392 PROCEEDINGS OF THE AMERICAN ACADEMY. 



u and e, being out of phase with the current, are divided each into two 

 components Uf ui and Cr ei, the former being in phase with the current, 

 the latter in quadrature therewith. The maximum cyclic values of Ut 

 and Sr will be 816.5 volts each as at U, Figure 12, and the maximum 

 cyclic values oi Ui and ci = 1000 volts each. The undamped power of 

 the cophase components i and itr is the double-frequency/?;, of 3333.3 

 watts amplitude about the zero line oo, itself elevated 3333.3 watts. 

 The power of i and er will be an identical sinusoid. The total power of 

 cophase components is thus the sinusoid 2 }h of 6GG6.6 watts ampli- 

 tude, about the zero line oo, oo, itself elevated 6666.6 watts. The 

 reactive power expended by the quadrature voltage component of Ui 

 upon the current /, is the double-frequency sinusoid pi of 4082.5 watts 

 as at P, Figure 12. This power is in the magnetic field of the reactance. 

 The total power exerted by u upon i is the heavy double-frequency 

 sinusoid p, of 5270 watts amplitude, about the zero line oo elevated 

 3333.3 watts. 



The undamped energy of reactance magnetic flux is the double 

 frequency sinusoid Wi, of 1.66 joules amplitude, about the zero line qq, 

 elevated 1.66 joules. The undamped energy of dissipation in resistance 

 due to tir and /, is the double-frequency sinusoid iv^ of 1.3608 joules. An 

 identical sinusoid would represent the energy of dissipation due to Cr 

 and /; so that the total unattenuated energy of dissipation would be a 

 double-frequency sinusoid of 2.7216 joules amplitude, as at W, Figure 

 12. The total undamped energy of u acting on i is the heavy double- 

 frequency sinusoid w, of 2.151,65 joules amplitude, about the zero 

 line qq. 



If we apply the attenuation-factors of Figure 9 to the ordinates of 

 Figure 10, that is, multiplying the currents and voltages by "■", while 

 multiplying the powers and energies by e — ^'^, we obtain the curves of 

 Figure 11 (with the exceptions of w and v\). This diagram represents 

 the actual succession of events in the oscillating-current circuit. The p. d. 

 at terminals falls along u. The emf. of self-induction pursues the oppo- 

 site curve e. The current follows the heavy line /, reaching a maximum 

 of 3.04 amperes near to 45° of its phase, or 0.000()4 second after release. 

 The components of voltage in phase with the current — Ur and e.f — both 

 coincide with its curve. The quadrature components of voltage are Ui 

 and ei. The total component of voltage in phase with the current 

 follows the curve marked 2 u^. The power curve p reaches a maximum 

 of 2200 watts at about 60° of its phase. This power rapidly subsides, 

 and only crosses the zero line in feeble measure. The total dissipative 

 power is shown by the curve 2 j)?' 



