. 
On Polarization of Light by Refraction. 229 
_ The above expression is of course suited only to the case where 
the inclination x of the planes of polarization ab, ed, (Fig. 1,) is 45° ; 
al when this is not the case, the general expression is 
Cot p=cot x cos (i—7). 
"When the light passes through a second surface, as in a  singte 
ate of glass, the value of « for the secondssurface is evidently the 
value of 9 after the Ist refraction, or in general, calling 4 the inclina- 
tion after any number 7 of refractions, and ¢ the inclination after 
one relagetiods. 
Cot é=(cot ¢)" 
When éis given by observation we have 
Cot op=Vcot 4. 
“The general formula for any inclination x and any number n of re- 
fractions sis 
Cot 6==(cot x cos (i—7’))", and 
Cot p=V cot rcos (t—7’). 
And when «=45 and cot <=1 as in common light, 
Cot 6=(cos (i —2’))*- 
Cot p=V cos (t—7’). so 
we As the term (cos (i@-#))* can never become equal to 0, the planes 
of p ‘can never be brought into a state of coincidence in a 
plane. perpendicular to that of reflexion, either at the polarizing an- 
‘gle, or at any other angle. 
In order to compare the formula with experiment, I took a plate 
6 well annealed glass, which at all incidences separates the reflect- 
‘ed from the transmitted rays, and in which‘ m was ay boc tied 
= : obtained the following results. 
whe BS 
sf cesihen &, 
: is Sp pps ities 
Miistae bee ate Cee in lj at . 
i S Mecgaren” rey 
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Sy ee ee rs 
