International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. B. ch. 2.1, p. 192
Section 2.1.3.3. More than one symmetry element^{a}School of Chemistry, Tel Aviv University, Tel Aviv 69 978, Israel, and ^{b}St John's College, Cambridge, England 
Further alterations of the intensities occur if two or more such symmetry elements are present in the space group. The effects were treated in detail by Rogers (1950), who used them to construct a table for the determination of space groups by supplementing the usual knowledge of Laue group with statistical information. Only two pairs of space groups, the orthorhombic and , and their cubic supergroups and , remained unresolved. Examination of this table shows that what statistical information does is to resolve the Laue group into point groups; the further resolution into space groups is equivalent to the use of Table 3.1.4.1 in IT A (2005). The statistical consequences of each point group, as given by Rogers, are reproduced in Table 2.1.3.3.
Note. The pairs of point groups, 1 and and 3 and , not distinguished by average multiples, may be distinguished by their centric and acentric probability density functions.
^{†}The entry for the principal zone for the point group 422 was given incorrectly as 2 in the first edition of this volume.

References
International Tables for Crystallography (2005). Vol. A. Spacegroup symmetry, edited by Th. Hahn. Heidelberg: Springer.Google ScholarRogers, D. (1950). The probability distribution of Xray intensities. IV. New methods of determining crystal classes and space groups. Acta Cryst. 3, 455–464.Google Scholar