Ernst Öpik started his studies, being a student of the Moscow University. One of the first problems he was curious about was the absorption of light in the Galaxy and the possible presence of absorbing (invisible) matter in it. He developed a method to determine the density of matter near the Galactic plane using vertical oscillations of stars. He concluded that there is no evidence for large amounts of invisible matter near the Galactic plane (Öpik 1915).
The dynamical density of matter in the Solar vicinity was investigated again by Oort (1932), who arrived at a different answer. According to his analysis the total density exceeds the density of visible stellar populations by a factor of up to 2. This limit is often called the Oort limit. This result means that the amount of invisible matter in the Solar vicinity could be approximately equal to the amount of visible matter.
The work on galactic mass modelling in Tartu Observatory was continued
by Grigori Kuzmin. He developed a new method for galactic mass
modelling using ellipsoids of variable density, and applied the theory
to the Andromeda galaxy
(Kuzmin 1943),
using the recently published rotation data by
Babcock (1939).
Next Kuzmin turned his attention to
our own Galaxy. Here the central problem was the density of matter in
the Solar vicinity. The mass density can be calculated from the
Poisson equation, where the dominating term is the derivative of the
gravitational potential in the vertical direction. He found that this
derivative can be expressed through the ratio of dispersions of
velocities and coordinates in the vertical direction,
C = 
z
/ 
c;
here C is called the Kuzmin constant.
Kuzmin (1952a,
1955)
used data on the distribution of A and gK stars and
analysed the results obtained in earlier studies by
Oort (1932)
and others. He obtained a weighted mean value C = 68 km
s-1 kpc-1, which leads to the density estimate
= 0.08
Msun pc-3, in good agreement with direct
density estimates of all known stellar populations (including
estimates for the mass in invisible low-mass stars and white
dwarfs). Two students of Kuzmin made independent analyses, using
different methods and observational data
(Eelsalu 1959,
Jõeveer 1972,
1974)
and confirmed Kuzmin results.
The local density problem was studied again by Hill (1960) and Oort (1960); both obtained considerably higher local densities of matter, and argued that there exist large amounts of dark matter in the Galactic disk. More recently Bahcall (1984) constructed a new multicomponent model of the Galaxy and determined the density of matter in the Solar vicinity, in agreement with the Oort's (1932, 1960) results. The discrepancy between various determinations of the matter density in the Solar vicinity was not solved until recently. Modern data have confirmed the results by Kuzmin and his collaborators (Gilmore, Wyse & Kuijken 1989). Thus we came to the conclusion that there is no evidence for the presence of large amounts of dark matter in the disk of the Galaxy. If there is some invisible matter near the galactic plane, then it is probably baryonic (low-mass stars or jupiters), since non-baryonic matter is dissipationless and cannot form a highly flattened population. Spherical distribution of the local dark matter (in quantities suggested by Oort and Bahcall) is excluded since in this case the total mass of the dark population would be very large and would influence also the rotational velocity.