116 



polycrase, are directly isomorphous; the others can only be 

 classed together with them by a transformation of the axial 

 ratios, by which transformation, however, the indices of the 

 faces present often lose somewhat in simplicity ; with regard 

 to the minerals known from older times such a classing has 

 been attempted; here I shall attempt it for all of them. 



As a starting point I take the two mentioned minerals with 

 the axial ratios : 



in euxenite a:b:c = 0"364 : 1 : 0'ЗОЗ 

 in polycrase ^) a:b :c = 0-3638 : 1 : 0*3422 



According to Brögger^) aeschynite has the axial ratio 



a:b:c = 04816 : 1 : 0-6725. 



Brögger shows the crystalline form of the aeschynite to 

 be in many respects corresponding to that of the polycrase ; 

 if the a-axis is divided by Va and the c-axis by 2 we get: 



a:b:c == 0-3612 : 1 : 0-3362 



accordingly it is very similar to polycrase and through it also 

 to euxenite. 



Ardennite has about the same axial ratio as the former 

 mineral with the difference, that the c-axis is but the half: 



a:b:c == 0-4663 : 1 : 0-3135 



if the a-axis is divided by */з we get: 



a:b:c = 0*3497 : 1 : 0*3135. 



According to Brögger^) polymignite has the axial ratio: 



a:b:c == 0*71205: 1 : 0*512105 



in the same place he has shown that when the b- and a-axis 



») After Sheerer: Pogg. Ann. 62, 1844 p. 430. The axial ratios, other- 

 wise, are very varying in the different authors; thus Brøgger (Zeit- 

 schr. f. Kryst. Ill, 1897, p. 485) has: a:b:C = 0-34619 : 1 : 0-31243. 



^) Zeitschr. f. Kryst. III. 1879, p. 481. 



3) Zeitschr. f. Kryst. XVI. 1890 p. 388. 



