  We investigate the magnetic susceptibility of the classical Heisenberg
antiferromagnet with nearest-neighbour interactions on the geometrically
frustrated pyrochlore lattice, for a pure system and in the presence of
dilution with nonmagnetic ions. Using the fact that the correlation length in
this system for small dilution is always short, we obtain an approximate but
accurate expression for the magnetic susceptibility at all temperatures. We
extend this theory to the compound SrCr_{9-9x}Ga_{3+9x}O_{19} (SCGO) and
provide an explanation of the phenomenological model recently proposed by
Schiffer and Daruka [Phys. Rev. B56, 13712 (1997)].
