76 dove's experiments on the 



the two figures polarized perpendicularly to one another, we have ge- 

 nerally, 



Ig = COS- b — sin 2 a sin 2 (a — b) cos'^ ir ( J 



Ig =: sin- b + sin 2 a sin 2 (a — b) sin'- tt I |, 



in which A indicates the length of undulation for a definite colourj o—e 

 the diff"erence of path of both rays, and I the intensity of the polarized 

 light falling perpendicularly upon the crystal plate. Now if the axis of 

 the plate is made to form an angle of 45° with the plane of primitive po- 

 larization, that is to say, if we suppose a = 45°, we shall have, 



lo = cos- b — cos 2 b cos- it ( - — - J 



Ic =■ sin- b + cos 2 b sin^TT | \ 



If then liy any means we can make the difference between the paths of 

 both rays ecpial to an uneven number of quarter-undulations, the second 

 condition will also be satisfied as well as the first, viz. that of the equal 

 intensity. Suppose, for instance. 



= [(~^)^\ 



then will 



lo = cos'2 ^ — 2 ^0® 2 6 = 5 



\e = sin- b + \ cos 2 b = ^. 

 The diff'erence of path o—e depends on two quantities; on the thickness 

 of the plate, to which it is in direct proportion, and on the difference of 

 velocity of the two rays which pass through the plate, that is to say, on 

 the constant of double refraction. 



Airy's method consists only in varying the thickness of the plate by 

 splitting it, whilst the double refraction remains the same, until the dif- 

 ference between the paths of the rays is equal to an uneven number of 

 quarter-undulations. As biaxal mica under a perpendicular incidence 

 of the light is similar to an uniaxal crystal and best allows splitting 

 into larger plates, its application will therefore be preferable. I, on the 

 contrary, alter the double refraction of the substance, whilst the thick- 

 ness remains the same, until the required difference of path is obtained. 

 To alter the refraction of rays in a crystallized lamina by jiressure 

 or change of temperature, so that it may exhibit the desired effect in a 

 given thickness. Mould aff'ord no convenient practical arrangement. It 

 is, however, very easy by means of pressure or cooling to change the 

 uncrystallized into a double-refracting l)ody, which gives precisely the 

 required eff'ect. In the api)aratus proposed ))y Fresnel, consisting of 



