358 KENNELLY AND UPSON— HUMMING TELEPHONE. [July 20, 



ment, reckoned positively in the direction indicated, or clockwise. 

 The restoring force OR /.O may be analysed into two components 

 OT=OR sin 6, and OS^=OR cos 6 along the directions OV and 

 OX respectively. The component OT may be called the velocity 

 component, or T component, since it acts in the direction of the 

 velocity Oz', and against the retarding force Of. The component 

 Os may be called the 6" component, or the new elastic component. 

 It coacts with the elastic force OF that resists displacement. 



In order that the circular orbit may be retained, it is necessary 

 and sufficient that the T component of the restoring force shall 

 equilibrate the velocity-resisting force Of ; or, if R be the restor- 

 ing force, that 



R sin (9 + /' = o dynes 



If the T component should be less than the velocity-resisting force, 

 the system will lose energy. The orbit will spiral inwards until the 

 velocity has been sufficiently diminished to equilibrate the T com- 

 ponent, and permit a stable circular orbit of reduced radius to be re- 

 stored. If, on the contrary, the T component exceeds the velocity- 

 resisting force, the system will accumulate energy, and the orbit will 

 spiral outwards until the radius and velocity of the motion are suffi- 

 cient to restore equilibrium and permit a circular orbit of enlarged 

 radius to be maintained. 



In the condition of equilibrium represented in Fig. 16, we have 

 four forces acting on the particle, forming two separate equili- 

 brating pairs ; namely, a pair along the displacement vector Os, 

 which we may call the displacement pair, and a pair perpendicular 

 thereto, which we may call the velocity pair. Both these pairs rotate 

 together at some uniform angular velocity w, which will in general 

 differ from that which would hold for unretarded motion wq, as in 

 Fig. 14, or from that which would hold for retarded unreinforced 

 motion, as in Fig. 15. 



Considering the displacement pair, the first member is the elastic 

 force OF, modified by the new elastic force OS, to OF', Fig. 16. 

 The new virtual force of inertia is Of. Consequently 



OF' -f 0/ = o dynes 



