74 METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
THE OPTICAL CHARACTER OF BIREFRACTING MINERALS. 
The optical character of a mineral, whether positive or negative, depends 
by definition solely on the value of the bisector of the acute angle between 
the optic axes (optic binormals) ; it is, therefore, independent of the crystal 
system and pertains to all birefracting minerals; its determination, more- 
over, under the microscope is relatively simple and does not require elabor- 
ate apparatus. For these reasons the optical character is one of the most 
useful traits in the practical determination of minerals under the micro- 
scope. The crystal sections of birefracting minerals from which decisive 
interference figures can be obtained are those cut (i) exactly or nearly 
perpendicular to one of the bisectrices, (2) perpendicular to one of the 
optic axes, and (3) parallel to the plane of the optic axes. These sections 
and the methods applicable to them can be discussed for all birefracting 
substances if the uniaxial minerals be considered a limiting case of biaxial 
minerals for which zV = 0. The methods for the determination of the 
optical character are based in large measure on phenomena observed in 
convergent polarized light. For the simple observation of interference 
figures without measurement the method adopted by Lasaulx* of viewing 
the image C"D" directly in the rear focal plane of the objective (Fig. 32) 
is usually preferable to that requiring the use of the Bertrand lens and 
ocular; the first image C"D" is brighter and more sharply defined, although 
smaller than the image C""D"" observed in the second arrangement. In 
the formation of interference figures by this method the following factors 
have an important bearing and will be considered in some detail, as they 
are generally overlooked and entirely neglected. 
The first factor is the rotation of the plane of polarization of a wave 
transmitted through the lens system. Although the lenses are made of 
isotropic material throughout, still their surfaces exert, in general, a rotatory 
effect on the plane of vibration of any transmitted plane polarized light- 
wave. Fresnel was the first to develop the theory of refraction and re- 
flection for isotropic plates, and from his formulas the amount of rotation 
due to the influence of the boundary surfaces of a given isotropic plate on 
the plane of polarization of a transmitted wave impulse can be calculated. 
The formulas are standard and are developed in text-books on physical 
optics; the theory on which they are based is, however, usually presented 
in mathematical form and is difficult and involved, requiring close study 
to master its details.f 
In the following derivation, which is apparently novel and which is to be 
considered only as a convenient method of explanation for this particular 
case, the Huygens theory of wave propagation is assumed and the formulas 
are obtained directly by noting that in an isotropic medium, as air or glass, 
the forces are distributed in such a manner that a given light-wave may 
vibrate in any azimuth ; also that the planes of vibration for each direction 
Neues Jahrb.. 377-380. 1878; an ingenious method for obtaining interference figure* from very small 
grains was described by J. L. C. Schroeder v. d. Kolk (Zeitsch. wissen. Mikrosk.. 8. 459-461. 1893). He 
covered the section with a viscous liquid (glycerin) which contained a number of small air-bubbles and 
these served in place of the higher power objective. 
tin a recent number of the American Journal of Science ((4). Jl, 157-211, 191 1] the writer has reviewed 
the literature on thr i> irticu1.tr part of this subject which has to do primarily with the effects of the surfaces 
of crystal plates on transmitted liKht-waves and has presented the general theory from the standpoint of 
the electromagnetic theory of light. The results deduced from theory were found to agree fairly well with 
those of experiment and prove the importance of this factor. 
