( Ö7 ) 



possess a perfect plane of cleavage, it mny be cleaved in any case 

 along |111| with testaceons plane of separation. It adniits of no doubt 

 that the elementary parallelepipeds of the two cr3^stal structures are 

 in both phases pseudo-cubic rhombohedral contigurations and the 

 question then rises in what proportion are the molecular dimensions 

 of those cells in both crystals? 



If, in all crystal-phases, we imagine the whole space divided 

 into volume-units in such a manner that each of those, everywhere 

 joined, mutually congruent, for instance cubic elements, just contains 

 a single chemical molecule, it then follows that in different crystals 



J\I 



the size of those volume elements is proportionate to — , in which 



I\f represents tlie molecular weight of the substances and d the 



sp. gr. of the crystals. If, now, in each crystal phase the content 



of the elementary cells of the structure is supposed to be equal to 



31 

 this equivalent-volume — , the dimensions of those cells will be reduced 



for all crystals to a same length unit, namely all to the length 



of a cubic-side belonging to the volume-element of a crystal phase, 



whose density is expressed by the same number as its molecular 



M , , 



weight; then in that particular case V=z— = 1. If we now calculate 



the dimensions of such an elementary parallelopiped of a Bravais 



structure whose content equals the quotient — and whose sides are 



d 



in proportion to the crystal parameters a : ö -. c, the dimensions 



X, t^ and o) thus found will be the so-called topic parameters oïWiq 



phase which, after having been introduced by Becke and Muthmann 



independently of each other, have already rendered great services 



in the mutual comparison of chemically-different crystal-phases. In 



the particular case, that the elementary cells of the crystal-structure 



possess a rhombohedral form, as is the case with ditrigonal crystals, 



the parameters x> ^ and ^ become equal to each other (= (>). The 



relations applying in this case are 



<? = 



sin a . sm 



a 



sin 



V \^ A 2 



with nin 



A I 2 sin a 



If now these calculations are executed with the values holding 

 here: 5i = 207,5; Fe,0, = 159,G4; fZij; = 9,851 (Pekrot); t//,>,Os = 4,98, 

 then 



7 

 Proceedings Royal Acad. Amsterdam. Vol. IX. 



