( RYSTALLOGRAPHY 



19 



may IK- derived fnun the p;ir;iineters of Weiss, by dividing the 

 parameter- l>y (heir least common multiple and reducing the 

 fraction to the lowest terms; no\v each coefficient will stand as 

 a fraction in which the numerator is one. Let it be required to 

 convert 2 a : .'* b : 4c to indices. Dividing by 12, we have ^ a : A b : 

 reducing to the lowest terms, a : Jb : Jc, the three denomi- 

 nator- are then written 643 (read six, four, three) as the indices. 

 The same operation may be expressed thus : the reciprocals of 

 the parameters are written in the order of the axes, cleared of 

 fractions, reduced to their simplest form, and then written as the 

 indices. Taking the same parameters as before, 2 a : 3b: 4c, the 

 reciprocals are 3, 3, i ; cleared of fractions by multiplying by 12 

 and reducing to simplest form, the indices 643 are obtained as be- 

 fore. The reverse of this is necessary in order to obtain the param- 

 eters from the indices; it is almost unnecessary to point out that 

 the indices are always whole numbers and cannot be fractions. 

 When oo appears in the parameters its reciprocal takes its place 

 in the indices. The minus direction on the axes is indicated by 

 writing the sign above the figure, as 123. 



Examples of equivalent planes : 



PARAMETERS OF WEISS INDICES OF MILLEB 



111 



102 

 632 

 010 

 231 

 634 

 TlO 



Rationality of the indices. All crystals are formed by a regular 

 deposition of sheets of molecules. The relation of these sheets to 

 the point-system of which they form a part will determine the faces 

 and angles of the crystal, as well as the intercepts on the crystallo- 

 graphies! axes. Each intercept is determined by a definite number 

 of whole molecules, for it is impossible to divide a molecule and have 

 it possess the same properties ; when divided it becomes a substance 

 of a different character, belonging possibly to a different crystal 

 system. Every face possible on a crystal is determined by a whole 

 number of molecules which determine the relative size of the inter- 

 cepts. The ratio of the intercepts of any or all planes possible 

 on a crystal to any other plane on the crystal must be a rational 



