THE POLARIZATION OF LIGHT BY REFRACTION. 
141 
reflexion. Each refracting surface produces a change in the position of the 
planes of polarization, and consequently a physical change upon the trans- 
mitted pencil by which it has approached to the state of complete polarization. 
This position I shall illustrate by applying the formula to the experiments 
which I have published in the Philosophical Transactions for 1814. 
According to the first of these experiments, the light of a wax candle at the 
distance of ten or twelve feet is wholly polarized by eight plates, or sixteen 
surfaces of parallel plate glass at an angle of 7 8° 52'. Now I have ascer- 
tained that a pencil of light of this intensity, will disappear from the extraor- 
dinary image, or appear to be completely polarized, provided its planes of 
polarization do not form an angle of less than 88f° with the plane of refraction 
for a moderate number of plates, or 88^° for a considerable number of plates, 
the difference arising from the great diminution of the light in passing through 
the substance of the glass. In the present case the formula gives 
Cot 0 — (cos (i — i')) 16 and d = 88° 50' ; 
so that the light should appear to be completely polarized, as it was found to be. 
At an angle of 61° 0' the pencil was polarized by 24 plates or 48 surfaces. 
Here 
Cot 6 — (cos (i — i')) 48 = 89° 36'. 
At an angle of 43° 34' the light was polarized by 47 plates or 94 surfaces. 
Here 
Cot 6 = (cos (i — i')) 94 an d ^ = 88° 27'. 
It is needless to carry this comparison any further ; but it may be interest- 
ing to ascertain by the formula the smallest number of refractions which will 
produce complete polarization. In this case the angle of incidence must be 
90°. 
Hence <p = 56° 29' and (cos ( i — i')) 9 gives 88° 36', and (cos (i — i)) 10 
89° 4'; that is, the polarization will be nearly complete by the most oblique 
transmission through 4^ plates or 9 surfaces, and will be perfectly com- 
plete through 5 plates or 10 surfaces. 
Having thus obtained formulse for the quantity of light polarized by refrac- 
