236 On Polarization of Light by Refraction. 
The case, however, is different with the refracted light. The 
value of Q’ has one minimum at 0° and another at 90°, while its 
maximum is at 78° 7’, while the force has its minimum at 0° and — 
its maximum at 90°, where its effect is a minimum only because 
there is no light to polarize. At the incidence of 78° 7’, where the 
quantities Q, Q’, reach their maxima, the reflected light is exactly 
one half of the transmitted light; sin?g=cos?p and tan o/= cos p. - 
At 85° 50’ 40”,ewhere the transmitted light is one half of the 
reflected light, the deviation (:—i)=45°, and the quantity of po- 
larized light is one third of the transmitted light, one sixth of there- 
flected light, and one ninth of the incident light. Sin?’ : cos?o= 
reflected light : transmitted light, and cot¢’=sin(i—/). 
At 45° we have (i+7)+(i—7)=90° and o=(i-7), 
dep. oan c08 (6-+1/) » yg (sin (t¢—#))? 
_ Tan kd ere (vy and tan (s—7 eS ii 
At 56° 45’, the polarizing angle, the formula for reflected light 
becomes R=4(sin?(i—7/))? ; but at this angle we have 7/=90° —1, 
Hence we obtain the following simple expression in terms of the an- 
gle of incidence, for the quantity of light reflected by all bodies at 
the polarizing angle. oe 
_ R=4(cos 22)?. Be 
T have already mentioned the experiment of M. Arago with plates 
of glass, in which he found that “ at every possible inclination” the 
quantity of light polarized by transmission was equal to the quantity 
larized by reflexion. This conclusion he extends to single surfa- 
ces; but it is remarkable that the law is true of single surfaces in 
which he did not ascertain it to be true, while it is incorrect with re- 
gard to plates in which he believes that he has ascertained it to be 
true. As the consideration of this point does not strictly belong to 
the present branch of the inquiry, I shall reserve it for a separate 
communication, “on the action of the second surfaces of transpa- 
rent plates. upon light.”* . Beiet cs 
Allerly, December 29, 1929. 
_ * Inserted in the last number of this Journal. 
