386 PROCEEDINGS OF THE AMERICAN ACADEMY. 



and T, the period of current and p. d. is 2 tt/w. seconds (17) 



In the case considered w= 1224.75 radians per second, and 7" = 

 0.00513 second. 



The matter may be viewed in another direction by considering that 

 with the resistanceless circuit of Figure 3, the vector condition of the 

 p. d. in the circuit, at any instant t seconds after release is 



u = C7^e-'(-J''-o) = f/-^ey<oo« volts (18) 



where — j Wq of Figure 3 is the factor of the time in the exponential 

 variable e-''"*'. The effect of introducing a resistance /■ into the circuit 

 is to alter (18) to 



u = U^e-i^'-M) = £7pe-<(^-;<") = U^e-^^+^'-'i. volts (19) 



That is, the exponential time-factor —jmq of the resistanceless case 

 (Figure 3) is deflected from the — j direction to a direction making an 

 angle \^ with the direction of reference ; such that 



\^ = cos~^ (-^/^o)- radians or degrees (20) 



In the case considered, ^ = 50°.46'.06" = 0.8861 radian. 



The rotative vector- diagram of the resistant circuit is shown in Fig- 

 ure 8. OUq, measured to scale along the axis of projection — XOX, 

 is the initial p. d. between condenser terminals at release. U^ is the 

 initial position of the vector p. d. whose projection is OU^. In a cer- 

 tain sense, 06^o is a fictitious vector; because it has a value OUq 

 cosec (j> = 1291 volts, which is greater than the initial p. d. at the mo- 

 ment of release ; but, owing to the effect of damping, this seeming incon- 

 sistency gives rise to no error in the result. OE^ is the vector emf, 

 of self-induction in its initial position. Midway between OU^ and 

 OEf^ lies the vector current I^, whose projection on XOX is initially 

 zero. The cophase component Od (5.104 amperes), of the current 

 along Olio, is the dissipative component taking power from the dis- 

 charging p. d. while the component in quadrature thereto, dl^^ is the 

 reactive component, taking reactive power from Oif^. The "drop" 

 of vector I^r volts in the circuit would thus be a vector in line with 

 Iq and terminating at the point r. This would also be the resultant of 

 the two vectors OA^q and OU^. If we take a vector — /;• drop = OR^ 

 or Or reversed, we have three vectors OE^, Ol\, and Olt whose vec- 

 tor sum is zero. This triple set of vectors is to be rotated about the 



