The algebraic relations between one-phase seminvariants and Harker sections are described. One-phase seminvariants of the first rank can be estimated via the Fourier transform of single Harker sections, and one-phase seminvariants of the second rank can be estimated via the Fourier transform of pairs of Harker sections.

The algebraic relations between 1-phase seminvariants of first rank and Harker sections recently described by Ardito, Cascarano, Giacovazzo and Luic [Z. Kristallogr. 172 (1985) 25 -34)] are further on discussed. A special least-squares procedure is proposed for discriminating spurious peaks among those lying on Harker sections and for improving positional and thermal parameters of heavy atoms. The first applications show that 1-phase seminvariants of first rank may be reliably estimated also for crystal structures with medium weight atoms.Symbols m: order of the space group (it equals the number of symmetry operators) Ν: number of atoms in the unit cell t : number of atoms in the asymmetric unit Γ; ξ (xj, yj, zj): positional vector of the yth atom Cp = (R p , T p ): pth symmetry operator. R p is the rotational part, T p the translational part CpTj = RpT; + T p : positional vector of the atom symmetry equivalent to r, I: identity 3x3 operator u/Cj, C q ) = (C s -C,) τ/, interatomic vector between two symmetry equivalent atoms HS(C s , C 4 ): Harker section containing interatomic vectors u/C s , C q ) for .7 = 1,2,...