The observed magnetic susceptibility χ^{obs}(T) data of Ami et al. for the linear-chain cuprate Sr_{2}CuO_{3} are re-analyzed in terms of recent theory of Eggert et al. for the spin susceptibility χ(T) of the spin S=1/2 linear-chain Heisenberg antiferromagnet, which yielded the Cu-Cu exchange constant J/k_{B}=2150 K. Values for J', the exchange constant in the rungs, and J, that in the legs, were estimated for the S=1/2 two-leg ladder compound SrCu_{2}O_{3}, using the χ(T) data of Azuma et al. The analyses suggest that J'/J ≈ 0.5, contrary to the expectation that J'/J ≈ 1, and that J/k_{B} is very large ( ≈ 2000 K), similar to that in Sr_{2}CuO_{3}.
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