79 



The author has not adopted any particular dynamical theory, but 

 has deduced his results from Fresnel's expressions for the intensities 

 of reflected and refracted polarized light. When the angle of inci- 

 dence becomes greater than the critical angle these expressions be- 

 come imaginary. When the imaginary expressions are interpreted 

 in the way in which physical considerations show that they must be 

 interpreted, it becomes easy to obtain the expression for the intensity 

 of the light, whether reflected or transmitted, in the neighbourhood 

 of the spot. When the first and third media are of the same nature, 

 the following expression is obtained for the intensity (I) of the re- 

 flected light, the incident light being polarized in the plane of inci- 

 dence, and its intensity being taken for unity, 



In this expression p is the refractive index of the first medium, i the 

 angle of incidence on the surface of the second medium, or inter- 

 posed plate of air, D the thickness of that plate at the point con- 

 sidered, A the length of a wave in air, 2 the acceleration of phase 

 due to total internal reflexion. When the light is polarized perpen- 

 dicularly to the plane of incidence, it is only necessary to replace 2 9 

 by 2 <p , the angles 0, <p being those so denoted in Airy's Tract. The 

 intensity of the transmitted light is obtained by subtracting that of 

 the reflected light from unity. 



From the expression for the intensity, the author has deduced the 

 following results, all of which he has verified by observation. 



The spot is comparatively large near the critical angle, and becomes 

 smaller and smaller as the angle of incidence increases. Near the 

 critical angle the fainter portion, or ragged edge, of the bright spot 

 seen by transmission is broad ; at considerable angles of incidence 

 the light decreases with comparative abruptness. Towards the edge 

 of the spot there is a predominance of the colours at the red end of 

 the spectrum, causing the ragged edge to appear brown. Near the 

 critical angle the spot is larger for light polarized perpendicularly to 

 the plane of incidence than for light polarized in that plane : at con- 

 siderable angles of incidence the order of magnitude is reversed. 

 The difference is far more conspicuous in the former case than in the 

 latter, and in that case consists principally in the greater extent of 

 the ragged edge. When the incident light is polarized at an azimuth 

 of 45°, or thereabouts, and the transmitted light is analysed so as to 

 extinguish the light transmitted near the point of contact, there is 

 seen a central dark patch surrounded by a luminous ring. 



February 26, 1849. 



On a New Method of finding the Rational Roots of Numerical 

 Equations. By Robert Moon, Esq. 



The author proposes to found a new experimental method of find- 



