[ 305 ] 



XL. Intelligence and Miscellaneous Articles. 



EXPLANATION OF AN ANOMALY IN DOUBLE CIRCULAR 

 REFRACTION. BY M. CROULLEBOIS. 

 r PHE two inverse circular rays have a separate existence outside 

 "*■ the quartz ; to be convinced of this it is sufficent to repeat 

 the following experiment : — Taking a biquartz of 60 millim. thick- 

 ness, we pass interfering pencils, polarized or natural, through 

 each half; we then receive these pencils, superposed, upon the 

 horizontal slit of a direct-vision spectroscope. Under these con- 

 ditions we observe two distinct systems of curved longitudinal 

 fringes presenting the characters of inverse circular polarization. 

 If we explore the common field directly with the lens, we get two 

 lateral groups of vertical fringes, resulting from the interference 

 of rays of the same gyration unequally retarded in the biquartz. 



For a long time it was possible to believe that the distance, 

 estimated in fringes, of the two central bands gave the measure of 

 the circular birefringence for the middle rays of the spectrum. It 

 is far from being so ; the observed is always greater than the theoretic 

 displacement. For example, with a quartz of 42 millim. M. Billet* 

 ascertained that this distance amounts to 24 fringes and is more 

 than double the theoretic value, which would be 10*5. My pre- 

 sent purpose is to explain this disagreement between theory and 

 observation. Even in white light, with the lens only, the position 

 of the central fringe is often doubtful ; with the spectroscope, 

 employed as stated above, there is no longer any uncertainty. The 

 central fringe is always delimited by the two black lines equally 

 inclined in both directions from the vertical. Having made this 

 remark, let us return to the experiment, and suppose that the 

 observer has the group of circular fringes to the left ; the central 

 band answering to the different colours will be thrown back un- 

 equally. The displacement will be given by the formula 



f=K.e(n"-n') 9 



and will be proportional to the numbers 58, 62, 70, 80, 87, and 

 100 respectively for the lines B, 0, D, E, F, GL Thus the central 

 fringe of the violet is much more displaced than that of the red, 

 and the black line (place of those central fringes) is strongly in- 

 clined upon the vertical. To the right of this singular line BGr the 

 attendant bands become more and more oblique ; to the left, on 

 the contrary, they reerect themselves ; and as the distance between 

 two successive bands is greater in the red than in the violet, on 

 advancing towards the left we shall find two black lines inclined 

 symmetrically: it is there that the central fringe IK of the dis- 

 placed system must be formed. But how many fringes must we 

 go forward to meet with that central fringe? Let us observe, 1st, 



* Optique physique, t. ii. p. 243. 



Phil. Mag. S. 5. Vol. 12. No. 75. Oct. 1881. 2 A 



