INTRODUCTION. 



THE Theory of Screws is founded upon two well-known 

 theorems. One relates to a system of forces acting on 

 a rigid body; while the other relates to the displace- 

 ment of a rigid body. Although these two theorems 

 are to be found in many treatises on mechanics, yet 

 a discussion of them here, so far as they are necessary 

 for our purpose, may be useful. 



I. ON THE REDUCTION OF A SYSTEM OF FORCES APPLIED 

 TO A RIGID BODY TO ITS CANONICAL FORM. 



The Canonical Form. It has been discovered by Poin- 

 sot* that any system of forces which act upon a rigid 

 body can be replaced by a single force, 'and a couple in 

 a plane perpendicular to the force. Thus a force, and 

 a couple in a plane perpendicular to the force, constitute 

 what may be called the canonical form of a system of forces 

 applied to a rigid body. 



It is easily seen that all the forces acting upon a rigid 

 body may, by transference to an arbitrary origin, be com- 

 pounded into a force acting at the origin, and a couple. 

 Wherever the origin be taken, the magnitude and direc- 



See Appendix I. 



b 



