KENNELLY. — OSCILLATING-CURRENT CIRCUITS. 



387 



center 0, with the uniform angular velocity m, obtained from Figure 7. 

 But instead of rotating in simple circles, as in the resistanceless case of 

 Figure 2, the three vectors of Figure 8 rotate in equiangular spirals, 

 the angle of each spiral being <^ as defined in equation 20. That is, 



i>>^ 



.Figure 8. Rotative vector-diagram of an oscillating-current circuit con- 

 taining resistance. Instant of release of condenser charge. 



the tangent to the spiral at any point makes with the radius vector the 

 constant angle ^. The vectors rotating with the uniform angular 

 velocity w of formula (16), describe equiangular spirals because energy 

 is dissipated from the system in the resistance r, and each vector 

 shrinks with time at the uniform exponential rate e"-'' ; or falls to 1/eth 

 of its value in a time t equal to the oscillatory time-constant. Since, 

 however, all three vectors shrink at the same exponential rate, and 

 since their vector sum in Figure 8 is initially zero, their vector sum will 



