236 ELEMENTARY CHEMICAL MICROSCOPY 



Crystals belonging to the tetragonal and hexagonal systems 

 (uniaxial crystals) possess two indices. Crystals belonging to 

 the orthorhombic, monoclinic, and triclinic systems (biaxial crys- 

 tals) have three indices. 



In uniaxial crystals one value corresponds to that given by the 

 ordinary ray and the other to that given by the extraordinary 

 / ray. The first value is found in that direction through the crys- 

 ; >tal where the light vibrations are transmitted transverse to the 

 vertical crystallographic (and in this case optical) axis and is 

 designated by the Greek letter co; the second value is observed 

 \when light is transmitted through the crystal parallel to the 

 vertical axis. This index is designated by the Greek letter . The 

 double refraction of uniaxial crystals is said to be strong when co 

 is greater than e, and weak when the reverse is found. When the 

 refractive index co is greater than e, the crystal is said to be opti- 

 cally negative and when less than , optically positive. Some 

 crystallographers prefer to designate the two refractive indices 

 by the letters a and 7. In this case 7 a expresses the strength 

 of double refraction and when a is greater than 7 the crystal is 

 optically negative. 1 



In biaxial crystals three different values for the rate of light 

 transmission can be found, or in other words biaxial crystals have 

 three axes of elasticity or directions of vibration ; the axis of maxi- 

 mum rate of vibration transmission is commonly designated by 

 the German letter a ; that of the minimum vibration by c and 

 the intermediate axis by b . Since there are three axes of elas- 

 ticity, three different values for the index of refraction may be 

 obtained, the smallest value a in the direction of the maximum 

 axis a , the greatest value 7 in the direction of the axis c and an 

 intermediate value /3 in the direction of the b axis. The double 

 refraction of the crystal will be strong or weak according to how 

 much greater 7 is than a. To determine whether a biaxial crys- 

 tal is optically positive or negative requires data other than 

 refractive indices (see Chapter XI, page 249). 



1 In order to be sure of the values for of and e, a number of different crystals 

 should be tried out. co will be constant in all of them, will differ slightly accord- 

 ing to the position of the crystals. 



