481 
of the double refraction in strained glass. 
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 19 5 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 w^as 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 w T as 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 t 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 I A k 2 , 
A being the area of cross-section and k its radius of gyration 
about a horizontal line through its centroid in its plane. 
The difference of phase is therefore 
27 rr 2 ttMt Cy 
A A k* A 
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 2ir y that is, 
when 
yMrC I A A k 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 
