to the Symmetry of Homogeneous Structures. 113 



duce a rotation which is not counterbalanced by one of the 

 opposite hand. 



Points thus capable of being regarded as simultaneously 

 forming two sets of distinct configurations which are enantio- 

 morphous to one another or nearly so, are easily found in 

 either of the enantiomorphous types in which all the coinci- 

 dence-movements taken together are identical with their own 

 mirror-images, i. e. in all of these types except Nos. 3, 4, 14, 

 15, 16, 17, 18, 19, 21, 22, 26, 27, 30, 31, 32, 33, 42, 43, 44, 

 45, 46, and 47. 



In the last-named types the presence of helical structures 

 of one hand without the helical structures enantiomorphous 

 to them seems to prohibit any arrangement leading to certain 

 compensation. 



Class 2. 



Parallel to those among the substances showing circular 

 polarization in the crystalline state only which owe the 

 property to complex grouping or intercalation of crystal 

 individuals, such as occurs in many cases of pseudo-symmetry, 

 we have 



Homogeneous structures, single individuals of which contain 

 no effective configurations, but which, when differently-orientated 

 twin individuals of them are intercalated, form such configura- 

 tions where the twin individuals meet, but not in two kinds 

 which are enantiomorphs. 



An example illustrating this may be presented by a twin 

 combination of type 48 *. 



For suppose that two identical homogeneous structures of 

 this enantiomorphous type, which contain no effective con- 

 figurations, are so intercalated that while their orientations 

 about an axis differ by 60°, one particular set of axes is 

 common to both f, and further that at least one set of the 

 singular points on these axes in one individual form, with the 

 corresponding set in the other individual, a single continuous 

 space-lattice. There are two ways in which this may happen, 

 either the axes of one individual may have the same, or they 

 may have the opposite orientation to that of the axes of the 

 other individual. 



* Zeitschr.f. Kryst. xxiii. p. 31. 



t A case in which the system of axes taken alone always possesses 

 higher symmetry than the structure to which it belongs has been selected. 

 Where this is not the case, for twinning of the nature described to occur, 

 higher symmetry of the system of axes will have to subsist as a special 

 condition, e.g. for individuals possessing rhombic symmetry when 

 twinning thus to have common axes, the axes, taken alone, must be so 

 situated as to form a system in trigonal or hexagonal symmetry. 



