DISPERSION IN ARTIFICIAL DOUBLE REFRACTION. 305 



genuine stress-strain diagram. It will therefore, as is well known, take the shape 

 shown in fig. 13, the stress falling off rapidly as the strain approaches and passes 

 what is known as the yield-point. 



The corresponding curve for the overlapping part of the other beam is shown by 

 AQD, and the stress effective in producing the optical effect is the sum of the two 

 ordinates RP, RQ. It is obvious from the figure that PQ is a maximum in the 

 middle. Thus the peculiar shape of the band is likewise accounted for on this 

 hypothesis. 



Now let the straight line BI give the stress-diagram which would be obtained for 

 the same bending moment if HOOKE'S law held. This straight line and the curve 

 must then be so related that the first moment about BX of the areas APCB and AIB 

 are equal. 



Let L be the extremity of the ordinate through the mid-point of AB. Draw BL 

 cutting AC at J and the tangent at L cutting AC at T, BX at U. The stress-strain 

 curve is always convex inwards, therefore CPLB always lies on one side of TU as 

 shown. 



Now the triangles BLU, TLJ are clearly equal. Hence area CPLJ > area BSL. 

 And the mean distance from BX of the area CPLJ > mean distance from BX of the 

 area BSL. Therefore first moment of CPLJ > first moment of BSL, or first moment 

 of ABJ > first moment of ABLC. Therefore, if ABI and ABLC have the same first 

 moment, ABI < ABJ, or BI must lie to the left of BJ. 



If BI cut ML in K, then ML > MK. That is, the actual measured stress is 

 greater than the computed stress. Therefore the observed values of A. exceed those 

 that would be obtained if HOOKE'S law held by a difference rapidly increasing with 

 the stress. 



The result is a progressive increase in the value of 7-AX/AW, such as is actually 

 observed. The discrepancies which have appeared are therefore explained. 



Incidentally this confirms the conclusion (which indeed seems highly probable on 

 theoretical grounds) that the stress-optical effect is dependent upon the stress that 

 is, the molecular strain and not upon the molar strain. The latter, which is the 

 sum of both plastic and elastic effects, is the quantity measured in most extension 

 experiments, and is usually denoted by " strain " simply. 



25. Conclusion. 



This completes the account of the results reached so far. The next step would be 

 to obtain glasses of suitable chemical composition to show the effects discovered in a 

 much stronger degree and thus allow of more precise determinations. Research in 

 this direction is being undertaken, and it is hoped that the results will form the 

 subject of a future communication. 



VOL. CCVII. A. 2 R 



