DYNAMICS OF A RIGID BODY. 115 



sive wrenches on which correspond to all the screws 

 of C as instantaneous screws. Since a wrench on TJ, 

 and one on X, make the body twist about some screw on 

 C, it follows that the cylindroid (r;, X) must have a screw 

 p in common with C f . The wrench on X might be re^ 

 solved into two. one on TJ, and the other on /o, and the 

 latter might be again resolved into two wrenches on any 

 two screws of C. It therefore follows that X must be- 

 long to the screw complex of the third order, which may 

 be defined by 77, and by any two screws from C f . Take 

 any three screws reciprocal to this complex, and an^ 

 two screws on C. We have then five screws to which X 

 is reciprocal, and it is therefore geometrically deter- 

 mined ( 28). 



When X is found, the cylindroid (TJ X) can be drawn, 

 and thus p is determined. The position of p on C' will 

 point out the screw on C, about which the body will 

 commence to twist, while the position of p on (rj, X), and 

 the known intensity of the wrench on ?;, will determine 

 the intensity of the wrench on X. 



t 2 



