1889. J Rotation of the Plane of Polarisation of Light. 



duo 

 dz 



sin 



4w tan kz + m. (8.) 



He obtains it by setting in equations (2) and (3) /3 = k.z. This 

 relation is not correct, since it only represents the variation of /3 with 

 doable refraction, whilst (3 also varies with rotation. 



To show the effect of this mistake, we will consider the particu- 

 larly simple case where the incident vibration is along the x axis 

 alone, and where the double refraction is so much stronger than the 

 rotation that we can replace sin co by w. 



The correct differential equations are — 



^ = — ku tan B + m ~] 



dz 



dp 

 dz 



&™ sin 2/3. 



(9.) 



Mr. Ward's is- 



dz 



= — ho tan Jcz -f ra. 



(10.) 



The solution of the simultaneous differential equations (9) is — 



m . 7 

 uj — — sm kz 



(ii.) 



P = 2 Z ' j 



whilst Mr. Ward obtains for this case by integration of (10)- 



iv — — cos kz loge tan 



(7T kz\ 

 l + t) 



(12.) 



From (11) it follows in accordance with experiment that w = 

 when kz, the difference of phase, is a multiple of tt. Mr. Ward 

 concludes from (12) that co = when kz is a multiple of 7r/2. 



To conclude : Mr. Ward's single differential equation must be re- 

 placed by two simultaneous differential equations. The conclusions 

 which Mr. Ward draws from his equation are hence in part incorrect, 

 in part not properly proved. 



[Reference may also be made to Professor Willard Gibbs's investi- 

 gation of " Double Refraction in perfectly Transparent Media which 

 exhibit the Phenomena of Circular Polarisation," ' Amer. Jo urn. 

 Sci.,' June, 1882. — R.] 



