157 



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 {heliro'ides 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 no 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 s be the 

 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 

 and contrary to that which the rotation of the substance would give 

 if there were no twist. But the effect on the plane of vibration, due 

 to an angular velocity w, of rotation of the substance, is, as we have 



seen, one turn in -^- wave lengths ; and therefore it is one turn in 

 \ 



8^j-j. wave lengths when the angular velocity is. Hence the 

 A. s" s 



effect of a twist amounting to one turn in a length, *, a small fraction 

 of the wave length, is to cause the plane of vibration of a wave to 

 turn round with the forward propagation of the wave, at the rate of 



n 4 a 3 



one turn in 8 ; wave lengths, in the same direction as that of a 

 A. 



point kept on one of the screw surfaces. 



From these illustrations it is easy to see in an infinite variety of 

 ways how to make structures, homogeneous when considered on a 

 large enough scale, which (1) with certain rotatory motions of com- 

 ponent parts having, in portions large enough to be sensibly homo- 

 geneous, resultant axes of momenta arranged like lines of magnetic 



