6l4 ADAMS AND WILUAMSON : BIREFRINGENCE; AND STRESS 



optical effect produced is proportional to the amount of the 

 stress. 



The ratio TD/W , however, is not independent of the dimen- 

 sions of the block, but it is readily seen that W lah is the pressure 

 and that D la is the path difference (6 and a are the dimensions 

 of the block measured transversely to the direction of thrust, 

 a being in the direction of the beam of light (see Fig. i)). More- 

 over, the ratio 



Bla bD 

 or 



W/ab W 



is the birefringence produced by unit pressure and is de- 

 pendent only on the nature of the glass. It is interesting 

 to note that only one dimension of the block needs to be mea- 

 sured. The second column of table 2 gives for each kind of 

 glass the weighted mean value of D/W in mm per kg., and in 

 the third column are values of b, the width of the block in cm., 

 i. e., the length of an edge perpendicular both to the direction 

 of thrust and the direction of the beam of light. The quantity 

 bD/W as shown in the fourth column is then the birefringence 

 produced by a pressure of i kg. per sq. cm. For reasons which will 

 appear later it may be useful to know the rigidity and compres- 

 sibility of each of the various kinds of glass. In the last two 

 columns of table 2 are given the rigidity and compressibility 

 calculated according to the method described by Hovestadt,^ 

 except for ordinary crown glass, the compressibility of which 

 we measured by a method already described.*'' These calcu- 

 lated elastic constants are of course only approximate values, 

 but are probably sufficiently accurate for our present purpose. 

 All of the results in the fourth column lie between 2.57 X 

 io~^ and 3.20 X 10 ~^ except for two comparatively uncommon 

 glasses. It is a curious and unexpected circumstance that for 

 the more generally used optical glasses a given stress should 

 produce so nearly the same amount of birefringence. The heavy 



* H. HovESTADT, Jena glass. Transl. by J. D. and A. EvERETT. London, 1902; 

 pp. 155-160, 185-193. 



\ * L. H. Adams, E. D. Williamson and J. Johnston. Journ. Amer. Chem. Soc. 

 41: 12-42. 1919. 



