16 
MR. POWER ON THE ABSORPTION OF THE SOLAR RAYS, ETC. 
From these two equations we may readily derive the following, 
p— 2 cos 
/2ttc\ 
V A )'hk~^k* — 
giving for the motion of an ethereal particle, in general, an ellipse having its centre 
in the axis of the ray and its plane perpendicular to that axis. 
The constant c determines the difference of phase of the two component waves ; if 
the phases be coincident, we have c=0, in which case the above equation becomes 
k 
z =h^ 
The particle, therefore, performs its vibration in a straight line inclined to the axis 
k 
of y, that is, to the plane of incidence at an angle whose tangent is j. 1 shall call 
this the angle of orientation : denoting it by y, we get 
tan 2y= 
2 h 2 hk 
_k*—h?-k r 
h? 
In general it is not difficult to show, by the usual method of transformation of coor- 
dinates, that the major axis of the elliptic orbit, whose equation has been exhibited 
above, makes with the plane of incidence an angle of orientation (y) determined by 
the equation 
2 hk / 2 7tc\ 
taa 2 r=TF=P c0S {— )■ 
7T 
If h — k, y=- in both cases; the linear radius of vibration and the axis major of 
the elliptical vibration are therefore inclined to the plane of incidence at an angle 
of 45°. 
In the particular case of h—k, and c=p 
tan 2y=^ ; 
and is therefore indeterminate, but in that case the equation becomes 
y'-\ -z*=h 2 . 
each particle therefore describes a circle about a point in the axis of the ray, and all 
traces of orientation disappear. 
It is needless to state that the three cases, which have here been briefly discussed, 
are those usually distinguished as belonging to plane polarized, elliptically polarized, 
and circularly polarized light. 
12. By the theory of superposition of small motions we are at liberty to consider 
