  We have performed measurements of the magnetic susceptibility of NaV$_2$O$_5$
between 2 and 400 K. The high temperature part is typical of spin 1/2 chains
with a nearest--neighbour antiferromagnetic exchange integral $J$ of 529 K. We
develop a model for the susceptibility of a system with finite chains to
account for the low temperature part of the data, which cannot be fitted by a
standard Curie-Weiss term. These results suggest that the next
nearest--neighbour exchange integral $J_2$ in CaV$_4$O$_9$ should be of the
order of 500 K because, like $J$ in NaV$_2$O$_5$, it corresponds to corner
sharing VO$_5$ square pyramids.
