76 DOVE’S EXPERIMENTS ON THE 
the two figures polarized perpendicularly to one another, we have ge- 
nerally, 
I, = cos? 6 — sin 2a sin 2 (a — b) cos? t (=) 
A 
in which A indicates the length of undulation for a definite colour, o—e 
the difference 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, 
J, = cos?6b — cos 2 b cos? r (°=*) 
I, =sin?é + sin 2a sin 2 (a—)) sin? r (° ‘); 
I. = sin? b + cos 2 6 sin? o=*). 
If then by any means we can make the difference between the paths of 
both rays equal 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, 
sex [(22=2)a], 
then will 
The difference 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 pressure 
or change of temperature, so that it may exhibit the desired effect in a 
given thickness, would afford no convenient practical arrangement. It 
is, however, very easy by means of pressure or cooling to change the 
uncrystallized into a double-refracting body, which gives precisely the 
required effect. In the apparatus proposed by Fresnel, consisting of 
