88 Professor Airy on the 



I shall suppose with Fresnel, that by a ray polarized in one 

 plane is meant a ray whose vibrations are entirely perpendi- 

 cular to that plane ; that consequently the vibrations forming 

 the ordinary ray in the crystal are entirely perpendicular to the 

 principal plane passing through that ray, and that those form- 

 ing the extraordinary ray are wholly parallel to that plane. 



I*. Now suppose a pencil of polarized light to fall with a 

 small angle of incidence on a plate of calc spar cut perpendi- 

 cular to its axis. Let us conceive ourselves looking in the di- 

 rection of the incident ray; and let fig. 15. represent the pro- 

 jections (on a plane perpendicular to the incident ray) of the 

 planes of polarization of the polarizing and analyzing plate, and 

 of the principal plane of the crystal passing through the inci- 

 dent ray. Let P°Ap 2 the plane of polarization (or of reflection) 

 at the analyzing plate, make an angle a with P^Ap x the original 

 plane of polarization; and let CAc the principal plane of the 

 crystal passing through the ray make the angle <p with the 

 former plane. The displacement of the particles of ether pro- 

 duced by the wave as originally polarized, may be represented 



by c.sin — - (vt—x), where \ is the interval of space between two 



waves, x the distance measured from any arbitrary point, t the 

 time since the ether at that point was at rest, and v the velocity of 

 the wave. (This applies even after the wave has passed through 

 any media, provided we take for x the space which would 

 in the same time have been described in air). And this dis- 

 placement is entirely perpendicular to P^,. This may be re- 

 solved into c.sin — .(vt — a;). cos (a + <p) perpendicular to AC, and 



A 



* The Phenomena, and the investigations corresponding to them, are numbered in the 

 same way. 



