Dr. Campbell's Memoranda of 1907 and 1912

S mentioned in the preceding article by Dr. Jewett, the first and second of the three following memoranda were the basis of methods of designing transpositions for voice-frequency circuits. They applied particularly to non-loaded circuits but the theory was readily extended to cover loaded circuits. In an earlier and more general study written in 1904, Dr. Campbell considered the involved equations necessary to an exact solution of the crosstalk problem and deduced simplifying approximations and convenient artifices for avoiding lengthy derivations. He first assumes a line having the circuits substantially perfectly balanced to each other by means of very frequent transpositions. He then considers the effect of an unbalanced condition in a short length of line such as might arise from an irregularity in wire or transposition spacing or an unbalanced series impedance which might be due to a poor joint. Dr. Campbell refers to such effects as "slight alterations in the impedances, mutual impedances and admittances of the system." He shows how the crosstalk can be readily computed if these alterations in impedance and admittance are known. He then considers the case of a short untransposed length in which the coupling between circuits is systematic rather than accidental. He shows that the crosstalk in such a short length can be computed in terms of mutual impedances and admittances in just the same manner used for accidental coupling in a short length nominally perfectly balanced.