This chapter describes two problems initially studied in the 1930s, a few years

after the discovery of galaxies. In later years, they were revisited and, a posteriori,

appeared to be important precursors of the problem of dark matter, which

in the meantime had emerged clearly from the study of the rotation curves of

spiral galaxies. In reality, the early studies of clusters of galaxies

and of the vertical dynamics of the solar neighborhood had failed to provide

decisive evidence for the existence of dark matter. In fact, for both cases significant

confusion remained until the end of last century. Then, with the advent

of fresh data from the Hipparcos mission, it was proved that from the vertical

dynamics of the solar neighborhood there is no evidence for the presence

of dark matter in the disk. In turn, with the combined use of improved X-ray

observations and of gravitational lensing clusters of galaxies were eventually

shown to be associated with large amounts of dark matter, which, in contrast to the case of galaxy halos, appears to be more concentrated with respect to the distribution of visible matter. The closing dynamical section describes the properties of the self-gravitating slab model, often used to describe the local properties of galaxy disks.