II. ON THE INTENSITY OF LIGHT WHEN THE VIBRA- 

 TIONS ARE ELLIPTICAL. 



[Edinburgh Journal of Science, April, 1831.] 



ACCORDING to the opinions commonly received, the intensity of 

 light, in the undulatory hypothesis, is proportional to the ris 

 viva, which again is proportional to the square of the greatest 

 velocity. Now the greatest velocity will be the same in an 

 ellipse and a right line which have the same period, if the 

 greater axis of the former be equal to the whole extent of the 

 latter ; so that in elliptic vibrations the intensity would be in- 

 dependent of the minor axis, which is far from being true. I 

 would propose the integral Sv*dt so remarkable for its mecha- 

 nical properties as the measure of the intensity, the integral 

 being extended to the whole time of a vibration. This gives 

 precision to the notion of vis viva, and leads, moreover, to an 

 elegant result ; for if a and b denote the semiaxes of the ellipse, 

 and T the time of vibration, the integral, by an easy calculation, 



27T 2 



will be found equal to -=- (a 2 + & 2 ), showing that for the same 



colour the intensity is proportional to the sum of the squares of 

 the semiaxes, and that for different colours it increases with the 

 rapidity of the vibrations, as it would be natural to suppose 

 a priori, 



This theorem assigns very simply the reason why two por- 

 tions of light polarized at right angles do not interfere ; but to 



