368] THE THEORY OF PERMANENT SCREWS. 407 



Neglecting the small quantities 6-^ ... &c. we have 



-r = 0, &C. 



d6.de, 

 Introducing these values we obtain 



dT 



These may be regarded as the generalization for any material arrangement 

 whatever of the well-known Eulerian equations for the rotation of a rigid 

 body around a fixed point. If there are no external forces then i\&quot; , . . . rj n &quot; 

 are all zero, and the equations of movement assume the simple form 



AT 





368. The Restraining Wrench-chain. 



If a mass-chain be twisting about an instantaneous screw-chain 0, the 

 mass-chain will, in general, presently forsake 6 and gradually adopt one 

 instantaneous screw-chain after another. It is however possible, by the 

 application of a suitable wrench-chain, to compel the mass-chain to continue 

 twisting about the same screw 6 with unchanged twist velocity. We now 

 proceed to the discovery of this restraining wrench-chain when no other 

 external forces act on the mass- chain. 



As all the accelerations of 6 must vanish, the co-ordinates of the wrench- 

 chain required are obtained by imposing the conditions 



1 = 0; a = 0,...0 n =0. 



We therefore infer from the general equations of 366, that if IJ L &quot;, . . . r) n &quot; 

 are the co-ordinates of the restraining wrench-chain we must have 



1 dT 



1 dT 



