of the Crossing of Rays. 
59 
complication consists only of the change in this ellipse in pass- 
in o- from one point to another. Hence a model might he con- 
structed to represent the crossing of homogeneous ^ rays by 
placing a number of ellipses to represent the motion at a 
number of separate points, through which the light might be 
supposed to be passing. If we further simplify the case by 
considering only rays parallel to one plane, and suppose them 
to be plane-polarized so that the vibrations are parallel to the 
same plane, the whole motion will be parallel to that plane, 
and might be represented by means of diagrams. 
The case worked out in this paper is that of three rays of 
equal intensity parallel to one plane, plane-polarized so that 
the vibrations are parallel to that plane, and meeting one 
another at equal angles. 
Take any point 0, and let PO P, Q' Q, E' E be the rays 
through 0. Take any other point T in the same plane; draw 
T X, T Y perpendicular and parallel respectively to t" P. 
Let p, q, r be the distances from of the feet of the perpen- 
diculars drawn from T on P' P, Q' Q, E' E respectively; 
these distances being considered positive if drawn towards 
P, Q, E, and negative if drawn towards V, Q', E'. Then it 
may be shown that 
p + q + r=0. ...... (1) 
The position of T may be defined by any two of these quan- 
tities. The equations p — const., q — const., r— const., are equa- 
