Mr. W. Barlow on Crystal Symmetry. 



35 



the latter system to that given by fig. XIV., and which result 

 from the addition of a centre of inversion, it is evident that fig. 

 XXV. gives the only selection from the repetitions of fig. XVI. 

 which will fulfil the required conditions ; the selection shown 

 by fig. V.is precluded because the added repetitions are identical 

 and not merely similar to those of the quarter system shown 

 in fig. HI. 



The following table gives the results arrived at : — 



Table of the Derivation of Types which display Mirror- 

 Image Similarity of Parts but do not contain Centres 

 of Inversion. 



Type not identical with its own 

 Type identical with its own The i nvers i on mirror image which has half 



mirror-image which dis- type from the repetitions of the derived 



plays half the repetition of w hich it is type ' consequently one- 



an inversion type and has derived fourth the repetitions of 



no centre of inversion. the corresponding inversion 



type. 

 None derived from Fig. XII. 



Fig. XXIII. (Gadolin fig. 46) XIII. Fig. I. 



None derived from XIV. 



Fig. XXIV. (Gadolin fig. 34) XV. Fig. II. 



XXV. ( „ 54) XVI. III. 



None derived from XVII. 



Fig., XXVI. (Gadolin fig. 31) XVIII. Fig, VI. 



XXVII. ( „ 43) XIX. II. 



XXVIII. ( „ 55) XX. III. 



XXIX. ( „ 37) XXI. IV. 



XXX, ( „ 40) „ VIII. 



XXXI. ( „ 49) XXII. IX. 



XXXII. ( „ 52) „ V. 



As before, an instance of an elementary form of homo- 

 geneous structure which presents the same symmetrical 

 arrangement of similarly related directions as is found in the 

 corresponding centred type can be obtained for each of the 

 ten types enumerated in the first column ; the method of 

 accomplishing this is precisely that previously adopted*. 



The complete list of types of symmetrical arrangement 

 .of the similarly related directions found in homogeneous 



* See pp. 22 & 33. 

 D2 



