INDUSTRIAL MATHEMATICS 281 



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

 of the Research Laboratories of the Westinghouse Electric and Manu- 

 facturing 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 bearings 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 micro- 

 phones that generate alternating voltages corresponding 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 automobile 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 gauge 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 studying 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 mathe- 

 matical theory. They are, in fact, examples of the use of mathematics to 

 avoid the use of mathematics. 



Mathematics in Some Particular Industries 



Communications 



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 



