Industrml Research 



283 



an "image current" as a substitute for the currents 

 induced in a conducting ground by a transmission line 

 above it, and a host of other common procedures could 

 be cited as similar instances of simplification based 

 upon more less valid mathematical reasoning. 



The second example is furnished by Dr. E. U. Condon, 

 Associate Director of the Research Laboratories of the 

 Westinghouse Electric and Manufacturing Company : 



(r) In the manufacture of rotating machinery it is of extreme 

 importance to have the rotating parts dynamically balanced, in 

 order to reduce to a minimum the vibration reaction on the bear- 

 ings which unbalance produces. Theory shows the phases and 

 amplitudes of the bearing vibrations produced by excess masses 

 located at various places on the rotor; conversely, by solving 

 backward from observed vibration data, one can compute what 

 correction is needed to eliminate the unbalance. Recently a 

 most valuable machine has been developed which not only 

 measures the unbalance, but also automatically shows what 

 correction should be made, thus eliminating the necessity for 

 these calculations. 



The rotor to be balanced is whirled in bearings on which are 

 mounted microphones that generate alternating voltages corre- 

 sponditig to the vibrations of the bearings. These voltages are 

 fed into an analyzing network, which automatically indicates 

 the correction needed in order to achieve dynamic balance. In 

 some cases the output of the balancing machine has been arranged 

 to set up a drilling machine so it will automatically remove the 

 right amount of metal at the right place. These machines are 

 finding application in the manufacture of small motors, of auto- 

 mobile crankshafts, and in the heavy rotors of power machines. 



In the same class would come the isograph, by means 

 of which the complex roots of polynomials can be 

 located; the tensor gage which registers the principal 

 components of strain in a stressed membrane without 

 advance knowledge of the principal axes; and slide 

 rules for a great variety of special purposes such as 

 computations with complex numbers, the calculation 

 of aircraft performance, aircraft weight and balance, 

 and the like. Perhaps we ought also include in the 

 same category the use of soap-bubble films for the study 

 of elastic stresses in beams, the use of current flow in 

 tanks of electrolyte for the study of potential fields, and 

 the use of steel balls rolling on rubber membranes 

 stretched over irregular supports as a means of study- 

 ing the trajectories of electrons in complicated electric 

 fields. These are all mechanical methods for saving 

 mathematical labor, but they are more than that, for 

 they all rest upon a foundation of mathematical theory. 

 They are, in fact, examples of the use of mathematics 

 to avoid the use of mathematics. 



Mathematics in Some Particular Industries 



Commvnications. — The communication field is the 

 one in which mathematical methods of research have 

 been most freely used. This is due partly to the fact 

 that the transmission of electric waves along wires 

 and through the ether follows laws which are partic- 

 ularly amenable to mathematical study; partly also to 



the fact that so much of the research has been central- 

 ized in a single laboratory, thus bringing together a 

 large number of engineers into a single compact group 

 and justifying the employment of consultative special- 

 ists. Most important of all, however, is the fact that 

 there are two devices — -vacuum tubes and electrical 

 networks — without which modern long-distance teleph- 

 ony would be impossible; and one of these, the elec- 

 trical network, is and has been since its earliest days 

 almost entirely a product of mathematical research. 

 Mathematics has thus been as essential to the develop- 

 ment of Nation-wide telephony as copper wire or 

 carbon microphones. 



Number of Mathematicians: The Mathematical re- 

 search Department of the Bell Telephone Laboratories 

 contains 14 mathematicians. Perhaps an equal num- 

 ber of men scattered through various engineering 

 departments should also be classified as mathematicians 

 according to the definition adopted for this report. 

 Say a total or 25 or 30 for the Bell Laboratories, a few 

 more for the Bell System as a whole, and perhaps 40 

 or 50 for the entire communication field including the 

 companies interested in radio and television. A few 

 of these men carry on a considerable amount of experi- 

 mentation, but their significant work is theoretical. 



In addition, there is a much larger number of men 

 who use mathematical methods extensively in their 

 daily work but whose mental type is not that which we 

 have described as mathematical and who arc therefore 

 not included in the numbers quoted above. This is 

 true in particular of the engineers who have the responsi- 

 bility for designing networks. 



Uses of mathematics: Mathematical activity is 

 most intense: (1) in designing wave filters and equal- 

 izers; (2) in studing transmission by wire and ether, 

 the concomitant problems of antenna radiation, and 

 reception, inductive interference between lines, etc.; 



(3) in studying various problems related to the standard 

 of service in telephone exchanges, such as the amount 

 of equipment required, the probability of delays and 

 double connections, the hunting time of switches, etc. ; 



(4) in providing a rational basis for the design of in- 

 struments, such as transmittei'S and receivers, vacuum 

 tubes, television scanning devices, etc.; (5) in develop- 

 ing efficient statistical methods for the plarming and 

 interpretation of experiments and for controlling the 

 quality of manufactured apparatus. 



Future prospects: During the last 20 years the num- 

 ber of men employed in communication research has 

 increased with great rapidity, but this rapid expansion 

 appears to be about over. A large increase in the 

 mathematical personnel of the industry therefore ap- 

 pears unlikely. It seems inevitable that the problems 

 will increase in complexity, and that theoretical methods 

 will become increasingly important, but it is believed 



