  The critical properties of the $S=1/2$ Heisenberg two-leg ladders are
investigated in a magnetic field. Combining the exact diagonalization method
and the finite-size-scaling analysis based on conformal field theory, we
calculate the critical exponents of spin correlation functions numerically. For
a strong interchain coupling, magnetization dependence of the critical
exponents shows characteristic behavior depending on the sign of the interchain
coupling. We also calculate the critical exponents for the $S=1/2$ Heisenberg
two-leg ladder with a diagonal interaction, which is thought as a model
Hamiltonian of the organic spin ladder compound
${Cu}_2({1,4-diazacycloheptane})_2{Cl}_4$. Numerical results are compared with
experimental results of temperature dependence of the NMR relaxation rate
$1/T_1$.
