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A geometry has been devised for goniometer heads in which orientation of the crystal is achieved by rotation about two axes, one of which has a fixed inclination to the alignment direction while the second precesses about the first; this arrangement can be exploited to give devices of excellent inherent mechanical stability over the entire range of adjustment with overall physical dimensions which are invariant with setting angle. Two different designs based on this geometry have been constructed, both of which exhibit the expected stability and are simple to adjust to fine limits. These heads are compatible with the I.U.Cr. specifications for goniometer head supports and are small enough for use with most cameras and diffractometers in common use.