of the double refraction in strained glass. 481 



behind the slit, together with the induction coil I, and the Leyden 

 jar J used to reinforce the discharge. 



The focal length of the collimating lens L was about 195 cms. 



The focal length of the collecting lens L' was about 56"5 cms. 



The distance of the analyser and telescope from the scale was 

 about 150 cms. The cone of light entering the Nicol and tele- 

 scope was limited by a circular diaphragm of aperture 1 cm. 



The beams used were cut from thick plate glass and were 

 made for me by the London and Manchester Plate Glass Com- 

 pany. They exhibited very little imperfect annealing in the 

 polariscope. The chemical composition of the glass was unknown, 

 but its density was about 2"50. 



3. The theory of the appearances seen was as follows. Suppose 

 we have a very narrow pencil of homogeneous light, traversing 

 horizontally, at a distance y above the central line a beam of 

 thickness r bent under a couple M, the relative retardation will be 



r=CrT, 



T being the horizontal tension (or pressure) in the beam at 

 distance y from the axis. When the beam is under a pure couple 

 this is the only stress, and it remains constant from cross-section 

 to cross-section. 



Now T = My/Ak\ 



A being the area of cross-section and k its radius of gyration 

 about a horizontal line through its centroid in its plane. 



TT CyMr 



Hence r = \ 7 .. . 



A& 2 



The difference of phase is therefore 



2irr _ 2ttMt Gy 

 \ ~ AF X' 



Now if the polarizer and analyser are crossed, with their principal 

 planes at about 45° to the vertical, there will be darkness in the 

 field of view if the difference of phase = a multiple of 2tt, that is, 

 when 



yMrC/\Mc 2 = n, 



n being any integer. Accordingly if the narrow pencil be made 

 to converge to a point on a transparent scale and this point be 

 viewed through a telescope or otherwise, it will appear unillu- 

 minated. 



Now if we can obtain a series of such thin pencils, corre- 

 sponding to each point of the scale, we shall see, if the light be 



