  An asymptotic solution of the thermodynamics of a BCS superconductor
containing spin 1/2 and 7/2 magnetic impurities, obtained recently in Ref. 1 is
exploited to derive the expressions for critical magnetic field
$H_{\mathrm{c}}(T)$ . The credibility of the resulting theoretical equations,
which depend on the magnetic coupling constant $g$ and impurity concentration
$c$, is verified on the experimental data for the following superconducting
alloys: LaCe, ThGd and SmRh$_{4}$B$_{4}$. Good quantitative agreement with
experimental data is found for sufficiently small values of $c$. The
discrepancies between theoretical and experimental values of
$H_{\mathrm{c}}(T)$ for larger values of $c$ in case of LaCe and ThGd are
reduced by introducing the concept of the effective temperature $\tilde{T}$,
which accounts for the Coulomb interactions between the electron gas and
impurity ions.
  At low temperatures, the critical magnetic field is found to increase with
decreasing temperature $T$. This enhancement of the critical magnetic field
provides evidence of the Jaccarino-Peter effect, which was experimentally
observed in the Kondo systems like LaCe, (La$_{1-x}$Ce$_{x}$)Al$_{2}$ and also
in the pseudoternary compounds, including Sn$_{1-x}$Eu$_{x}$Mo$_{6}$S$_{8}$,
Pb$_{1-x}$Eu$_{x}$Mo$_{6}$S$_{8}$ and La$_{1.2-x}$Eu$_{x}$Mo$_{6}$S$_{8}$.
  The effect of an external magnetic field ${\mathcal H}$ on a BCS
superconductor perturbed by magnetic impurities was also studied. On this
grounds, by analyzing the dependence of superconducting transition temperature
$T_{\mathrm{c}}$ on ${\mathcal H}$ of (La$_{1-x}$Ce$_{x}$)Al$_{2}$, we have
shown, that for certain parameter values, external magnetic field compensates
the destructive effect of magnetic impurities.
