282 Professor Airy oh a remarkable 



turning' farther, the white spot contracts and vanishes, and the 

 dark spot diminishes till the axis of the tourmaline is again in 

 the plane of reflexion. 



The plate of metal used in these experiments was a telescope 

 speculum, with tolerably bright surface. To guard against all 

 sources of error from want of contact of the lens and the metal, 

 a broad flat ring of thick sheet lead was placed on the lens, 

 and was sometimes loaded with a weight of about six pounds, 

 distributed over its circumference. The changes in question 

 therefore had no connexion with the changes" of colour in the 

 central spot when the lens and glass plate are not perfectly in 

 contact. And it will easily be seen that they have nothing in 

 common with the change from black to white produced in some 

 of Sir W. Herschel's experiments (Phil. Trans. 1807 and 1809). 

 the latter being merely a substitution, by a kind of slight of 

 hand, of the rings of transmitted light tor those of reflected light. 



The explanation of this phaenomenon will be found in the 

 expression for the intensity of rings produced by the interference 

 of two streams of reflected light, the quantity of light reflected 

 being expressed by Fresnel's formula. If < be the angle of inci- 

 dence within the glass and »' the corresponding angle of refraction, 

 and if the light be polarized in the plane perpendicular to the 

 plane of reflexion (that is, if the vibrations of the particles of 

 ether take place wholly in the plane of reflexion), and if the 

 extent of displacement in the vibrations before incidence be re- 

 presented by fl.sin — (vt— x), then that in the vibrations after 

 reflexion from the second surface of the glass Will be 



tan (t - i ) 2 7T 



a . t rr ■ sm — - (vt-x). 



tan (« + 1 * 



