Mr. W. Barlow on Crystal Symmetry. 



33 



identical with its own mirror-image which has already been 

 described. 



Therefore a complete list of all centred types which contain 

 a centre of inversion is furnished if, for every system which 

 is not identical with its own mirror -image, a corresponding 

 system is found having all the coincidence-movements of this 

 system, and also in addition the set of similar repetitions 

 involved by its possession of a centre of inversion. 



To obtain the diagram of these types let each of the 

 identical normals drawn through corresponding points in the 

 types already traced be produced through the centre to meet 

 the sphere a second time in a set of points which are there- 

 fore the inverts of the points of the first set. The references 

 to the resulting figures are given in the following table : — 



Table of the derivation o£ Types which have Centres of 

 Inversion. 



The type identical with its own Is derived from the type not 



mirror-image and possessed of identical with its own 



a centre of inversion which is mirror-image traced above 



shown by and represented by 



(PI. I.) fig. XII. (Gadolin fig. 57) (PI. I.) fig. I. 



XIII. ( „ 42) II. 



XIV. ( „ 56) III. 



XV. ( „ 36) IV. 



XVI. ( „ 51) V. 



XV1L ( „ 30) . VI. 



(PL II.) fig. XVIII. ( „ 28) (PL II.) tig. VII. 



XIX. ( „ 39) VIII. 



XX. ( „ 48) IX. 



XXI. ( „ 33) X. 



XXII. ( „ 45) XI 



Instances of elementary homogeneous structures which 

 present the same symmetrical arrangement of similarly re- 

 lated directions as is respectively presented by the types 

 possessed of centres of inversion just enumerated, can be 

 arrived at by the method already described *. For if the 

 identical bodies placed at the points of a network possessed 

 of adequate symmetry have individually the symmetry of the 

 type intended to be illustrated, i. e. a centre of inversion as 



* See p. 22. 

 Phil. Mag. S. 6. Vol. 1. No. 1. Jan. 1901. D 



