CHAPTER IX. 



HARMONIC SCREWS. 



104. Definition of an Harmonic Screw. 



We have seen in 97 that to each screw 6 of a screw system of the nth 

 order corresponds a screw X, belonging to the same screw system. The 

 relation between 6 and X is determined when the rigid body, and also the 

 screw system which defines its freedom, are completely known. The physical 

 connection between the two screws 6 and \ may be thus stated. If an 

 impulsive wrench act on the screw \, the body, if previously quiescent, will 

 commence to move by twisting about 6. 



We have also seen ( 102) that to each screw 6 of a screw system of the 

 nth order corresponds a certain screw 77 belonging to the same screw system. 

 The relation between 6 and 77 is determined when the rigid body, the forces, 

 and the screw system which defines the freedom, is known. The physical 

 connexion between the two screws 6 and 77 may be thus stated. If the body 

 be displaced from a position of equilibrium by a twist about 6, the evoked 

 wrench, when reduced ( 96) to the screw system, acts on 17. 



The rigid body being given in a position of equilibrium, and the forces 

 which act on the body being known, and also the screw system by which the 

 freedom of the body is prescribed, we then have corresponding to each screw 

 of the given screw system, two other screws X and 77, which also belong to 

 the same screw system. 



Considering the very different physical character of the two systems of 

 correspondence, it will of course usually happen that the two screws X and 77 

 are not identical. But a little reflection will enable us to foresee what we 

 shall afterwards prove, viz., that when 6 has been appropriately chosen, then 

 \ and 77 may coincide. For since n 1 arbitrary quantities are disposable in 

 the selection of a screw from a screw system of the nth order ( 69), it follows 

 that for any two screws (for example X and 77) to coincide, n1 conditions 



