  The results of the complex study of galactic open cluster Trumpler 2 are
presented. In order to obtain the proper motions the positions of 2600 stars up
to the limit magnitude B ~ 16.25 mag in the area 80x80 arcmin around the
cluster were measured on 6 plates with the maximal epoch difference of 63
years. The root-mean error of the relative proper motions is 4.2 mas/yr. The
catalogue of BV magnitudes of all the stars in the investigated area was
compiled. Astrometric selection of the cluster members within the region of
R<16 arcmin from the center of the cluster was made by means of the W.Sanders
method. In that field 192 stars were found to have the individual membership
probability greater then 85%, 148 of them are situated within the
+/-3sigma_(B-V) band around the main sequence of the cluster. They are
considered to be cluster members by two criteria. The U-B ~ B-V diagram plotted
for the astrometrical cluster members by the data taken from the Washington
catalogue of the UBV photometry in the galactic cluster fields (Hoag et
al.1961) made it possible to redefine the value of the color excess E(B-V)=0.40
mag. The superposition of the MS of the cluster with the ZAMS Schmidt-Kaler
leads to the coincidence at the value of the apparent distance module
(V-Mv)=10.50 which corresponds to the distance r=725 pc. The luminosity and
mass functions of the Trumpler 2 were constructed and the value of the slope
Gamma=-1.90+/-0.22 was determined. The cluster age of 8.913x10^7 yr was
determined. It is shown that the red giant on the late stage of the evolution
(st N.1095) belongs to cluster and indicates the brightness variability. The
possibility that the number of both known and recently discovered variables are
cluster members was considered. Tables 2,3,3A,5 will be only available in the
electronic form.
