388 BELL SYSTEM TECHNICAL JOURNAL 



fact that, as the axis of the rotor rotates toward that of the appHed torque, 

 the component of the spin which is normal to the axis of displacement pro- 

 gressively diminishes. To interpret the lirst term, we let — increase in- 

 definitely. The second term then becomes negligible, and when we divide 



through by -r- , the left side becomes -— . But the time increment which 

 ^ ^ dt d(i> 



accompanies a finite increment of (p is now infinitesimal, and so this may be 



called the partial with respect to (p, with / constant. 



We have then 



D 



dt \dif> di dt; 



?here 



^ = 7,0^1 - a\^j^dt y (17a) 



dt 



■ar)(np I <p dt. (18a) 



Substituting for -^ from (16a) in (14a), 

 dt 



d(p 



dj . 



We may interpret t~ as an mstantaneous stiffness to rotation and define 

 dip 



an instantaneous local generalized stiffness by the relation 



V = -p (19a) 



Similarly from (10a) we may define an instantaneous density by the relation 



P = F2. (20a) 



Then we may speak of an instantaneous velocity c given by 



.^ = ", (21a) 



