398 THE THEORY OF SCREWS. [359 



(f) which is evoked by the action of the forces. It will, of course, generally 

 happen that the chain 6 is different from the chain &amp;lt;. It can however be 

 shown that 6 and &amp;lt;/&amp;gt; are not in every case distinct. There are n different 

 screw-chains, each of which regarded as a will have the two corresponding 

 screws 6 and &amp;lt; identical. Nor is it difficult to see what the effect of such a 

 displacement must be on the small oscillations which follow. A wrench is 

 evoked by the displacement, and since 6 and &amp;lt; coincide, that wrench is 

 undistinguishable from an infinitely small impulsive wrench which will 

 make the system commence to twist about a. We are thus led to the 

 result that 



There are n screw-chains such that if the system be displaced by a twist 

 about one of these screw-chains, and then released, it will continue for ever to 

 twist to and fro on the same screw-chain. 



Following the language previously used, we may speak of these as 

 harmonic screw-chains, and it can be shown that whatever be the small 

 displacement of the system, and whatever be the small initial velocities with 

 which it is started, the small oscillations are merely compounded of twist 

 vibrations about the n harmonic screw-chains. 



