406 NEUMANN ON A METHOD OF ESTIMATING THE 
which is polarized at right angles to the plane of incidence, and 
one which is polarized in a plane parallel to it, expressing the 
intensity of the former by p* P*, and of the latter by p!* P?. I call 
the intensity of the ordinary ray w? P?, and that of the extra- 
ordinary w? P?, When the incident light is polarized in a plane 
parallel to that of incidence, I call its intensity S*. The intensity 
of that component of reflected light which is polarized parallel 
to the plane of incidence, would be s*S*; that polarized perpen- 
dicularly would be s'? S*, and the intensities of the ordinary and 
extraordinary rays would be o!? S? and o'?S*. We are nowina 
condition to express the intensity of the reflected and refracted 
light, when the incident ray is polarized in any azimuth. P? 
and S? would represent the intensities of the component rays of 
the incident light, R,? and R,? those of the reflected ray, and 
those of the ordinary and extraordinary ray would be D? and D!?. 
The ray R,* is composed of p? P? and s!? S?; these are two rays 
having the same origin polarized in the same direction; they 
form a compound ray the intensity of which is (py P+s'S)?. The 
ray R,’ is likewise composed of the rays p’ P? and s? S%, its 
intensity is consequently (py! P+s8)?. The same applies to D! 
and D". We thus have | 
R, =p P+¢s' 8S, 
R, = p' P+s S, 
D! =o’ P+0'S, 
D! = wo! P+o!S, 
In consequence of the assumed perfect transparency of the 
medium, we have 
P?+S°=R,?+R,?+ D?+ D'. 
This equation must apply, whatever the values of P and 8S, 
which are independent of one another, may be. If for R,, R,, D! 
and D", we substitute their values, the equation resolves itself 
into the following three formulz :— 
l axigre + p ate a2 SE w!!2, 
1= sl? 452 +)? 4 ol, 
O=ps'+ p's+ alo!+ wo", 
One of the two rays composing the ordinary ray may be ex- 
pressed as half an undulation behind the other, by a proper ar- 
rangement of P and 8, %. e. by the proper arrangement of the 
azimuth of polarization of the incident ray ; then each ray will 
diminish the intensity of the other, and at a certain value of 
ue they will completely destroy one another; this value of ae 
