328 MA<;M-;TISM 



We may obtain the actual rotation bv noting tlmt the 

 forward propagation of a circular disturbance with spied D i> 

 represented by 



- - 



where is the angle the radius makes \\illi a fixed direction per- 

 pendicular to the line of propagation, the distance X being 

 measured from a starting-point on the line at which 0= " when 

 t = 0. For at any fixed point the angle 6 gro\\> at tin r.v 

 or at each point there is circular motion, and at di>tance ./. fJ = 

 when x = r/, or the displacement which is at ./ = when / = 

 is propagated forward with velocity r. 



Now let an equal circular disturbance, but with opposite 

 rotation, 6, travel forward with a ! -^ \rlocifv ;'. Then the 

 direction of disturbance at ./ at time / \\ill ta 



as.siiming that it is at ./ = u when / 0. 



It is easily seen that the sum of two displacement-. < ach >i and 



0+& 



in directions 9 0', is in tliv direction 5 , and is in magnitude 



% 



That is, it is in the direction ^ -), 



% \ V V / 



and its magnitiKi- 



1 



It is, then, a simple harmonic vibration in a constant din 

 at a constant point, but as we travel forward the direction t 

 round in the positive direction of w at a rate per unit dist. 



i,> 1 1 ,. ; !' 



i 



or if n is the frecjueney of revolution. IO that to = %-n. we may 

 put the rotation of the plane of polari-ation 



rv 



. 



and in the direction of rotation of the faster-moving constituent. 

 So far this is meiely a geometrical representation of the 



