M.irilliM.ITICS IX IXiyiSTRI.II. Rr.SI-.IRCII ?.*.! 



riu' ti-li'phonii- iik-al. wliicli is tin- perfect reproduction of speech, 

 with articulation which is indistinguishable from face-to-face con-' 

 vcrs;ition, involves extensive and exhaustive investigations in many 

 tields, in particular in mechanics, acoustics and electromagnetism, 

 since each telejihonic conversation involves oscillations in the air, 

 in solids and in the ether. Fortimately, the foundations of the 

 mathematical theon,- in these three tields had been securely laid by 

 the time Alexander Graham Bell effected their harmonious coopera- 

 tion in his first telephone. It is impossible for us to be too well 

 informed concerning the consequences of the mathcmatioal laws in 

 these three fields. 



It is characteristic of many problems encountered in industry that 

 a great number of independent variables are involved, far too great 

 a number for the best solution to be reached simply by trained judg- 

 ment. Consider the transposition problem of the telephone system, 

 which is this: on pole lines, long lines between cities, for example, 

 several wires — sometimes a great number of wires — are strung along 

 in close proximity. Each pair of wires receives inductive effects 

 from the electric waves carried by every other pair, producing so- 

 called crosstalk. To reduce such effects, the pairs of wires are trans- 

 p<ised according to a set plan; that is, the positions of the two wires 

 are interchanged, an expedient analogous to the twisting of a pair 

 of wires. It is necessary to consider not only the ideal location of 

 the transpositions in each pair of wires, but also the practical irregu- 

 larities which occur in the actual placing of the transpositions. One 

 of the practical problems, in fact, is to determine the allowable tol- 

 erances limiting the irregularities in the location of loading coils 

 and transpositions, since these irregularities modify the crosstalk 

 and also the transmission efficiency by an amount which must be 

 determined by the laws of probability. 



Transpositions were originally intrcxluced with complete success 

 about thirty years ago, and yet at the present time this subject is 

 lieing more actively studied than ever; this is due to the extended 

 use of phantom circuits and the new uses of carrier frequencies, that 

 is, high-frequency speech-carrying currents which are superposed 

 on ordinary telephony. 



To illustrate the way in which problems in industrial mathematics 

 l)ecome, step by step, more complex by the progressive inclusion 

 of one factor after another, brief reference may be made to the loaded 

 cable circuit. The first successful telephone cable circuits could \^ 

 treated mathematically on the basis of Kelvin's simple cable dif- 

 fusion theorj-. To allow for the ignored inductance and to deter- 



