622 ADAMS AND WILLIAMSON: BIREFRINGENCE AND STRESS 



internal stress corresponding to the observed color we find, by 

 referring to a chart^'' showing Newton's color scale in terms of 

 optical path-difference, that a first-order red corresponds to a 

 retardation of about 530 mm or 530 X 10 ~^ cm. The birefrin- 

 gence then is the path-difference per unit of length, that is, 



530 X io~^ 



= 53 X 10 ~^ Now, according to table 2, a bi- 

 refringence of 2.57 X io~^ corresponds in ordinary crown glass 

 to a (uni-directional) pressure of i kg. per sq. cm. Hence the 



53 X io~^ 



observed birefringence corresponds to a stress of , = 



2.57 X 10-^ 



20.6 kg. per sq. cm. or 300 lb. per sq. in.^^ 



In conclusion, we shall note the change in refractive index 



produced (i) by a hydrostatic pressure of 1000 kg. per sq. cm. 



acting on a block of light flint glass; and (2) by a uni-directional 



P <7 



pressure of 1000 kg. per sq. cm. According to table 3, - and - 



are, for light flint glass, respectively, 0.306 and 0.213 J ^ is 0.61 X 



10"^ kg. per sq. cm.; a is 0.222; and n is 1.57. Substituting these 



values in Equation (6) we have 



10^^(1 -o.444)(o.6i2 +0.213)1.57 



n^ — n = An = ; z = 0.00118, 



0.61 X 10*^ 



The index of refraction is thus increased 0.0012 by a pressure 



(hydrostatic) of 1000 kg. per sq. cm., and this change in index is 



independent of the plane of polarization of the light. On the 



other hand, for the case of a uni-directional pressure, we use 



Equations (3b) and (3c), and suppose that, as in Fig. 3, the 



pressure is exerted along OY, and that the ray of light travels 



along OX. Then 



Hy — n = Aw„ = 



1.57 X 1000 



— - — ^(0.213 - 0.444 X 0.306) = 0.00020 



0.61 X 10^ 



^^ See, for example, the chart in J. P. Iddings, Rock Minerals (191 1) ; or N. H. WiN- 

 CHELL, Optical Mineralogy (1909). 



'' We have observed, in poorly annealed glass, stresses very much higher than 

 300 lb. per sq. in. By taking into account the sign of path-difference in polarized 

 light, it is easy to show that the stress in the center of a slab of unannealed glass 

 consists of a tension in all directions parallel to the large surface of the slab. 



