292 McN air— A Method in Teaching Optical Mineralogy. 



Art. XXVII. — Note on a Method in Teaching Optical Miner- 

 alogy ; by F. "W. McN air. 



The writer has for some years given a short non-mathemati- 

 cal course in polarized light as related to crystals, for the pur- 

 pose of preparing students to take up optical mineralogy, the 

 latter being applied in turn to the study of rocks. The course 

 has been necessarily very brief, non-mathematical, and confined 

 to the bare essentials needed to develop its applications. Under 

 these conditions an attempt has been made to give the student 

 a logical basis for his conclusions, to develop in him some 

 ability to reason about observed phenomena, and so to render 

 him as far as may be independent of mere rules of procedure. 



In the effort to condense the course, and to base its entire 

 structure on the smallest possible number of new ideas, the 

 form of the wave shell and the deductions therefrom have been 

 rested as directly as possible upon the so-called reciprocal ellip- 

 soid, as introduced by McCullagh. It will be remembered 

 that this ellipsoid, whose equation is 



2 2 2 



x y z 



a 1 + b> + c* ' 



is constructed on semi-axes proportional to the square roots of 

 the elasticities in the three principal directions. In the usual 

 notation, these axes are named so that <z> J>c and their direc- 

 tions are labeled respectively A, B and C. This ellipsoid gives 

 the wave shell, or ray surface, by the following construction : 

 if through the center perpendicular to a given ray direction a 

 plane is passed, the section is an ellipse, and if on the ray 

 direction, distances be laid off proportional to the semi-axes 

 of the ellipse the locus of all points so determined is the 

 wave shell. Furthermore, the vibration directions belonging 

 to the given ray lie in planes determined by the ray and the 

 axes of the elliptical section. 



If one may judge by the text books, the ellipsoid, whether 

 that of Fresnel or this of McCullagh, is used in the non- 

 mathematical presentations of this subject to obtain the wave 

 shell, or rather its three principal sections, and is then imme- 

 diately abandoned. The device which occurred to me some 

 years since, and which I have found useful in obtaining results 

 with my students, is to carry the use of the ellipsoid into a 

 considerable number of the applications of the theory to the 

 properties of crystals. The "section cut from the ellipsoid" 



