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The axis of x we take here in the direction of the original linear 
vibration occuring in the plane z = 0; moreover, in conformity 
with the notation employed above, we use suffix 1 when dealing 
with the right-handed circularly-polarized wave and suffix 2 when 
dealing with the left-handed circularly polarized wave. 
A simple geometrical construction is easily obtained. In Fig. 1. 
let Ox be the axis of x and let 0M 1 and OM 2 represent the dis¬ 
placements due to the two component circular vibrations. We have 
(2) 
x OM 2 — nÇt — ^. 
ON so that xON be = Ox , then 
N0M 2 = Q ; 
if Oy is a line bisecting NOM 2 , either of the angles JVOy, 
represents the angle ip. If OA makes with Ox an angle 
precisely = tp, the major axis of the ellipse will coincide with OA. 
It appears at once that 
(5) M l OA = AOM t = n^t — izQ+j') 1, 
thus the direction OA is always along the line bisecting the angle 
m ± om 2 . 
Consider a plane 
(6) z = const. 
and suppose t = z/c v Then the point M x is evidently on the axis 
Ox and the angle xOM 2 at the same time is = 6. Hence the dir¬ 
ection OA in the plane is along the line bisecting the angle xOM 2 
at the time considered. 
§ 7. Let a be the major semi-axis, / the minor semi-axis of 
the ellipse; let us introduce a symbol (p defined by 
( 3 ) 
Draw 
( 4 ) 
hence 
yOM i 
( 1 ) 
We know the angle (p admits of being measured in actual experi¬ 
ment; its value in several cases has been carefully recorded by 
