  We present a theoretical and experimental study of a quasi-one-dimensional
zigzag antiferromagnet (N_2H_5)CuCl_3, which can be viewed as weakly coupled
Heisenberg chains with a frustrated interaction. We first discuss generic
features of the magnetic properties of the zigzag spin chain between the nearly
single chain case and the nearly double chain case, on the basis of the finite
temperature density-matrix renormalization group (DMRG) calculations. We next
show the experimental results for the magnetic susceptibility and the
high-field magnetization of a single crystal of (N_2H_5)CuCl_3 above the Neel
temperature T_N=1.55K. By comparing the experimental data with the DMRG results
carefully, we finally obtain the ratio of the nearest and next-nearest exchange
couplings as J_1/J_2=0.25 with J_2/k_B=16.3K. We also investigate the
three-dimensional (3D) coupling J' effect by using the mean-field theory
combined with the DMRG calculations. The estimated value J' \sim 0.04J_2
supports good one-dimensionality of (N_2H_5)CuCl_3 above T_N.
