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 oj; 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 e. 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 oo is greater than e, the crystal is said to be opti¬ 
cally negative and when less than e, 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.^ 
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 w and e, a number of different crystals 
should be tried out. co will be constant in all of them, e will differ slightly accord¬ 
ing to the position of the crystals. 
