  A theoretical description of the interacting Bose-system is proposed. It is
based on the extrapolation of the results obtained for the systems with a small
number of particles N=2, 3, 4, etc. to the bulk case of N=\infty. It is shown
that already the system with N=12, 13 behaves almost as a bulk in a wide
temperature range. Special attention is paid to the phase transition in these
systems. The hard sphere potential is used in calculations. The sequence of
heat capacity maxima is approximated as C^{max}_N/N\simeq13.6-aN^{-\epsilon}
with \epsilon=0.0608 giving the value of bulk heat capacity as 13.6 while
experimental value is close to 16. The temperature of \lambda-transition is
estimated as 2.1-2.3 K versus experimental 2.17 K. Quite good qualitative and
satisfactory quantitative agreement with the experimental data has been
achieved.
