MICROSCOPICAL PETROGRAPHY 491 
means of extinction angles on known crystal faces) and with it the 
crystal system of the mineral. 
Similarly for any given crystal section we can determine, in 
parallel polarized light, (a) its optic ellipsity or the axiality of its 
optic ellipse (relative lengths of the two axes of its optic ellipse); 
(0) its refractive indices y’ and a’ (lengths of the major and minor 
axes of its optic ellipse); (c) its birefringence (measured by the 
difference in lengths of the major and minor axes of its optic 
ellipse); (d) relative positions of the axes of its optic ellipse to any 
crystallographic direction observed on the section (extinction 
angle). 
These properties vary to a certain extent with the color of 
light used and give rise to phenomena of color and color dispersion 
which are useful in mineral diagnosis. These are briefly: color; 
pleochroism; absorption; dispersion of mineral; variation in the 
principal birefringences; dispersion of the bisectrices; dispersion 
of the optic axes. 
With this brief statement in mind of the optical features which 
are made use of in practical mineral determination, it will now be 
in order for us to show that the methods of microscopical petro- 
graphy measure up to the requirements emphasized in the intro- 
duction and are furthermore simple and easy of application. For 
this purpose it will be convenient to group the optical and crystallo- 
graphic properties into two classes: those of the first class (optic 
ellipsoidity, optic ellipsity, optical character of mineral, color, pleo- 
chroism, absorption, dispersion of the optic axes, dispersion of the 
bisectrices, crystal habit) being ascertained ordinarily by direct 
observation without measurement, while for the second class 
(refractive indices, birefringence, extinction angles, optic axial angles, 
cleavage angles) the numerical results of actual measurement are 
required. This distinction is drawn somewhat arbitrarily and is 
not meant to imply that the properties of the first group are 
strictly qualitative in their nature but that they are treated at 
the present time in ordinary petrographic microscopic work as 
qualities of an object rather than quantities which must be defi- 
nitely measured. With greater refinement in the methods of 
determination, some of the properties of the first class will un- 
