  A transition in a spheroidal particle from the paraelectric to the
ferroelectric phase as well as dynamic susceptibility are studied without
approximation in the paraphase. It is assumed that the surface charge is
compensated and the boundary condition for the polarisation is P=0, i. e. with
zero polarisation at the surface of the particle. There is an infinite number
of resonance frequencies in the dynamic dielectric function within the
quasistatic approximation. The paraphase properties of the dielectric response
of the particle are discussed. The transition temperature decreases with
decreasing diameter d of the particles inverse quadratically. There exists such
a critical diameter that for the particles with the diameter below the critical
one the ferroelectric phase is absent. Comparison of the experiment with
theoretical results is carried out. Introduction of a dead layer thickness
leads to a very good agreement of theory with the experiment for $PbTiO_{3}$
and to a good agreement with the experimentfor $BaTiO_{3}$.
