M.rmi-M.ITICS [X IXDUSTRl.ll. lil:Sr..lRCIl 553 



nit-nt aiul wiili-ly sustaini-d oHtpi-ratioii ro(|iiiri'il. Soiiu- i>f tin- <)|)|)()r- 

 liinitics oflVrctl by ihcip ok-ctriral powi-r from \'ia^;ara, l)y liiRli- 

 voltaijo electric power lines, and by lar^e steam tiirl)ines may 'lie 

 mentioned. It is often left to the industrial mathematician to reap 

 the harvest from seeii miwu under adverse circumstances \)y pure 

 mathematicians. 



The industrial mathematician may hope to n.ake some return for 

 the debt which he owes the pure mathematician. He may introduce 

 new mathematical problems, of which industry is an inexhaustible 

 source. He may point out the api)lication of pure mathematical 

 results, stimulating further investigations along the same lines. 

 He may assist mathematicians generally by promoting the prepara- 

 tion of needed tables and In' creating a conuuercial dem.uid for 

 calculating machines and other brain-saving devices. 



The opportunities presented by industrial mathematics are bound- 

 less, because mathematics is the key to extrapolation in time, and 

 industr\- is absolutely dependent upon prediction. The position of 

 mathematicians in industry must eventually correspond with the 

 importance of the function which tiiev' mav' perform. 



Tr,\ininc. I'"(ir Indisikiai. MAriii:M.\Tics 



In industry we are concerned with mathematics not as an objective, 

 but only as a tool. It follows that the reciuired training in math- 

 ematics should develop a wide acquaintance with the available 

 mathematical tools and practical skill in their use. It is important 

 to note the distinction between the using of tools and the making 

 of tools. I'nder primitive conditions the workman makes his own 

 tools, but in a highly organized society the tools are made by spe- 

 cialists, who provide the workman with an endless variety of imple- 

 ments superior to anything which he himself could make. By long 

 experience the tool designer has discovered how best to adajit the 

 tool to its intended use in order to economize the workman's time 

 and energy as much as possible. Furthermore, the substitution of 

 one tool for another with the minimum number of motions is made 

 possible by the use of interchangeable parts and systematically 

 arranged cabinets. 



But no complete line of mathematical tools is for sale across the 

 counter; only a limited numlx^r of numerical and algebraic tables 

 and a few types of calculating machines are supplied as ready-made 

 tools. By far the larger part of known mathematical tools must be 

 sought for in the literature of the subject, but there they may be 



