II. ON THE INTENSITY OE 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 -vis 

 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, 



2?r 2 

 will be found equal to (a? + # 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 



