316 Mr Filon, On the variation with the wave-length 



uniform for the neutral tint of second order, it was no longer uni- 

 form for the neutral tint of first order. 



4. I then proceeded to investigate what the effect of such a 

 want of uniformity must be. Near the middle of the block, at a 

 distance from the compressing planes, the stress must be very 

 nearly that due to a bending moment M (amount unknown) about 

 a horizontal axis at right angles to the plane of loading, super- 

 imposed upon a uniform pressure T equal to the calculated mean 

 pressure. 



The actual stress at any point is therefore 



71, M V 

 + (abK*y 



where a, b are the thickness and breadth of the block, K the 

 radius of gyration of its horizontal section about the diameter 

 parallel to the side a, y is the horizontal distance of the point 

 considered from this diameter. 



Denoting this by T + Sy, we have relative phase-retardation of 

 the two components of the ray traversing the glass at distance y 

 from the vertical mid-plane 



= 2^(T+Sy). 



The intensity of the light restored, due to a beam of light of 

 cross-section dxdy, will be 



~wCa(T + Sy)~ 



J.sin 2 



dxdy, 



X 



if the axes of the Nicols are inclined at 45° to the stress, 

 A being the original intensity of the light per unit area of cross- 

 section. 



Hence the total intensity of the light restored, when the 

 aperture is a rectangle of height 2h and breadth 2k, is equal to 



-hJ -k { X J 



T being now the stress corresponding to the centre of the rect- 

 angular aperture. 



This integral is easily evaluated and reduces to 



2^m Sm \TX~) C0S Hi— J. 



2Ahk 



The darkest part of the black band will then correspond to the 



