4 20 THE THEORY OF SCREWS. [383- 



applied on the screw corresponding to R, to prohibit the body from changing 

 its instantaneous screw. 



Let be the pole of the axis of inertia, then, if I A be a chord drawn 

 through , the points / and A correspond to a pair of conjugate screws of 

 inertia ( 135). It further appears that A is the instantaneous screw corre 

 sponding to an impulsive wrench on R ( 140). Therefore the effect of the 

 wrench on R when applied to control the body twisting about 7 is to com 

 pound its movement with a nascent twist velocity about A. Therefore A 

 must be the accelerating screw corresponding to /. We thus see that 



Of two conjugate screws of inertia, for a rigid body with two degrees of 

 freedom, either is the accelerator for a body animated by a twist velocity about 

 the other. 



384. Calculation of T. 



In the case of freedom of the second order we are enabled to obtain the 

 form of T, from the fact that the emanant vanishes, that is, 



If we assume that T is a homogeneous function of the second degree in 

 0i and 2 , the solution of this equation must be 



T = M 2 + zseA + Me, 2 + H (6&amp;gt;;0 2 - o&y + (0/0 2 - #/ e,) (A0, + M), 



in which L, S, M, H, A are constants. If we further suppose that 0, and #./ 

 are so small that their squares may be neglected, then the term multiplied 

 by H may be discarded, and we have 



T = M 2 

 whence 



Thus, for the co-ordinates of the restraining screw, supposing the screws of 

 reference to be reciprocal, we have 



from which it is evident that 



which is, of course, merely expressing the fact that 77 and 9 are reciprocal. 



385. Another method. 



It may be useful to show how the form of T, just obtained, can be derived 

 from direct calculation. I merely set down here the steps of the work and 

 the final result. 



