999 



UNDULATORY THEORY OF LIGHT. 



other in the second quadrant — that is to say, indicating that there are two such 

 circular sections. 



The inclination to a of the normals to these circular sections — that is, of the 

 directions of progress of the waves of wlticli they are the j>lancs — will, of course, 

 have for tangent the reciprocal of the expression just given ; or, if a' represent 

 this inclination, 



tana'=±^ / 



[49.] 



If the wave front of the incident light coincide with one of these circular 

 sections of the surface of elasticity, it appears, from the principles already laid 

 down, that the wave can have no determinate plane of polarization. For all 

 the radii of the section being equal, the elastic forces are in cquilibrio in every 

 azimuth ; and there will be no lateral force to deflect the molecular movements. 

 If, in the first expression foregoing, we make i=c, the denominator becomes zero, 

 and the tangent is infinite, or tanOO^. The two circular sections then coincide 

 in the plane of he at right angles to a, and the crystal is a negative crystal of 

 one axis. If «=&, tanai=:0, and the two circular sections meet in the plane of 

 ah at right angles to c, and the crystal is positive. If a=c, then, since h is the 



mean axis, all the axes are equal and tana^- ; an indefinite value, signifying 



that the circular sections have no fixed positions; or that all the sections are 

 circular. 



Let us now apply the principles we have been con- 

 sidering to the phenomena presented by crystals cut 

 across the axis of greatest elasticity, or the line inter- 

 mediate between the optic axes. In the accompany- 

 ing figure, let QRQ'S represent one-half the surface 

 of elasticity, in which SC=«:, QC=h, RC=c. Let 

 PP parallel to IIR' represent the direction of molecu- 

 lar movement in an incident wave, whose direction 

 , of progress is S'S. Let AA represent the direction 

 '^ of free molecular movement in an analyzer with which 

 the crystal is observed. Also let QNOQ' represent 

 one of the circular sections of this surface. The 

 ellipse QIIQ'R' is the section of the wave with the 

 surface of elasticity ; and the axes QQ' and RR' are 

 the directions into which it turns all molecular move- 

 ments in its plane. But PP being parallel to RR', 

 is already in one of these directions, and hence this 

 wave passes through without modification ; but en- 

 countering the analyzer crossed upon it, is suppressed. 

 If, instead of a single plane wave, we suppose 

 many waves more or less inclined to each other, con- 

 vergent toward S, and all having the general direction of molecular movement 

 PP, their intersections with the surface of elasticity will be ellipses whose axes 

 are variously directed. There are two planes, however, SQ,Q' and SRR', which 

 will contain the axes of all sections made by waves normal to them. For it is 

 easily seen that, if the plane QRQ'R' turn about RR', this line RR' will always 

 be the minor axis of the section. If the same plane turn about QQ', this latter 

 line will be the major axis of the section until the turning plane reaches the 

 position QNQ/, when the section will be circular. Afterwards it will be again 

 elliptical with QQ' for its minor axis. It follows that all the convergent waves 



Fi- 63 



