12 NEW YORK STATE MUSEUM 



axes a-a, b-b and c-c (fig. 25) of the ratio or unit lengths of sulfur, 

 that is to say, 



a-a: b-b: c-c: = 0.813: 1: 1.903 

 possible crystal faces of sulfur might have intercepts 

 a: b: c: == .813 : 1: 1.903 

 3a: b: c: = 3(.813) : 1: 1.903 

 a: b: £c : = .813 : 1: i(1.903) 

 oo : b: c: == oo : 1 : 1.903 etc. 



The quantities by which the ratio distances of any substance 

 must be multiplied to give the intercepts for any ordinary 

 crystal form of that substance are infinity and such simple num- 

 bers as 1, 2, 3, -J, i, |, etc. Fig. 25 shows the crystal resulting 

 from the combination of the crystal forms a:b:c: and a: b:^c of 

 sulfur. 1 



Systems of crystallization 



Crystals of all known forms, however varied and complicated, 

 may be classified under the following six systems of crystalliza- 

 tion, which will be taken up in detail. 



1 Isometric 4 Orthorhombic 



2 Tetragonal 5 Monoclinic 



3 Hexagonal 6 Triclinic 



1 Instruments employed for the measurement of interfacial angles are 

 known as goniometers and are represented by two types: 1) contact 

 goniometers which measure on a graduated half circle the angle obtained 

 by directly applying to the faces of the crystal two pivoted arms; 2) reflec- 

 tion goniometers which operate on the principle of reflection from the 

 brilliant crystal faces of the image of a point of light. The crystal is at- 

 tached to a rotating graduated circle on which the required angle is read. 

 Of the two types the latter is by far the more accurate particularly for 

 small crystals. 



The polarizing microscope, which is extensively used in determining the 

 optical properties of minerals and in the study of rocks, differs from the 

 ordinary microscope in three essential features. 



1 It is equipped with a revolving stage centered in the axis of the micro- 

 scope and graduated on the circumference. 



2 Below the stage is inserted a device which polarizes the light that 

 passes from the reflector, that is to say only those rays of light that 

 vibrate parallel to a certain plane are transmitted. 



3 Above the stage is placed a similar polarizing device called the 

 analyzer which transmits the light that vibrates in planes perpendicular to 

 the plane of the lower polarizer. 



These two polarizing devices, known as nicols prisms or " nicols," 

 are constructed from cleavage rhombohedrons of transparent calcite and 

 are so arranged that they are readily inserted or removed. 



