238 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
The author explains carefully the method of calibrating the wedge, 
and gives the usual demonstration, according to Fresnel’s theory, of the 
formulae relating to the nature and intensity of the interference tints 
produced in doubly refracting bodies in parallel polarized light. For 
the ordinary conditions of work with the nicols crossed and the principal 
section of the wedge orientated at ± 45° to the plane of primitive polar- 
ization the intensity J of the ray from the analyser is given by 
T . 2 (N 0 — N f ) D 
J = Sim 7 r — , 
where N 0 and N e are the indices of refraction of the doubly refracting 
body corresponding to the ordinary and extraordinary rays, D the thick- 
ness of the wedge at the given point, and A. the wave-length of the 
light. 
The intensity of the coloration will be a maximum when 
(N 0 -N«)D = ( 2 i + l)^ 
where h is any whole number. 
The tints given by the wedge between crossed nicols thus corre- 
spond to those of Newton’s rings, since the rings which have the maxi- 
mum intensity are those for which the relation holds : 
2e = (2£ + l)A 
A j 
where v e is the thickness of the layer of air. 
Now, in the case of the wedge the difference of path 0 of the ordinary 
and extraordinary rays is given by 
e = (N.-N.)D 
If, therefore, the wedge is examined in homogeneous polarized light 
of wave-length A, it will present bright parts corresponding to thick- 
nesses such that the difference of path 0 is equal to an uneven number 
of half wave-lengths, and dark parts where the thickness is such that the 
difference of path is equal to an even number of half wave-lengths, i. e. to 
a whole number of wave-lengths. 
This gives a first means of calibrating the wedge, viz. by determining 
what is the difference of path of the two interfering rays and, therefore, 
the thickness for each point of the wedge. 
In the case of the selenite, according to the determinations of 
Descloiseaux and Angstrdm, in sodium light (A = 0*589 /x), 
for the axis of elasticity c : n g = 1 *5297 ; 
for the axis of elasticity a : n p = 1 * 5206 ; 
whence n g — n p = 0*0091. 
We have, therefore, for the first dark band 
0*0091 = 0*589 /x; 
for the second, 
0*0091 D 2 = 1*178 /x, 
and so on. 
