in Petrographio Microscope Work. 135 



Fletcher, who suggested in his masterly paper on " The Opti- 

 cal Inclicatrix and the Transmission of Light in Crystals " the 

 optical inclicatrix (index-ellipsoid) as the surface best suited to 

 meet the situation. Fletcher's treatment of the problem is 

 remarkably clear and convincing and his suggestions have been 

 adopted in many of the recent text-books on physical crys- 

 tallography. Throughout his essay he considers primarily the 

 rays and the ray directions, with only subordinate treatment of 

 the wave-front normals and their derivation from the optical 

 inclicatrix. 



The ray directions are the paths followed by the light 

 through the crystal ; they are, in short, the lines along which 

 the light energy flows and are of fundamental significance in 

 crystal optics. But in petrographic microscope work, the 

 observations are not made within the crystal plate itself and 

 the interest centers chiefly in the phenomena produced, after 

 emergence, by the light waves as a result of the changes which 

 they have experienced during their passage through the crystal. 

 In rock thin-sections the crystal plates are very thin and most 

 of the observations are made in either central or slightly oblique 

 illumination. Under these conditions it is simpler and more 

 direct to consider only the wave-front normals (i. e. directions 

 perpendicular to the wave-fronts) and to leave the rays entirely 

 out of the discussion. This statement does not mean that the 

 significance of rays should be passed over in silence but simply 

 that for the working petrographer the conception of the wave- 

 front normals is sufficient to explain practically all the phe- 

 nomena which he encounters. The exclusive use of wave-front 

 normals renders, moreover, the application of the optical 

 indicatrix direct and easy to grasp. Although this mode of 

 applying the optical indicatrix is different from that recom- 

 mended by Fletcher, it seems to the present writer to be better 

 adapted for this particular phase of crystal optics and if employed 

 consistently would do much to facilitate the presentation of 

 microscopical petrography. 



For a given mineral the optical indicatrix or index ellipsoid 

 is, in the most general case (biaxial minerals), a triaxial ellipsoid 

 whose principal axes are directly the three principal refractive 

 indices of the mineral for the particular wave length of light 

 employed. Having once obtained this ellipsoid and its position 

 in the crystal relative to the crystallographic axes or other 

 definite directions, it is possible, by its use, to predict quanti- 

 tatively the optical behavior of any plate cut from the crystal. 

 If the plate be considered to pass through the center of the 

 ellipsoid,* the surface of the ellipsoid intersects the plate in an 



*In any given crystal all plates, cut parallel to a definite plane, have 

 identical vectorial properties ; any plane may, therefore, be considered to 

 pass through the center of the index ellipsoid. 



