when exposed to Polarized Light. 189 



column of the table, which agree with those observed within 

 the limits of the errors of observation. In the case of txiater 

 and glass, too, where the azimuth of disappearance was ob- 

 served to be about 79° or 11°, the formula gives 79° 28', or 

 10° 32', at an incidence of 56° 45'. 



In order to ascertain the relation between the mutual incli- 

 nation of the planes of polarization of the interfering pencils 

 when they produced black-centred or white-centred rings, I 

 have computed the following table for an incidence of 56° 45'. 



Azimuth of polarized Film of ivater and glass. 



light. +(p —(p'" Indination of planes <p and (p'". 



180 0"| M7„7e-centred 



45 157 28 L'^/'.^^cenueu 



4 124 34J ""'"S^- 



34 90 No rings. 



19 58 471 



57 24 42 „, , , , 



^ _ , \Blacic-cex\ived 



7 9 13 1 ""8^- 



oJ 



By taking <p positive, or on the right-\\s.n(\. side of the plane of 

 reflexion, then <p"' must be negative, or on the left-hand side 

 of that plane*; hence -f<p, — <p"' will be the mutual inclina- 

 tions of the planes of polarization of the interfering pencils, 

 and we obtain the important law. 



That when two polarized ■pencils reflected from the surfaces 

 of a thin plate lying on a reflecting surface of a different refrac- 

 tive power interfere, half an tmdulation is not lost, andwuiTV.- 

 centred rings are produced, provided the mutual inclination of 

 their planes of polarization is greater than 90°; and that when 

 this inclination is less than 90°, half an tmdidation is lost, and 

 BLACK-centred riiigs are produced ; when the inclination is 

 exactly 90°, the peticils do 7iot ititeyfere, and no rings are pro- 

 duced. 



At an incidence of 45° upon water and glass, where the 

 signs of (p and <p"' are the same, the maximum difference in the 

 planes of polarization is 23° 12', which takes place in azimuth 

 70° 30'; and at an incidence of 10° the greatest difl^erence is 

 2° 16', which takes place at an azimuth of about 45°. 



In the case o{ soap and plate glass, where the black-centred 

 rings appear beyond the incidence of 71° 45', the difference 

 of inclination in the planes of the two pencils is also less 

 than 90°. 



1 was now desirous of examining the phaenomena of a per- 

 • See Philosophical Transactions, 1830, p. 70, fig. 1. 



