DR. CAMPBELL'S MEMORANDA OF 1907 AND 1912 



569 



f^^^^ Hcv-v" 



-<jyir 



)e- 





^OD- 



.-Z Y e- 



Fig. 3. 



ECXJlZ)^ 

 8kK 



Ey's-txT 



^Y'e-^>^ 



Fig. 4. 



whence the current produced is Ecf'^iX + Z)/8kK. The currents 

 entering and leaving the phantom may be resolved into E{ Y'j2 

 + F")g-T^/4, leaving 1, 2 and entering 3, 4 and £ F'e-)'^/4, leaving 1, 2 

 and 3, 4 in parallel and entering 2. The precise distribution of this 

 last component depends upon the structure of the system, but as it 

 flows symmetrically down the two sides of the phantom, it cannot 

 introduce crosstalk. The first component divides equally between 

 the two ends of the line, and this is the capacity unbalance current. 

 The currents are therefore completely shown in Fig. 4. Allowing for 

 the attenuation of the currents in reaching the ends of the line, we have 

 the formulae given below: 



If a phantom (1, 2-3, 4) and its side circuit (1-2) have the trans- 

 mission constants {K, T) and {k, 7) and the length (/) and are sym- 

 metrical throughout, then the crosstalk which will be introduced 

 between them by the addition, at the distance (x) from the trans- 

 mitting end, of small impedances (r, s, t, u) in the conductors, mutual 

 impedances (m, n, p, q) between the conductors of the two side circuits 

 and direct admittances (a, b, c, d; e,f, g, h) between the conductors of 

 the two side circuits and between these conductors and the remainder 



