Probability Theory and Telephone Transmission Engineering

N telephone transmission engineering a frequent problem is that of determining the effects of random manufacturing variations upon the value of some characteristic (for instance, a transfer admittance, or a driving-point impedance, or a current-ratio) of a transmission system or network. 1 In certain cases, such effects may be of great or even controlling importance in the performance of the system and hence must be fully taken into account when designing the system and when making calculations for predicting its performance. For example, in a multi-pair telephone cable the crosstalk between any two pairs is directly proportional to (strictly, a linear function 1 Such problems have in the past been handled by various approximate methods the most satisfactory of which for many purposes was t h a t described in a paper by George Crisson, entitled, "Irregularities in Loaded Telephone Circuits," published in this Journal for October, 1925. The method given in the present paper, while necessarily more involved than approximate methods, yields more precise results; and this additional precision is expected to be of importance in practice. Moreover, there has been an increasing need for a comprehensive paper covering the entire ground, and it is hoped that the present paper meets this need to a measurable extent. In Crisson's paper references will be found to various engineers in the Bell System who had previously contributed to specific probability problems of the type dealt with in Part II of the present paper.