  Measurements of specific heat between 80 mK to 4 K and electrical resistivity
between 80 mK to 10 K were carried out for polycrystalline CePt3Si samples cut
into small pieces (typically $\sim $10 mg). In the specific heat measurements,
we observed an antiferromagnetic transition jump at TN = 2.2 K for all the
samples, while the heights have large variations. As regards superconductivity,
we observed two distinct transition jumps at Tcl $\sim$ 0.45 K and Tch $\sim$
0.75 K, which were the same for all the samples. From the measurements of
specific heat and resistivity, systematic relations were found between
antiferromagnetic and superconducting transitions. We conclude that
antiferromagnetism, whose transition temperature is 2.2 K, coexists with
superconductivity, whose transition temperature is Tcl. In this sample,
residual electronic specific heat coefficient in the superconducting state
$\gamma_{\rm s}$ was quite small, and specific heat divided by temperature
below Tcl decreased almost linearly with decreasing temperature. In order to
reveal the characteristic properties of the magnetism and superconductivity of
the CePt3Si system, it is important to study the two superconducting phases
with Tcl and Tch, respectively.
