Experiments have been carried out which demonstrate the possibilities of the method of ‘magnetic hyperfine-structure alinement’ for the orientation of nuclei. Single crystals of composition (1% Co, 12% Cu, 87% Zn) Rb
2
(SO
4
)
2
, 6H
2
O were cooled by adiabatic demagnetization to 0·01°K. The crystals contained a small quantity of radioactive
60
Co, which decays by
β
-emission followed by two
γ
-rays in cascade. The anisotropic distribution of the
γ
-rays from the oriented
60
Co nuclei was measured by an array of Geiger counters around the cryostat. The largest anisotropy observed was 33%, and the change in this anisotropy as the crystals warmed up to 1°K was fitted to theoretical curves where the only unknown parameter was the magnetic moment of
60
Co, for which a value of 3·5 ± 0·5 nuclear magnetons was deduced.