ADAMS AND WILLIAMSON: BIREFRINGENCE AND STRESS 619 



it is sufficient to add the three Equations, (3^), (3b), and (3c). 



n — fix . n — fix 

 Then, since is approximately equal to , we have 



= ^(2 - 4(7)- + - (i - 20-)- = 



fi E V E V 



|'(. - ..)(^^ + ?) (6) ■ 



E \ V v/ 



E 

 By putting — r = K, in which K is the modulus of vol- 



3(1 - 2(t) 



ume-elasticity,^^ the equation becomes 



Wv - n 



- a? * !) 



n 2,K^ 



which expresses in terms of known or measurable quantities 

 the effect of hydrostatic pressure on the index of refraction, which 

 of course under these conditions remains independent of the 

 plane of polarization of the light. 



COMPARISON WITH POCKBL'S RESULTS 



The optical effects of stress on several kinds of glass have 

 been studied by Pockels,^^ who loaded rectangular plates of 

 the glasses and measured with a Jamin interferometer the abso- 

 lute retardation of a ray of light vibrating parallel to the direc- 

 tion of pressure. He also measured the birefringence with a 

 Babinet compensator and from the two series of measurements 



P q . 



calculated the values of - and - . His results are shown in table 



V V 



3. The first column describes the glass, the second gives its 

 number in Winkelmann's list;^^ in the third and fourth columns 

 are the elastic constants of the glass; the index of refraction n 

 is shown in the sixth column, and the percentage of lead oxide 

 in the seventh. In the next two columns are the results of 



P Q 



Pockels' determination of - and -, the coefficients which occur 



V V 



12 I /K = 13, the compressibility at constant temperature. 



13 F. Pockels. Ann. Phys. (4) 7: 745. 1902. 

 " Compare HovESTAdT, op. cit., p. 146. 



