I9I2.] 



THE LAW OF RATIONAL INDICES. 



113 



Goldschmidt^' attempts to explain the relative frequency of crys- 

 tal forms by a different method from that of Bravais. Assuming 

 (lOo) and (oio) as the primary faces in the zone [lOo: A^o:oio] 

 secondary faces result by the addition of the indices. Thus adding 

 lOO and oio, index by index, we have as the first complication, no. 

 Adding lOO and no, also no and oio, we have 210 and 120 as 

 the second complication and so on. The relative frequencies of 

 crystal forms for the hko zone are, according to Goldschmidt's law 

 of complication, in the following order. 



100 



OIO 



Although Goldschmidt's law of complication accounts in a gen- 

 eral way for the relative frequency of crystal forms it does not 

 fully explain the observed facts. According to Goldschmidt (210) 

 and (120) should be of equal frequency as should also (310), 

 (320), (230), and (130). Yet (120) occurs on 66 orthorhombic 

 minerals while (210) occurs on only 48. The form (130) occurs on 

 43 orthorhombic minerals while the other three forms mentioned 

 occur on only 29, 22, and 20 minerals respectively. Out of 206 

 combinations of anglesite^^ fi20) occurs 34 times and (210) only 

 twice. The explanation of these apparent discrepancies is that in 

 the orthorhombic system the a-axis is shorter than the &-axis and 

 consequently molecules are more closely packed along ( 120) than 

 along (210). Hence (120) is more frequent than (210). With 

 many orthorhombic crystals, for example cordierite, chalcocite, 

 chrysoberyl, columbite, and witherite (130) occurs to the exclusion 

 of (120). 



In the monoclinic system the a-axis is either shorter or longer 



" Zeitsclirift fib- Krystallographie ii>id Mineralogie, Vol. 28, pp. 1-35, 414- 

 451 (1857). Abstract by Moses, School of Mines Quarterly, Vol. 25, pp. 

 415-420 (1904). 



^* Hermann, Zeitschrift fiir Mineralogie, Vol. 39, p. 478 (1904). 



