  Experimental data for the magnetic susceptibility and magnetostriction of
CuGeO_3 are analyzed within a one-dimensional antiferromagnetic model with
nearest ({J_1}) and next-nearest neighbour interactions ({J_2}). We show that
the ratio of the exchange constants in the antiferromagnetic chains of CuGeO_3
amounts to ${J_2}/{J_1}$ = 0.354(0.01), i.e. it is significantly larger than
the critical value for the formation of a spontaneous gap in the magnetic
excitation spectrum without lattice dimerization. The susceptibility data are
reproduced by our numerical results over the temperature range from 20K to 950K
to a high degree of accuracy for ${J_1} = 80.2 (3.0)$ and ${J_2} = 28.4 (1.8)$.
The pressure dependence of the exchange constants is estimated from
magnetostriction data. Furthermore, the specific heat data are checked on
consistency against the calculated entropy of the above model.
