96 Mr. Maskelyne on the Crystal Molecule. [April 1, 



ordered arrangement in the physical properties of the various crystals 

 that illustrate them. 



The definition of the terms crystallographic axes, parameters, indices, and 

 morphological axes being necessary for elucidating what was to follow, were 

 given. Thus crystallographic axes are geometrical directions, determined by the 

 intersections of any three planes of the crystal. They are taken as axes of co- 

 ordinates, and called severally x y and z, and such are chosen as express in the most 

 simple and smallest numbers the relations of all the planes of the crystal to one 

 another. These relations are indicated by the Law of Crystallography, viz., by 

 this, that a plane parallel to any facette will cut these axes at certain definite relative 

 distances, measured from the centre at which the axes cross, and controlled by the 

 principle to be next enunciated. Certain of such planes can always be found in 

 every crystal species for which the ratios of these distances are simpler than in 

 any others . The distances for such particular planes are called the parameters of 

 that species, and their values are generally indicated by the letters a h and c, which 

 represent the distances measured severally along the axes x y and z. The ratios 

 of these parameters cannot be expressed (except, of course, where they are equal) 

 by any rational numbers. In this respect they bear some analogy to the chemical 

 equivalents ; thus in topaz the parameters are 



a ; 6 : c : : 1.: 0.5284 : 0.47698 approximately. 



Now every facette on any topaz crystal must cut the axes at distances, the ratios 

 of which are represented by very simple fractions of these numbers, such as 



i 1 i &c. 



Hence any facette represented by the form (423^ will be parallel to a plane 



\ c cutting the axes x y zm points whose distances along these axes 



* - are found by the proportions i a along axis x: ^b along axis y : 



n / i ^ along the axis z. Just as by the law of definite propor- 



7 ^ ><^ „ y tions in chemistry, if the equivalent of iron be taken as 28.042 



7^ * and of oxygen 8. 



2 We have 28.042 . . . iron + 8 oxygen, forming one oxide of iron, 



JL 2 X 28.042 . . . iron +3x8 oxygen forming another do. 



4, 2, 3, are the indices of that facette, and by the symbol (423) is indicated 

 a group of eight facettes which the law of symmetry of the system requires, and 

 which will, therefore, be found on every complete topaz crystal that carries one of 

 these facettes of that form. The indices are generally indicated by the letters 

 h k I, which, therefore, express rational numbers, while the parameters aha 

 always (where unequal) express irrational numbers. 



The term morphological axis was defined as an axis round which the facettes 

 are symmetrically an-anged, but which is not necessarily a crystallographic axis 

 (e.g., in the rhombohedron). 



The terms elasticity, and axes of elasticity, were next^xplained— the former 

 term as implying a power of counter-resistance to any force tending to displace 

 the particles of the crystal (e.g., the compressing force of a blow, or any vibration, 

 such as sound, &c.), the axes of elasticity being those directions in the crystal 

 along which alone the displacement and the counter resistance opposed to it by the 

 crystal, coincide and operate in the same line. A force acting in any other 

 direction is met by counter-forces distributed along the directions of these axes 

 of elasticity. 



These definitions being explained, the speaker entered on a short illustration 

 of the laws of crystallographic symmetry in crystals, exhibiting, by means of 

 diagrams, their general morphological relations, so far as was necessary for the 

 subsequent discussion, and pointed out the analogy in complex crystal forms, 

 with the symmetiy of certain floral types of form. 



The representation of the magnitude and directions of the axes of elasticity in 

 each crystalline system was shown to be possible by means of one of three solid 

 figures. 



These, in the case of the octahedral system— from the mutual convertibility 



