| Abstract: | Summary A consideration of symmetry in any object or process entails essentially a correlation between parts of a unit or between unit and unit. Enquiry must be made as to what is geometrically distinguishable or indistinguishable and an attempt undertaken to discover the pattern underlying apparent disorder.Crystallography has been the science in which the principles of symmetry have been most extensively applied and received their fullest development. Naturally enough, the system evolved for formulating the symmetry inherent in crystals has been adapted to the specific problems the crystallographer sets out to solve.Such researches, however, go far beyond the bounds of ordinary geometric crystallography and are, in particular, an essential requisite for mastering the problems of stereochemistry. It is, therefore, obviously desirable to find a method of formulation which can be applied to any or all the problems in which the question of symmetry arises, such as the systematic ambiguities or the possible deformations of objects or processes endowed with symmetry. To this end the Element of Symmetry, traditional starting point of investigations into symmetry, must be replaced by the covering operations as such.Symmetry formulæ can be deduced, which beyond merely describing the features involved, permit the detailed numerical calculation of their development and variation. In this respect they must prove of value not only to the chemist in his investigation of isomers etc., but can usefully be adopted also by the crystallographer.A short introduction into this new method of formulation is given in the preceding pages. |
