304 



DR. L. N. G. FILON ON THE 



This showed that the relative retardation was greater for light passing through at 

 mid-level than for light passing through the edges of the beams. 



Such an effect can be explained only in two ways. Firstly, by supposing that 

 the law of stress across the section does indeed remain linear, but that the relative 



I/I OLE T 



H/CH 



Jusr 



LOAD 

 Fig. 12. Appearances of band for glasses 2783. 



retardation is not proportional to the stress, increasing less rapidly for large stresses 

 than for small, since here (the overlapping being assumed for simplicity to be J height 

 of beams) |T + |-T produces more effect than T. 



Such an effect, however, would imply an increasing falling off of the values of A 

 from the values which would be obtained if the linear law held. The result would be 

 a progressive decrease, instead of a progressive increase, in rA\/AW r . 



Secondly, we may suppose that HOOKE'S law fails or stress is not proportional to 

 strain. Consider a beam bent under constant bending moment. The axis will take 

 the form of a circular arc. If we imagine the circle completed, then the symmetry 

 shows that the cross-sections must remain plane and all pass through the centre of 

 the circle. 



It follows easily that, whatever be the law of stress, if we can neglect end effects, the 

 extension follows a strictly linear law. 



C IT 



Thus if AB (fig. 13) represent the vertical axis of such a section, and the stress at 

 any point R in AB be set off as RP perpendicular to AB, the locus BPC of P is a 



