HARMONIC SCREWS. 73 



CHAPTER VIII. 



HARMONIC SCREWS. 



74. Definition of an Harmonic Screw. We have seen 

 in 67 that to each screw of a screw complex of the 

 n th order corresponds a screw X, belonging to the same 

 screw complex. The relation between and X is deter- 

 mined when the rigid body, and also the screw complex 

 which defines its freedom, are completely known. The 

 physical connexion between the two screws 9 and X 

 may be thus stated. If a wrench act on the screw X for 

 a short time, the body, if previously quiescent, will com- 

 mence to move by twisting about ( 67). 



We have also seen (72) that to each screw 9 of a 

 screw complex of the n th order corresponds a certain 

 screw rj belonging to the same screw complex. The 

 relation between and n is determined when the rigid 

 body, the forces, and the screw complex which defines 

 the freedom, is known. The physical connexion between 

 the two screws and rj may be thus stated. If the body 

 be displaced from a position of equilibrium by a twist 

 about 0, the evoked wrench, when reduced ( 66) to the 

 screw complex, acts on r\. 



The rigid body being given in a position of equili- 

 brium, and the forces which act on the body being 

 known, and also the screw complex by which the freedom 

 of the body is prescribed, we then have corresponding to 

 each screw 9 of the given screw complex, two other 

 screws X and TJ, which also belong to the same screw 

 complex. 



Considering the very different physical character of 



