136 R. W. G. Wyckoff — Theory of Space Groups 



occupy sucli special positions that tlie 192 equivalent 

 points reduce to four. 



It is thus seen that with compounds which crystallize 

 in the systems of higher symmetry, these special positions 

 become of the utmost importance. A knowledge of all 

 of these special cases is highly desirable as an aid in 

 determining the structure of crystals. 

 the simpler cases. ^' 



Niggii^^ records 



1 — 







7« 



/^'^^^ 



u 



1 



1 









h 



l/^^-^^\ 



1/ 1 









Fig. 4 (A). — The side-centered monoclinic unit of structure, rm'. (000) 

 and P (0, Ty, Tz) are taken as the two points associated with the unit. 



Fig. 4 (B).— The simple cubic unit of structure, T,. (000) may be taken as 

 the single point of the lattice associated with the unit cube. 



Fig. 4 (C).— The body-centered unit of structure, V^" . (000) and P , , , (r^, 

 Ty, Tz) are the lattice points associated with the cube. 



Fig. 4 (D).— The face-centered unit of structure, T,'. O (000), P (0, Ty, r^), 

 P / (^-x> ''".vj 0) ^1="^ P / / (■'"xj 0, Ty) are the lattice points associated with the unit. 



^•^ P. Niggii, op. cit. 



" In the course of the development of a generally useful method for study- 

 ing crystals, the writer has been engaged for some time in working out all 

 of these special cases and expects to be able to present them in the near 

 future. Some of the results to be given in the following paper are based 

 upon this work. 



