if we put 
tan yon (6) 
tan S=tan2wvsin(x +x) (7) 
1—sin 2 cos (x +x) (8) 
we T-+sin2ycos(x +x’) 
Then according to the interpretation, before alluded to, 
of /—1, the angle 3 will denote the change of phase, oF 
the retardation of the reflected light; and a will be the 
amplitude of the reflected vibration, that of the incident vi- 
bration being unity. The values of m'’,x’, for any angle of 
incidence, are found by formule (3), (4), the quantities m, xX, 
being given for each metal. The angle x’ is very small, and 
may in general be neglected. 
Secondly, when the incident light is polarized perpendi- 
cularly to the plane of reflexion, the expression 
tan (i—7) 
tan ( +4’) 
treated in the same manner, will become 
a (cos0 — V—lsind), (9) 
if we make 
tany’=mm', (10) 
tand’—tan2y/ sin(x— x’), (11) 
gal” = 
os” sin2y’cos(x—x) , (12) 
T+ sin2ycos(x—x’)’ 
and here, as before, & will be the retardation of the reflected 
light, and a’ the amplitude of its vibration. 
The number ua may be called the modulus, and the 
angle x the characteristic of the metal. The modulus is 
something less than the tangent of the angle which Sir David 
Brewster has called the maximum polarizing angle. After 
two reflexions at this angle a ray originally polarized in a 
