DR. CAMPBELL'S MEMORANDA OF 1907 AND 1912 559 



charges on the wires of the disturbing circuit but also of the charges 

 induced by the disturbing circuit on all other wires. Thus, the electric 

 shielding effect of other wires is taken into account. Magnetic 

 shielding is ignored since this is unimportant with a line transposed at 

 intervals very small compared with the wave-length. Dr. Campbell 

 gave data for comparing the relative importance of the electric and 

 magnetic components of the disturbing field and showed that for 

 severe exposures both effects are of importance. 



The equations given in the latter part of the memorandum of 

 September 14, 1907, formed a basis of transposition design. They 

 show how the crosstalk in a long transposed line may be computed 

 with sufficient accuracy by simply summing up the effects computed 

 individually for each short element of line. This important approxi- 

 mation is discussed in some detail in the earlier memorandum of 1904. 

 Dr. Campbell prophetically says, "It must, however, always be borne 

 in mind that we are working only with a first approximation and that 

 in certain cases it may be necessary to continue the investigation to a 

 higher order of approximation." In making the approximation. Dr. 

 Campbell was, of course, thinking of voice frequency telephone 

 circuits and at such frequencies, if the interval between transpositions 

 is sufficiently short to guard against noise due to irregular power 

 exposures, that interval will be but a very small fraction of the wave- 

 length and it is unnecessary to consider the second approximation or 

 as Dr. Campbell says to calculate "crosstalk-of-crosstalk." 



When transpositions were designed for carrier frequency operation 

 up to 30 kc. it was obviously impracticable to make a transposition 

 interval a very small fraction of the wave-length and "crosstalk-of- 

 crosstalk" could not be ignored. In other words, it was necessary to 

 consider the crosstalk in each short element of line from the disturbing 

 circuit into all the other wires on the line, the propagation of these 

 crosstalk currents (and charges) along the line, and their effect in 

 inducing currents in the disturbed circuit in other short elements of 

 line. This effect has been termed interaction crosstalk since it 

 takes account of the interaction between elements of line instead of 

 simply summing up individual effects in each element. Thus it 

 indeed proved true that "in certain cases" it was necessary to continue 

 the investigation to a higher order of approximation. 



I. Crosstalk Formul.^ for Non-Loaded Circuits* 



Take first the simple case of two perfectly symmetrical uniform 

 circuits having the same transmission constants, which terminate at 



* Memorandum dated September 14, 1907. 



