1896,] NEW YORK ACADEMY OF SCIENCES. 49 



from below with its glass sides normal to the axis of the micro- 

 scope and the stage of the microscope is rotated to the position 

 of extinction. A second plane is then brought normal to the 

 axis, the extinction again determined and so on. 



2. Orientation of the Optical Principal Sections and Finding 

 the Plane of the Optic Axes. 



In biaxial crystals light transmitted in any direction parallel 

 to an optical principal section, that is to a plane through any 

 two of the axes of elasticity, is resolved into two components 

 vibrating at right angles to the direction of transmission one in 

 the plane, the other at right angles thereto. 



If therefore the principal planes of the nicols are horizontal 

 and vertical and the crystal is manipulated until a principal sec- 

 tion is horizontal, the light will be extinguished and will remain 

 so through an entire revolution of the crystal b}- the horizontal 

 circle K. 



Conversely, darkness throughout such a revolution proves 

 that a principal section is horizontal. 



In the orthorhombic system the axes of elasticity coincide 

 with the crystallographic axes and the principal sections with 

 the planes of symmetry, and therefore are easily oriented. 



In the monoclinic S3'stem the crystal axis, b, is always an axis 

 of elasticity, the plane of symmetry is always a principal section 

 and the two other axes of elasticity lie somewhere in that plane 

 at right angles to each other. 



The other two principal sections are determined by adjusting 

 the apparatus as previously described and mounting the crystal 

 with the plane of symmetry vertical and the ortho axis b from 

 left to right. In this position the line of sight is in the plane 

 of symmetry, that is, in a principal section, there will, therefore, 

 be complete extinction throughout a revolution around the 

 ortho axis b by the arc Xi . 



But the other principal sections are planes through b and some 

 line in the plane of symmetry, hence at some angle of rotation 

 of Li one of these planes will become horizontal and then revolu- 

 tion by K will also give darkness throughout ; ninety degrees 

 from this the other plane will be found. 



One of the three planes, usually the one normal to the plane 

 of symmetry, will contain the optic axes, and these will be recog- 

 nized by the brightening of the field due to inner conical refrac- 

 tioa. 



Transactions N. Y. Acad. Sci., Vol. XVI., Sig. 4, January 25, Iso". 



