10 TWISTS AND WRENCHES. 



tute a wrench of which we should also know the in- 

 tensity. 



There is one special feature which characterises that 

 portion of the Dynamics of a rigid body which is dis- 

 cussed in the present essay. We shall impose no restric- 

 tions on the form of the rigid body, none on the character 

 of the constraints by which its movements are limited, 

 and but little on the forces to which the rigid body is 

 submitted. The restriction which we do make is that 

 the body, while the object of examination, remains in, or 

 indefinitely adjacent to, its original position. 



As a consequence of this restriction, we here make 

 the remark that the amplitude of a twist is henceforth to be 

 regarded as a small quantity. 



If it be objected, that with so great a restriction as 

 that just referred to, only a limited field of inquiry re- 

 mains, the answer is as follows : A perfectly general 

 investigation could yield but a slender harvest of inter- 

 esting or valuable results. All the problems of Physical 

 importance are special cases of the general question. 

 Thus, a special character in the constraints has pro- 

 duced the celebrated problem of the rotation of a rigid 

 body about a fixed point. To vindicate our particular 

 restriction it seems only necessary to remark, that the 

 restricted inquiry still includes the theory of Equilibrium, 

 of Impulsive Forces, and of Small Oscillations. 



Whatever of novelty may be found in the following 

 pages will, it is believed, be due to the circumstance 

 that, with the important exception referred to, all the 

 conditions of each problem are of absolute generality. 



