90 Professor Airy on the 



Now it must be remarked (as a general theorem which we 

 shall use hereafter without further explanation) that an ex- 

 pression of the form 



2tT 27T 



JE . sin — - (vt — x) + F . cos- — (vt—x) 



A A 



may always be put under the form 



2tt / , XG> 



JWTF 7 .sin^(vt-x + ^), 



A V 27T / 



F 

 where tan G=~, and G is constant for that ray. It is plain 



that this expresses a periodical vibration similar to that which 



we have all along supposed, and whose coefficient instead of c is 



y/Et + F-. It is convenient to take the square of this coefficient 



as the measure of the intensity of light: and thus E' 2 + F- will 



represent the intensity in all cases similar to that before us. 



In the present instance, the intensity or the sum of 

 the squares of the multipliers of the sine and cosine of 



2tt, ' . 



— [vt - x) IS 



A 



c" {cos' 2 a + <p . cos 2 <p + sin 2 a + <p . sin <p 



2-7T 



+ 2 cos — 9 . sin a + <b . cos a + <p . sin <p . cos $} 

 X 



gp Q— 



= — {1 + cos 2 . a + <p . cos 2(f> + cos — - © . sin 2 . a + (j> . sin 2<f>}. 



Thus we have a general expression for the intensity of the 

 light when polarized light passes in any one direction through 

 the crystal, and after being reflected by the analyzing plate, is 

 received on a screen. If we suppose polarized light to fall in all 

 possible directions (within certain limits) upon the crystal, we 

 must give all possible values to 6 and <£, and we shall have the 



