  Ordinary multi-component silicate glasses belong to a class of amorphous
insulators normally displaying no special form of magnetism, save for the
Larmor dominant diamagnetism from the constituent atoms' core electrons and the
extrinsic Langevin paramagnetism due to the ubiquitous Fe-group dilute
paramagnetic impurities. Here we show that the macroscopic magnetisation of
three case-study glass types measured in a SQUID-magnetometer cannot be
explained solely by means of the Larmor-Langevin contributions. In particular,
we reveal a novel {\em intrinsic} contribution to the bulk magnetisation due to
the amorphous structure itself, a contribution that is peculiar both in its
temperature and magnetic-field dependence and represents the first true
magnetic effect in nominally non-magnetic glasses. The only theoretical
interpretation we know of for such an effect and which can consistently explain
the experimental data demands the re-thinking of the atomic organisation of
glasses at the nanometric scale.
