Polarization of the Light reflected by the Sky. 109 
prism is turned through an angle v, one image will have a bright- 
ness A sin?v, the other Bcos*v ; and if they are equal, A sin?v 
cos? v—sin?v 
et ee =cos 2v. The amount of 
os?v+sin2v 
=Bcos*v, hence p = 
aving given p’ and p”, we wish to determine p and w.. Evi- 
dently p’=pcos2w, and p=pcos2 (45°—w)=psin2w. Taking 
/ 
their quotient gives tang 2w =P and the sum of their squares 
gives p=Wp'2 +72, This method, though elegant theoreti- 
cally, does not appear very accurate practically, as the plane is 
More accurately determined by covering the end of the polar- 
. “ 
imeter with a cap containing a plate of selenite, thus converting 
Now it is commonly assumed that the difference in two such 
Images will be perceptible, when the difference in brightness, 
divided by the brightness of either, equals a certain fraction - 
in which a equals about 80. By differentiation it may be 
proved that the error in p or dp corresponding to any yalue of 
2 
@ is given by the formula dp=*P , from which the error in 
