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National Resources Planning Board 



that this trend will be matched by progressively better 

 trained engineering personnel, rather than by an in- 

 creased number of mathematicians. Indeed, unless the 

 qualifications of the mathematicians rise progressively 

 with those of the engineers, it may turn out that less 

 rather than more will be employed. 



Electrical manufacturing. — Substantially all the re- 

 search in the power fields is carried on by a few electrical 

 manufacturers. The power companies usually accept 

 and exploit such equipment as the manufacturers 

 supply, and contribute to improved design principally 

 through their criticisms of past performance. Many of 

 their engineers, however, are individually active in the 

 invention and development of improved equipment. 



Number of mathematicians: The number of mathe- 

 maticians in the industry is smaller than in communica- 

 tions, and is not easy to estimate because their work is 

 less segregated from other activities. The total num- 

 ber who would here be rated as mathematicians is 

 probably about 20. 



As in communications, some are engaged partly in 

 experimental work. There are some, however, whose 

 relationship as consultants is clearly recognized, and 

 there is evidence that management is becoming in- 

 creasingly conscious of the nature and value of their 

 services. 



Uses of mathematics: Mathematical activity is most 

 intense: (1) in studying structural and dynamic prob- 

 blems, such as the strain, creep, and fatigue in machine 

 parts, vibration and instability in turbines and other 

 rotating machinery, etc., (2) in appraising the evil 

 effects of suddenly applied loads, lightning or faults 

 upon power lines, and their associated sources of power, 

 and devising methods to minimize these effects, (3) in 

 studying system performance, particularly the most 

 effective or economical location of proposed new equip- 

 ment, and the evaluation of performances of alternative 

 transmission or distribution systems, (4) in refining the 

 design of generators, motors, transformers and the like, 

 so as to improve their electrical efficiency and reliability, 

 and in similar improvement of the thermal efficiency of 

 turbines, (5) in the design of miscellaneous instruments 

 and apparatus. 



Statistical methods are being introduced into manu- 

 facturing and research, but are not yet utilized to the 

 same extent as in telephony. 



Future prospects: The amount of money spent on 

 development in these industries is gradually increasing, 

 and as in other fields the problems are becoming more 

 complex. Hence a slow increase in the number of 

 mathematicians seems probable, with rising standards 

 in the qualifications required, not only as to mathe- 

 matical training, but as to temperament and personality 

 as well. 



The petroleum industry. — The petroleum industry 



consists of many producing units of various sizes, highly 

 competitive in character, and surrounded bj' a number 

 of consulting service organizations, all of which are 

 small. The larger producing companies — and within 

 their resources, the service units also — maintain re- 

 search laboratories. They tend to be secretive about 

 the developments which take place in these, sometimes 

 to a surprising degree. Hence there is much duplica- 

 tion of effort, particularly in such matters as the design 

 of instruments for geophysical prospecting, and in 

 methods of interpreting the data derived from them. 



Number of mathematicians: The industry employs 

 more mathematicians than is generally appreciated, 

 some of them men of very considerable ability. The 

 total of first-rank men is perhaps 15 or 20. Due to the 

 small size of the individual research staffs, however, 

 most of these men carry considerable project responsi- 

 bility along with their theoretical work. This is the 

 normal state of affairs in small groups : the abnormality 

 is the lack of contact with, and stimulus from, similar 

 men in other companies. 



Uses of mathematics: Petroleum research extends in 

 three directions: prospecting for oil, producing it, and 

 refining it. 



There are five recognized methods of prospecting: 

 gravity, seismic, electric, magnetic, and chemical. In 

 the first four, important mathematical problems arise in 

 designing sufficiently sensitive instruments and in in- 

 terpreting data. The fifth requires the use of statistical 

 methods. 



Research on methods of producing a field has led to a 

 few mathematical studies of underground flow, and 

 would undoubtedly give rise to others if the results of 

 these studies could be profitably applied. However, 

 since the rate at which oil is brought to the surface is 

 almost entirely determined by law, and the same is 

 indirectly true of well location also, mathematical 

 consideration of the subject is largely sterile, at least so 

 far as American oil fields are concerned. 



The third activity — refining — is essentially a chemical 

 industry. Hence the following remarks by Dr. E. C. 

 Williams, Vice President in charge of research of the 

 Shell Development Company, presumably apply not 

 only to the petroleum business, but to manufacturing 

 chemistry in general: 



The two chief problems in chemistry are (aside from the 

 identification on substances): The calculation of chemical equi- 

 librium and the calculation of the rates of attainment of 

 these equilibria. Tlie first problem, involving thermodj'namics 

 and statistical mechanics, is rather well understood and usually 

 by very simple computations information sufficiently accurate for 

 industrial application, at least, can be found. Frequently, when 

 several equilibria are possible simultaneously, complicated 

 equations arise, but we rarely solve them directly, but rather sot 

 up tables of the dependent variable (the per cent conversion 

 possible) as a function of the independent variables (temperature, 



