400 THE THEORY OF SCREWS. [360- 



which expresses the freedom of the body ( 96). It may sometimes appear 

 that the intensity of the necessary wrench on 77 vanishes. The body in 

 such a case requires no coercion beyond that of the original constraints to 

 preserve 9 as the screw about which it twists, and when this is the case we 

 shall describe as a permanent screw. This use of the word permanent 

 does not imply that the body could remain for ever twisting about this 

 screw, for the movement of the body to an appreciable distance will in 

 general entail some change in its relation to the constraints. The character 

 istic of the permanent screw is the absence of any acceleration in the body 

 twisting about it, using the word acceleration in its widest sense. 



In the earlier parts of the chapter we shall discard the restrictions 

 involved in the assumption that the material arrangement is only a single 

 rigid body. The doctrine of screw-chains (Chap, xxiv.) enables us to extend 

 a considerable portion of the present theory to any mass-chain whatever. 

 Any number of material parts connected in any manner must still conform 

 to the general law, that the instantaneous movements can always be repre 

 sented by a twist about a certain screw-chain. In general the mass-chain 

 will have a tendency to wander from twisting about the original screw-chain. 

 In such cases the position of the instantaneous screw-chain cannot be 

 maintained without the imposition of further coercion than that which the 

 constraints supply. This additional set of forces may be applied by a 

 restraining wrench-chain, the relation of which to the instantaneous screw- 

 chain we shall have to consider. Sometimes it may appear that no restraining 

 wrench-chain is necessary beyond one of those provided by the reaction of 

 the constraints. The instantaneous screw-chain is then to be described as 

 permanent. 



361. Different properties of a Principal Axis. 



Another preliminary matter should be also noticed, because it exhibits 

 the relation of the subject discussed in this chapter to some other parts of 

 the Theory of Screws. In the ordinary theory of the rigid body there are, 

 as is well known, two distinct properties of a principal axis which possess 

 dynamical significance. We may think of a principal axis as the axis of a 

 couple which, when applied impulsively to the body, will set it rotating 

 about this axis. We may also think of the principal axis as a direction 

 about which, if a body be once set in rotation, it will continue to rotate. 

 The first of these properties by suitable generalization opens up the theory 

 of principal screw-chains of inertia, which we have already explained in 

 previous chapters. It is from the other property of the principal axis that 

 the present investigation takes its rise. It is important to note that two 

 quite different departments in the Theory of Screws happen to coalesce in 

 the very special case of a rigid body rotating around a point. 



