DR. CAMPBELL'S MEMORANDA OF 1907 AND 1912 



563 



eWk 



4. 1 



r'\A. 



4/ 



Fig. 3. 



former circuit of Fig. 4. If there is no unbalance Z so that we have 

 the original uniform system the current E/lk starts out on 1/2 and at 

 the point of mutual impedance unbalance it becomes Ec'^'^llk. 

 Circuit 1/2 therefore behaves like a primary of impedance 2k (for the 

 two ends of the line are in series) containing e.m.f. Re~~^''. The circuit 



Ee- 



2k 



2ke" 



Fig. 4. 



3/4 acts as a secondary of impedance Ik. If the mutual impedance 

 between the two lines is now made Z without any other change the 

 current on 3/4 at x is 



U^ - Z2 ' 



which is attenuated by the factor e'"^"" in reaching the transmitting 

 end of the line, making the crosstalk 



F7 

 ^^ Ak' 



or approximately 



1 



1-^ 



4k^ 



EZ 

 AI, = — 7TT, e~^^^ as Z is small. 



4:k^ 



