F. E. Wright — Measurement of Extinction Angles. 351 



satisfactory in all its details.* For the purposes of this paper, 



however, these disturbances may be considered vibrations of 



ether particles about positions of rest and in a plane normal 



to the line of wave propagation. Adopting this, view chiefly 



as a matter of easy expression, we may assert that in plane 



polarized light the disturbances or vibrations are confined to 



a plane, each particle vibrating then with simple periodic 



motion, to and fro, pendulum like, along a straight iine. An 



equation which satisfies such a periodic vibration and which 



has been found to represent satisfactorily the ether disturbances, 



is the following : 



2tt 

 y ~ a sin -fft (* — O ( L ) 



in which a represents the amplitude, T the periodic time, -^ffr 



the initial phase, t the time which has elapsed at any given 

 instant, and y the distance of the ether particle from its posi- 

 tion of rest. The velocity of the ether particle at any instant 

 is given by 



dy 2tt 2tt 



v —j t = a ~y cos t^ (t-tj 



and if m be its mass, its kinetic energy is 1/2 mv 2 . 



The above equation shows that v varies from to ; 



accordingly the average kinetic energy during a complete 

 vibration will be 



Yj V 2 mv dt = ~ T r~J 2cos ~T~( t — t J dt 



o o 



V/-TA 4tt \ wiflVf, , t . 4tt. -IT 



—J (^1+cos ™ (t-t : ))rti = -^- \J + — sin T (t-t L ) j 



ma tv . 



Xow, a vibrating particle possesses at any instant a definite 

 amount of kinetic energy and also a definite amount of poten- 

 tial energy, and the sum of these two amounts of energy 

 remains constant throughout the vibration, so that as the 

 kinetic energy in the particle increases its potential energy 



* These theories, as well as the mathematical treatment of the same, are 

 given in the standard text-books on light (Preston's Theory of Light ; P. 

 Drade, Lehrbuch d. Optik, and many others ; also Kosenbusch-Wiilfmg, 

 Mikrosk. Physiographie i, 1 ; and Duparc and Pearee, Traite" de Technique 

 Mineralogiqne et Petrographique). 



ma 



