OPTIC AXIAL ANGLE. IQI 
optic axes. In 1890, A. C. Lane* described practically the same method, 
discussed its accuracy under different conditions, and gave a graphical solu- 
tion of the above equation. He applied the method especially to the study 
of the amphiboles and pyroxenes. 
In 1896 E. von Fedorowf proved that it is possible to measure the bire- 
fringence -y /3 and ft a by use of the universal stage fitted with glass seg- 
ments of specially high refractive index and with the Fedorow mica com- 
parator, and thus to ascertain the optic axial angle from the same formula 
either by graphical means or by calculation. Recently J. Uhligt has re- 
described the method of Michel-LeVy and Lane and discussed its accuracy 
under different conditions. He determined the path-difference by means 
of the Michel-LeVy color chart. The chief sources of error in this method 
are: (i) sections are rarely found cut precisely normal to a bisectrix or 
optic normal; (2) the thickness of the thin section is usually not the same 
throughout; (3) if white light and the color chart be used for determining 
the order of the interference color, the determination of the path-difference 
is only approximately correct. If the mineral be weakly birefracting the 
determination by this method is of little value. Under favorable condi- 
tions rough approximations to the correct optic axial angle can be obtained 
in a short time. To facilitate such determinations Plate 9 has been drawn, 
which is a graphical solution of the equation 
yo. A b 
the abscissae indicating directly y a, the ordinates, /3 a, (indicated by 
y'af in Plate 9), and the curves the corresponding axial angle V. Lane's 
application of this method to parallel intergrowths of different amphiboles 
and pyroxenes has proved especially valuable. 
G. Ce*saroll has described a method for ascertaining the optic axial angle 
on a section parallel to the plane of the optic axes. He measures the path- 
difference of two points along the diagonals in adjacent quadrants of the 
interference figure and from this calculates the optic axial angle. The 
method, however, is in general too inaccurate to be of much service. 
EXTINCTION ANGLES OF PLATES IN ZONES WHOSE AXES LIE IN THE PLANE 
OF THE OPTIC BINORMALS. 
This method is particularly adapted to monoclinic minerals, as amphiboles 
and pyroxenes, and may be of service in a rough estimation of the optic 
axial angle of such a mineral. The underlying principle of this method 
is again the rule of Biot-Fresnel, and mathematical formulae suitable for its 
solution have been developed by Michel-Levy, Ce*saro,H Harker,** Lane.ft 
Daly.Jt Ferro,llll Souza Brandao and others. These formulae show that 
*Amer. Jour. Sci. (4). 39, 33-58. 1890; 43, 79, 1892. 
tZeitschr. Kryst.. 25, 349-336. 1896. 
tCentralblatt f. Min.. 1911. 303-312. 
1 1 Bull. Acad. roy. Bclg. Classe des Sciences, 1906. 
5Michel-Levy et Fouquc' ,Mine>alogie Micrographique, 72-76, 1879. 
1A. Cesaro. Mem. del' Acad. Roy. d. Sci. d. Belg.. 54, 26, 1893. 
**A. Marker, Miner. Magazine, 10, 239, 1894. 
ttSee Daly, Proc. Amer. Acad. Arts and Sci.. 34, 314, 1899 
tiR. A. Daly. Proc. Amer. Acad. Arts and Sci., 34, 314-323, 1899. 
IIJIA. A. Ferro. Rivista di Mineralpgia, etc. Padua, 20, 1-14. 1908; Zeitschr. Kryst., 32, 332. 1899. 
||V. de Souza Brandao, Communicacoes da Dirreccao dos Services Geologicos, 4, 1-28, 41-36. 1900; 6, 
339-364. 907. 
