88 JAMIN ON METALLIC REFLEXION. 



1st. One of the images will be a maximum, the other a mini- 

 mum, if we place the principal section of the analysing prism in 

 the direction of one of the axes of the ellipse. 



It is to be also remarked that the formulae (12.) and (13.) give, 

 for A^ and A''^ on one side and for B^ and B'^ on the other, equal 

 values; therefore 



2nd. The intensity of the vibration in the direction of the axes 

 of the ellipse is proportional to the square of their lengths ; 

 whence it results that, if the principal section of the prism coin- 

 cides^vi^ith the major axis of the ellipse, the vibration in the direc- 

 tion of this axis, that is to say the vibration of the extraordinaiy 

 ray, will be a maximum, the ordinary ray being a minimum. 



If we replace in formula (14.) the angle (so) by the value which 

 gives the direction of the axes, we find 



tan (8' - 8") = oo or S' - 8" = 90°; 



that is to say, that 



3rd. Every elliptical vibration may be decomposed into two 

 rays, polarized in the direction of two axes, whose intensities are 

 proportional to the squares of the lengths of these axes, and 

 whose phases differ by a quarter of an undulation. 



Lastly, if we seek the condition which must be satisfied by 

 the angle (w) in order that the intensities of the two images may 

 be equal, we must put 



A'2-B'2 = 0; 



which gives 



cot 2 w' = tan 2 « cos 8 = tan 2 w, 



2w' = 90°±2w, I.. . . (15.) 



«' = 45° ± « 

 Thus, 



4th. The two images are equal when the direction of the prin- 

 cipal section is inclined at 45° to that of the axes of the ellipse. 



These results may now be transformed into experiments. In 

 fact, to obtain the position of the axes of the ellipse, it will suf- 

 fice to find the direction of the principal section which gives to 

 one of the images the greatest, and to the other the least inten- 

 sity ; and if we wish to obtain the ratio of the lengths of the 

 axes, we must measure the ratio of the intensities of these 

 images. 



The first of these questions being the only one with which I 

 have occupied myself, I shall explain how the requisite precision 



