1871.] Dr. A. Scbrauf on Molybdates and Vanadates of Lead. 461 



the crystallographical system and the lateral angles of wulfcnite with the 

 pyramidal angle of descloizite*, 



Eosite having G2° 50', descloizite 63° 35', and wulfcnite 65° 47'. 



51° 5', „ 57° 35', „ 49° 50'. 



„ 51° 5', „ 44° 9', „ 49° 50'. 



The proportion of the principal axis of eosite to the same axis of wulfenite is 



1-375 _ 7-0085 

 1-574 8-0000' 



The pyramid of eosite could therefore be considered as a representative of 

 the pyramid 778 of wulfenite, and the crystals of eosite to be merely a new 

 form of the crystallographical form of the last-named mineral. Setting 

 aside the chemical differences, a number of crystallographical characters 

 may be alleged against the identity of these two minerals. All the crystals 

 of eosite carefully examined by me show only one dominant pyramid, 

 without any secondary pyramidal plane. The difference between the 

 angles of the pyramids of eosite and wulfenite amounts to only 3°. It would 

 have been too slight for admitting, with any degree of probability, that the 

 secondary pyramid (778), having grown out into a principal plane, has com- 

 pletely superseded the original principal pyramid, had not an alteration in 

 the chemical constitution of the substance been attended by an altered 

 arrangement of the atoms entering into the composition of the crystalline 

 molecule. 



§ 6. Crystallographical forms of Descloizite and Vanadinite. 



The similarity of the pyramidal angles of eosite and Peruvian descloizite 

 (the second one, as stated by M. Des Cloizeaux) led me at first to suppose 

 the existence of similar forms among the crystals of the carnation variety 

 B of vanadite or of dechenite. 



The crystalline agglomerations of dechenite are so confused that it was 



* I alluded, a number of years ago, to the necessity of beginning any crystallogenetic 

 theory with distributing the molecules of the elements constituting a combination ac- 

 cording to the three directions of space, which thus is differentiated in the required 

 way. In the case here in question the subsequently acceding substance (vanadium) 

 seems to have assumed its direction according to the principal axis, the molecules of 

 wulfenite having kept meanwhile their original direction along the secondary axis ; and 

 this supposition could, indeed, account for the successive transition of form from wulf- 

 enite into descloizite. However, such investigations could lead to any real, not merely 

 apparent, success only under condition of not being confined to the parameter of the 

 crystals, but also founded on the molecular values of the constituting elements. 



These ideas of mine, and the calculations of crystalline forms from the molecular 

 values of the elements founded on them, have been thoroughly discussed in several 

 of my publications. 



See Schrauf, Physikalische Studien (Vienna, 1867), c. xvi. p. 240 ; Lehrbuch der 

 Mineralogie, vol. ii. Krystall-Physik (Vienna, 1868), c, xi. p, 160 ; Pogg. Ann. 1867, 

 vol. cxxx. p. 3d, 



