Prof. Thomson on Polarised Light. 203 



wave, turns at a uuiform rate in the same direction as the rotation 



of the substance ; and that if — be the period of rotation of the sub- 

 (1) 



stance, and I and m the lengths of simple pendulums respectively 



isochronous with the vibrations of two plane waves of the same 



length, a, in the planes of maximum and of minimum elasticity of 



the substance, when destitute of rotation, the period of vibration in 



a wave of the same length in the substance when made to rotate will 



be 



27r 



i'-m 



and the angle through which the plane of vibration turns, in the 

 propagation through a wave length, will be 



TT X*_ 



4 nu)^ 



or the number of wave lengths through which the wave is propagated 

 before its plane turns once round, will be 



IT' 



where, as before. 



and u) denotes the angular velocity with which the substance is made 

 to rotate. 



If next we suppose the rod or cord to be slightly twisted about its 

 axis, so that its directions of maximum and minimum elasticity shall 

 lie on two rectangular heli9oidal surfaces (heli^otdes gauches), and 

 if, while regular rectilineal vibrations are maintained at one point of 

 it with a period to which the wave length corresponding is a very 

 large multiple of the step of the screw, the substance be made to 

 rotate so rapidly as to make the velocity of a point carried along one 

 of the screw surfaces in a line parallel to the axis be equal to the 

 velocity of propagation of a wave, it is clear that a series of sensibly 

 plane waves will run along the rod or cord with or without rotation of 

 the plane of vibration. The period of vibration of a particle will be, 

 approximately, the same as before, that is, approximately, equal to 



— . Its velocity of propagation will therefore be — -, and, if « be the 

 n 27r 



step of the screws, the period of rotation of the substance, to fulfil 



the stated condition, must be — , or its angular velocity — . Now 

 na s 



it is easily seen that the effects of the rapid rotation, and the effects 

 of the slight twist, may be considered as independently superim- 

 posed ; and therefore the effect of the twist, with no rotation of the 

 substance, must be to give a rotation to the plane of vibration equal 



P2 



