220 On the Problem of Total Reflexion. 



fleeted vibration which corresponds to it, by compounding the 

 uniradial reflected vibrations. 



It may be well to mention that, in a uniaxal crystal, the 

 plane of the extraordinary refracted vibration is always perpen- 

 dicular to the axis, and therefore the ellipse in which the vibra- 

 tion is performed may be easily determined by the remark in 

 p. 192. The plane of the ordinary vibration has no fixed po- 

 sition in the crystal; but if we conceive the auxiliary quantities 

 i, TJI, 1 (p. 188), to be compounded into an ellipse (as if they 

 were displacements), the plane of this auxiliary ellipse will be 

 perpendicular to the axis of the crystal. 



Whether the preceding very simple construction, for finding 

 the incident and reflected vibrations by means of the refracted 

 vibration, extends also to the case of liaxal crystals, is a point 

 which has not yet been determined, on account of the compli- 

 cated operations to which the investigation leads, at least when 

 attempted in any way that obviously suggests itself. 



