290 Mr. J. J. Thomson on 



substituting for ^, we get 



_ a x tan(& — r) 

 a2 "lanO + r)"' 



«i sin 2c 



«3 = 



sin (i + r) cos (i—r) ' 



For light polarized in the plane of incidence, if we consider 

 magnetic disturbances instead of electrical, the formulae for 

 the intensities will be got by exactly the same process as before; 

 hence writing /i^, fi 2 in the place of K 1? K 2 , and using the 

 same notation as before 



f f (/jl 2 tan r — /^ tan t) 



U o = U -i ; ■ ; i 



/ju 2 tan r + /*i tan i 



i _ ' 2vV 1 />& 2 sin i 



1 (fjb 2 tan r + fjii tanj) cos r" 

 If ^i=/*2? we get 



__ y sinfr-r) 



AC 9— — Ot 1 — : — -, C » 



2 ^mO + r)' 



sin2t 



«3 = «n 



sin (t + f) 



The first is the same as that given by Fresnel ; but the 

 second is not quite the same : Fresnel's formula is 



, , 2 sin i cos r 



3 1 sm {t + r) 



According to Maxwell's theory, the refracted ray is more in- 

 cos L > 

 cosr 



tense in the ratio -* 



Equation (10) will enable us to find the effect produced by 

 the motion of the dielectric on the velocity of light. To take 

 the simplest case, let us suppose the dielectric moving with 

 velocity u in the direction of propagation of the light, which 

 we shall take as the axis of x. 



* Since the above was written, I have found that the problem of the 

 reflexion and refraction of light, according to Maxwell's theory, has been 

 very fully treated by Lorentz, in Schlomilch, Zeitschrift, vol. xxii. 



