Royal Irish Academy. 387 



cumstance affords a method of directly and accurately testing the 

 truth of the formulae which Fresnel has given for the case of total 

 reflexion at the separating surface of two ordinary media ; for we 

 have only to measure the angle of the rhomb and the refractive index 

 of the glass, and to compute, by Fresnel's formula, the alteration 

 which the rhomb ought to produce in the difference between the 

 phases of the resolved vibrations ; which alteration of phase we may 

 then compare with that deduced, by means of the formula? (K.) and 

 (L.), from direct experiment. 



If, in each position of the rhomb, we measure the angle which the 

 plane of polarization of the emergent ray makes with the plane of 

 incidence on the metal, and call the two angles respectively y', y", 

 we shall have 



7 ' = 0'_/3', y" = d" + ft', .... (M.) 

 and therefore 



y' + y» = o' + 8" = 26, 2ft , = y"-y' + e'-6"; (N.) 

 from which it appears that if the rhomb were perfectly exact, that 

 is, if 0' and 0" were equal to each other, the angle would be half 

 the sum of y' , y", and the angle ft half their difference. It would 

 then be sufficient to measure the angles y' and y", in order to get 6 

 and ft accurately. And if the rhomb were erroneous, the true value 

 of 6 would still be half the sum of y' , y" ; but the true value of ft 

 would not be discoverable without measuring the angles &, 6' 1 , by 

 the help of which it can be deduced from the second of formula; (N.), 

 combined with the second of formula? (K.). Nor can we discover 

 whether the rhomb is erroneous or not, without measuring the angles 

 6', 6" ; and therefore as these angles must be measured in any case, 

 the former method of determining d and ft is to be preferred. 



In making experiments on elliptically polarized light, a plate of 

 mica or any other doubly refracting crystal, placed perpendicular to 

 the ray, may be used instead of Fresnel's rhomb. If the thickness 

 of the crystalline plate be such that the interval between the two 

 rays which emerge from it is equal to the fourth part of the length 

 of a wave, for light of a given refrangibility, the plate will, for such 

 light, perform all the functions of the rhomb ; the principal plane of 

 the rhomb being represented by the plane of polarization of one of 

 the emergent rays. But unless the light be perfectly homogeneous, 

 this method is liable to great inaccuracy in practice, since the effect 

 of the plate in producing or altering the difference of phase between 

 the two rays which interfere on their emergence from it, is inversely 

 proportional to the length of a wave, and will therefore be extremely 

 different for light of different colours, and will change very per- 

 ceptibly even within the limits of the same colour. It is true, the 

 effect of the rhomb also varies with the colour of the light : but this 

 variation is trifling compared with that which exists in the other 

 case. It was for this reason that I employed the rhomb in my ex- 

 periments, instead of a crystalline plate. The apparatus, however, 

 is much simplified by using such a plate ; and if any one chooses to 

 do so, and to work with homogeneous light, he must take care to 

 follow, in every respect, the directions which I have given for con- 



2 C2 



