236 ON THE COMPOSITION AND RESOLUTION OF STREAMS OF
Let the co-ordinates of, yr be measured in the principal planes whose azimuths are a, a 4-90°; let /3 be the angle whose tangent is equal to the ratio of the axes of the ellipse described, the numerical value of /3 being supposed not to lie beyond the limits 0 and 90° ; let v be the velocity of propagation, t the time, X the length of a wave, and put for shortness,
_
,)^ ........................ (1).
Then about the time t, and at no very great distance from a given point, suppose the origin, we may represent the displace-ments belonging to the given stream of elliptically polarized light by
of = c cos /3 sin (<£ + e), y' = c sin f$ cos (<£ + e) ...... (2).
If the light be convergent or divergent, c will depend upon <£, but for our present object any variation of c arising from this cause will not enter into account. The value of a, which deter-mines the direction in which % is measured, as well as that of y3, is given by the nature of the polarization. The polarization is right-handed or left-handed according to the sign of /3. As to c and e, the phenomena of optics oblige us to suppose that they are constant, or sensibly constant, for a great number of consecutive undulations, but that they change in an irregular manner a great number of times in the course of one second. The known rapidity of the luminous vibrations allows abundant scope for such a supposition, since c and e may be constant for millions of consecutive undulations, and yet change millions of times in a second. This series of changes, rapid with respect to the duration of impressions on the retina, but slow compared with the periodic changes in the motion of the ethereal particles, is exactly what we might have expected beforehand from a consideration of the circumstances under which light is produced, so far at least as its sources are accessible to us ; and thus in this point, as in so many others, the theory of undulations commends itself for its simplicity.
If c were constant c2 would be a measure of the intensity, so long as we were only comparing different streams having the same refrangibility. But since c is liable to the changes just mentioned, if we wish to express ourselves exactly, avoiding