570 nr.I.L SYSTEM TECHXIC.IL JOURh'AL 



tive values for these deviations similar to liie "mean error." Because 

 of the wa\- in which the eflfects of irregularities combine, this repre- 

 sentative deviation is taken as the square root of the mean of the square^. 

 of the deviations (r.m.s. deviation) of the indix'idual coils. If the 

 average deviation of a large group of coils is known, but the individual 

 deviations are not, it may be multiplied by 1.253.'? to obtain the 

 representative deviation on the assumpiioii that the dexiations 

 follow the normal law of errors. 



If then the representative deviation IIi, is substituted for the par- 

 licuiar deviatinn /;/, in equation (11), we obtain the representative 

 retk'ctioii coeHuieiit 



RL = nL ,^^. (25) 



Now in the usual case where no effort is made to select the loading 

 coils and so obtain a special distribution of the deviations the repre- 

 sentative deviation and the representative reflection coefficient are 

 the same for each coil. Substituting Rl for r\. r<>, etc., in equations 

 (17) to (24) each equation gives the representative value, at the 

 sending end of the line, for the current reflectetl from the correspond- 

 ing irregularity. 



According to liie laws for tiie coiiil)iiiali(>u of (k-viaiinns wiiirii are 

 demonstrated in treatises dealing with precision of measurements 

 the representative \alue of the current due to all the irregularities 

 would be the square root of the sum of the squares of the representa- 

 tive values of the different currents taken separately, consequently 

 I he representative in-phase current is 



/' = /„/?/. ^(cos'e^+^'cos-es+^'cos'eaH /l^<"-'>cos2e„) (26) 



and the representative quadrature current is 



/" = /,J?;,\/(sin=or-H74\sin-eo + A''sm=e'3+ ^'("-I'sin^e,,)'. (27) 



ii\- assuming liiat the re|)resentali\e in-pliase and quadrature 

 currents are etiual the following steps can be greatl>' simplified. In 

 view of the varying effects of frequency, distance from the sending 

 end and nature of the irregularity upon the phase relations iliis 

 appears to l)e a justifiable assumption, so combining 7' and 1" in 

 (Uiafiralure, 



1=1 =\\ 2-=. 



y/2 Vl+A*+A*-\- yl*(«-') (28) 



