i/^Hi.ci i..ih!iiii:s i.\ iAKii>i:i) lEi.i.riiosr. cum its 57i 



I'Or a tiniif iuiiiiIht of irri'niil.iiities, tli.ii is .1 Imilf line tciiuin.ilcd 

 In a ihtIciI nciwork jiisl Ik'xoiuI llu' «ll\ coil; 



which is obtained h\ siiiuniin^ up llu- sirics of trrms iiiidfr tlir radical 

 in i't|uation VIS). 



I'or an inliniii-l\ loiiv; lino .1" becomes zero since -4 <1 and 



/' =/"=^i'^\l A.^. (30) 



V2^1-^ 



/' corri'spnnds to the r.ni.s. ernir in tiic ordinary thct)r>' of iTrors, 

 consf(|iK'ntly the prob.ibilily function for the disiriliution of tiie in- 

 phase currents is : 



fhanijini; the accents, this ecjuation .dso applii's to the quadrature 

 components. 



The probability that the in-phase current lies between two near 

 b\- values i' and i'+di' is then equal to p' di' and the probability 

 that the quadrature component also lies between two values i" and 

 i"+di" at the same time is p'di'Xp"di". Transferring to polar 

 coordinates,' the probability that the total returni-d current will be 

 between a value «'= vi'^-1-/"- and a slightly different \alue I'+rf/ and 

 also have a phase angle between () and 0+dQ is 



P = .y-r,ie'^''dide. (32) 



Integrating with respect to the phase angle O between and 27r 

 to find the probability of obtaining a current between ( and i + di 

 of any pf)ssible phase displacement 



/• = ,„ / te 2/1 



di. (33) 



integrating between /,-. and intuiit\- gi\es llie prolialiilit\- that tiie 

 total returneil current will exceed the value //.. 



F^e'^VK (34) 



' Kor a more complete description of this 0|)eration, see "Advanced Calculus," 

 liy K. \\. Wilson, page .?')() et se(|. 



