1898.] 



on Magneto-Optic Botation. 



713 



that speed towards the right. Imagine, now, these two motions to be 

 united in a single particle. The vertical motions will be added 

 together, the right and left motions will cancel one another, and the 

 particle will have a motion of vibration m the vertical direction of 

 range equal to twice the diameter of the circles, and in the period of 

 the circular motions. 



The rate of increase of velocity of the particle at each instant is 

 the resultant obtained by properly adding together the accelerations 

 of the particles in the circular motions, and therefore the force which 

 must act on the particle to cause it to describe the vibratory motion 

 just described, is the resultant of the forces required to give to the 

 two particles the circular motions which have just been considered. 



Now, what we have done for any one particle may be conceived of 

 as done for all the particles in a wave. To understand the nature of 

 a wave in this scheme, we must think of a series of particles originally 

 in a straight line in the direction of propagation of the ray, as dis- 

 placed to positions on a helix surrounding that direction. Fig. A 



Fig. 11. 



of this diagram (Fig. 10), regarded from the lower end, and the black 

 spots on the model before you, show a left-handed helical arrangement. 

 Let these particles be projected with equal speeds in the circular paths 

 represented by the circle at the bottom of Fisj. A. On this circle are 

 seen the apparent positions of different particles in the helical ar- 

 rangement when it is viewed by an eye looking upwards along its 

 axis. This motion is shown by that of the black spots on the surface 

 of the model (Fig. 11), when I set it into rotation about its axis. 

 Let the particles be constrained to continue in motion exactly in this 

 manner. As the model shows, the helical arrangement of the par- 

 ticles is displaced along the cylinder. This is the mode of propaga- 

 tion of a circularly polarised wave, which is made up of helical 

 arrangements of particles which were formerly in straight lines 

 parallel to the axis. 



The direction of propagation of the wave is clearly from the 

 bottom of the diagram to the top^ and from the end of the model 

 towards your left to the other, when the particles have a right-handed 

 motion, and is in the contrary direction when the direction of rotation 

 is reversed. For a right-handed helical arrangement the direction of 



