156 



pendulum will remain steady, and the period will be n ; in other 

 words, the motion' of the pendulum will be the same as that of a 



O 



simple pendulum whose length is , or a harmonic mean be- 



e m 



tween the effective lengths in the two principal planes of the actual 

 pendulum. 



It is easy to prove from this, that if a long straight rod, or a 

 stretched cord possessing some rigidity, unequally elastic or of 

 unequal dimensions, in different transverse directions, be made to 

 rotate very rapidly round its axis, and if vibrations be maintained in 

 a line at right angles to it through any point, there will result, 

 running along the rod or cord, waves of sensibly rectilineal trans- 

 verse vibrations, in a plane which in the forward progress of the 

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



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

 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 



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

 propagation through a wave length, will be 



IT \ 4 



4 nu> 3 '' 



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

 before its plane turns once round, will be 



Snw 3 



"F" 5 

 where, as before, 



and w denotes the angular velocity with which the substance is made 

 to rotate. 



