72 



HABIT AND INTELLIGENCE. 



[chap. 



Para- 

 meters 



their 

 ratios. 



Eatios of 



intercepts 

 to para- 

 meters. 



If any face is produced till it cuts the tliree axes, the 

 portions of the axes intercepted between the point where 

 they intersect each other and the produced faces are called 

 Intercepts, the intercepts of that face. For every crystalline species, 

 certain faces may be found, the relations of which to the 

 axes are simpler than those of any other faces that are 

 possible in the species. The intercepts of these faces are 

 called the parameters of the species, or, to speak more 

 accurately, the parameters are the numerical ratios between 

 the intercepts of these faces. The parameters are constant 

 for the species. 



In many cases two, or all, of the three parameters are 

 equal. But when the parameters are not equal, they do 

 not stand in any simple numerical ratios to each other. 

 In topaz,^ for instance, the parameters are approximately 

 1, 0-5284, and 0-47698. 



It is a universal and very remarkable law of crystal- 

 lography, that the three intercepts of any face which is 

 possible in any species, stand to each other in ratios which 

 are either those of the parameters of the species or else 

 simple multiples or submultiples of the parameters. When 

 a face is parallel to an axis, as occurs for instance in the 

 cube, the intercept of that face on that axis is infinite. In 

 Professor Miller's crystallographic notation, instead of the 

 ratios of the intercepts to the parameters, the reciprocals 

 of the ratios are taken as the indices of any given face. 

 The reciprocal of infinity is 0. In this notation, when 

 the angles at which the axes intersect each other, and the 

 ratios of the parameters are known, the relation of any 

 face to the three axes may be expressed by the three 

 indices of the face ; and these are always capable of being 

 written as whole numbers, counting as a whole number. 

 An index is seldom higher than 6. Similar and opposite 

 faces have the same indices with opposite algebraic signs. 

 In topaz, for instance, there may be a face with the 

 indices 4, 2, 3 ; and as the values of the parameters of 

 topaz, as stated above, are 1, 0-5284, and 0-47698, the 



^ Mr. Maskelyne's Lecture on the Crystal Molecule as examined by 

 Light, at the Koyal Institution, 1st April, 1859. 



Miller's 

 notation. 



Topaz. 



