as follows. Spatially it is largely confined between the planes ± 1 kpc from the plane of symmetry. With regard to velocities, it is a cold subsystem in that the random motions within it (~ 20 km/s) are small compared to the systematic flow of rotational motion (~ 200 km/s). Finally, its composition is largely stellar with stars of all ages and masses being present. Few galaxies are known where the ratio of (gas/stellar) mass is > 10% (cf. Roberts 1975a), and the metal abundance is typically high with at most one percent of the stars having metallicity less than 1/4 that of the Sun (cf. Schmidt 1963). From this point of view the spiral parts are a relatively unimportant (in terms of mass and composition) sub-part of the disk system.

There exist two basically different approaches to the explanation of the structure and the evolution of galaxies. The conventional one is to consider galaxies as isolated self-regulating systems. This approach is, of course, largely justified. To illustrate the essential independence of the properties of galaxies from their intergalactic environment, it is enough to compare the mean densities within galaxies (10-24gcm-3) to the mean cosmological density (≲10-29 gcm-3).

According to the consequences of the density wave theory of spiral structure a shock wave is triggered in the interstellar gas leading to the formation of new stars (Roberts, 1969). The space and velocity distribution of the newly born stars is similar to those of the diffuse material which they have been formed from, i.e. they are strongly concentrated to the Galactic plane and have nearly circular velocities and small velocity dispersions. The velocity dispersions could increase in course of time by different stellar dinamical processes: encounters with large clouds of stars and gas (Spitzer and Schwarzschild, 1953; Julian, 1967; Barbanis and Woltjer, 1967), cooperative phenomena (Lynden-Bell, 1967), effect of non periodic orbits (Wielen, 1975), etc. If some of this processes has a time scale comparable with the time the star streeming needs between two consecutive passages of the density wave one expects an observable effect in the space distribution of A and late B type stars perpendicular to the Galactic plane. The Δt time difference between two consecutive passages equals 2.5×108 years near the sun. If the lifetime of stars is greater than this value their space distribution is a superposition of newly born stars with small velocity dispersion and stars born earlier and having greater velocity dispersion already. (Fig. 1.)

The concepts of a local standard of rest and a standard solar motion and the nature of the data giving rise to these concepts are so much part of the given knowledge of galactic astronomy that it hardly seems possible that anything new might be learnt from continued study of this subject. But the examination of local stellar kinematics is by no means a tidy subject, and the history of its development does conceal one or two peculiarities which bear reconsideration.

Since the density wave theory was introduced by Lin and Shu (1964) to explain the spiral structure considerable effort has been made to detect this kind of wave in our galaxy and to determine its parameters. Observations of the distribution and velocity field of gas and young objects show the present shape and location of the spiral pattern in our galaxy but tell little about its angular velocity. It was proposed by Strömgren (1967) to estimate this important parameter by calculating the places of formation of moderately young stars for which accurate space velocities and ages are known. This was done assuming that the majority of stars is formed in spiral arms so that the stellar birthplaces would outline the position of the spiral pattern at different epochs. Later, Yuan (1969) and Wielen (1973) calculated stellar birthplaces in the spiral potential given by Lin et al. (1969). These investigations showed no disagreement with the assumed density wave, however, the number of stars was too small to verify the assumed pattern speed.

It is believed that kinematical characteristics of a group of stars, as the velocity dispersion or the lag in rotation, change systematically with time. This kinematical evolution is widely used for the determination of stellar ages. In particular, velocity dispersion should increase with time owing to irregular galactic force field. A classical formula for the increase of stellar velocity v with the age τ

At Tbilissi, Prof. Blaauw (1975) reported on results of uvby photometry of F-type stars and showed a relation between the quantity Δm and the distance z to the galactic plane. This relationship could be interesting if Δm1 is a non ambiguous indicator of metallicity. It was found that the mean relative metal abundance decreases by a factor of about one third between 0 and 700 pc. The same type of relationship was obtained by M. Grenon (1976) for K giants and shows a lower variation of the metallicity with z.

The basic model of our Galaxy, like the Schmidt (1965) model, obeys the density law ρ(R) for the Galaxy based on divers evidence, less or better known from observation. The interpretation of the interstellar hydrogen radio profiles yields the rotation curve and the run of the force component in the radial direction. The Oort constants A, B known from radial velocities and proper motions of nearby stars, the distance from the Sun to the galactic center Ro established from the distances of RR Lyrae stars, the local density and density gradients in the vicinity of the Sun, known from the star counts, are involved in this basic model of the Galaxy. The r.m.s. velocity component in the z direction yields the approximate mass distribution in this direction. The model surface density is computed by integrating the density along the z direction in the model. The local surface density in the Schmidt model is 114 solar masses per pc2; it depends rather strongly on the assumed density variation in the outer part of the Galaxy.

We have solved the dispersion relation given by the theory of Lynden Bell and Kalnajs (1972) using models with spherical halos under the assumption that the halo population does not participate in the spiral arms. Especially we have studied the conditions under which the solutions of this dispersion relation reach corotation so that the excitation mechanism of the density waves due to the theory of Lynden Bell-Kalnajs is applicable. We have used as basic axisymmetric models the model of Schmidt (1965) (S-model) and the model proposed by Miyamoto and Nagai (1975) (M-model) On these models we have superimposed spherical halos so that in a sphere of radius 20 kpc there exists a given amount of mass with two different density laws: ρ as r-1 and p as r-2.