DYNAMICS OF A RIGID BODY. 175 



If a perfectly free rigid body be in equilibrium 

 under the influence of a system of forces as restricted 

 in 6, then six screws can be found such that each 

 pair are conjugate screws of inertia, as well as 

 conjugate screws of the potential, and these six 

 screws are called harmonic screws. If the body be 

 displaced from its position of equilibrium by a twist 

 of small amplitude about a harmonic screw, and if the 

 body further receive a small initial twisting motion 

 about the same screw, then the body will continue for 

 ever to perform small twist oscillations about that screw. 

 And, more generally, whatever be the initial circum- 

 stances, the movement of the body is compounded of 

 twist oscillations about the six harmonic screws. 



