554 BELL SYSTEM TECHNICAL JOURNAL 



mine the effect of acklwl iiuluclancc, Heaviside's much more com- 

 plete transmission forimilas were employed somewhat later. The 

 next stage was to allow for the effect of inductance which was not 

 uniformly distributed, liui liuiiped at regular intervals. Here the 

 steady state solution for sinusoidal vibrations of a loaded string was 

 employed, and the cutoff frequency due to internal reflections at 

 the loading coils determined. But with loaded cables of great length, 

 extending from New York to Chicago and beyond, the transient 

 state may be of such duration as to require consideration. The 

 loaded line does not transmit the impulse as a whole, but breaks it 

 up by reflection and transmission at each loading coil. Therefore 

 some of the impulses arrive after a few short backward reflections, 

 while other impulses may travel many times the length of the line, 

 due to reflections back and forth at many of the thousand loading 

 coils in the circuit. The calculation of the transient state at the 

 receiving end, due to the arrival of these impulses in groups, one 

 after another, involved the calculation of Bessel functions up to order 

 2000 and subsequent integration by an application of the principle 

 of stationary phase to Fourier's integral. 



Industri.vl AIathem.vtics as a Career 



It is true that the mathematician who takes up industrial work 

 is not entirely free to set his own problems; the industry which 

 he has chosen pro\ides these and it demands concentration upon 

 them. Such problems are often less inviting than the clear-cut, 

 tractable problem which the pure mathematician is at liberty to set 

 himself. Industrial problems may be most complicated to frame 

 and they may admit onh' of aiiproximate solution Iin- laborious 

 numerical methods. In addition to delimiting the nature of his 

 problems, the imperative needs of industry set time limits for tiuir 

 solution, and the nature of industry demands a financial \nuhi troni 

 industrial mathematics. But these restrictions of industry should 

 not make the work less attractive. On the contrary, restrictions 

 disclose the master. There is an inspiration in overcoming e\"en the 

 humblest difficulty standing in the path of progress. Restrictions, 

 even in the case of the most gifted, may be beneficial in concentrating 

 activities, thereby making up in depth what may seem lacking in 

 breadth. 



The industrial ni.ilhematician nun- ha\e a chance to attack many 

 large-scale investigations which would be impossible, except under 

 the patronage of industry, because of the exceptional material equip- 



