402 THE THEORY OF SCREWS. [362, 



been adopted. We call this screw-chain 0, and 6 denotes the twist velocity 

 with which the system moves round 0. 



Choose any n independent screw-chains, about each one of which the 

 mass-chain is capable of twisting. Then 6 can be decomposed into n com 

 ponents which have twist velocities 1} ... 6 n about the several screw-chains 

 of reference ( 355). 



Since everything pertaining to the position or the movement of the 

 mass-chain must necessarily admit of being expressed in terms of the co 

 ordinates of the mass-chain, and since the quantities 1} ... O n are definitely 

 determined by the position and movements of the mass-chain, it follows 

 that these quantities must be given by a group of formulae which may be 

 written 



&quot;n Jn\%i y H&amp;gt;n j #1 &amp;gt; Xnj- 



Let the mass-chain be stopped in the position A. Let it then be dis 

 placed to an adjacent position B defined by the following variations of the 

 co-ordinates 



where 8e is a small quantity. From this new position B let the mass-chain 

 be started into motion so that it shall have the same twist velocity as it 

 had just before being stopped in A and about the same screw- chain. This 

 condition requires that each of the quantities lt ... Q n shall resume its original 

 value unaltered by the stoppage and subsequent restarting of the mass- 

 chain from a new position. There must accordingly be an adjustment of 

 8x l} ... 8x n to satisfy the equations 



dx n 



Under these circumstances T has obviously not altered, so that we 

 have also 



dT dT . dT .. dT 



Let us assume, for brevity, the symbol A, such that 



* _ . d d 



dx l dx n 



