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XLI. On the Construction of Models and Diagrams to Illus- 

 trate the Propagation of Light in Biawals. By J. H. 

 Vincent, B.Sc, A.R.C.Sc, Assistant Demonstrator in 

 Physics at the Royal College of Science, London, S. W* 



IN the following paper it is proposed to furnish such data 

 as will render it possible to construct some models or 

 diagrams illustrating the optics of biaxnl crystals, with the 

 minimum expenditure of trouble. 



The diagrams of FresnePs Wave Surface which appear in 

 the text-books are restricted to the sections of the surface by 

 the principal planes, and, although solid models of the surface 

 are procurable, they scarcely lend themselves to educational 

 purposes so well as sectional models which students can 

 readily construct for themselves out of millboard. 



The Ellipsoid of Elasticity. 



The quadric 



«y + % 2 + cV = l 



is the first surface which a student encounters in approaching 

 the subject from FresnePs standpoint. It is the ellipsoid of 

 elasticity (the Optical Indicatrix of Fletcher) having 



as its semi-axes. The equation to the ellipsoid of elasticity 

 may also he written 



o o o 



x- ?/ z z ., 

 — 4. ■£. 1 = 1 



a i a T y — J- 



where /u 1? /* 2 , /z 3 are the principal indices of refraction. Let 

 the quantities fj, 1} fi 2 , /a 3 be taken proportional to the numbers 



3 ' 4 > 6 " 



The principal sections of ihe ellipsoid of elasticity are 



shown in figs. 1, 2, 3. In fig. 1 the full straight lines 



through the centre are the traces of diametral planes cutting 



the quadric in circular sections. These lines are inclined at 



an angle of 49° 51' to the positive and negative directions 



of the axis of so. The broken lines are the optic axes and 



are perpendicular to the circular sections. The semi-angle 



* Communicated by the Author. 



