278 BELL SYSTEM TECHNICAL JOURNAL 



and in the general problems where the flow constants vary with liquid-gas com- 

 position, etc., partial differential equations are found which can be solved by 

 approximate methods. On the basis of the solution of this mathematical problem, 

 aided by extensive laboratory determinations of the required constants, one is 

 able to find the best of several ways of producing from a given oil field." 



As a final example under the heading of economy, we may mention the 

 flight testing requirements imposed upon the aircraft industry by the Civil 

 Aeronautics Authority. Of these, Mr. E. T. Allen, Director of Flight and 

 Research of the Boeing Aircraft Company, says: 



(k) "It was formerly required that each type of transport plane must be tested 

 at all the altitudes at which it was intended to be flown, and at all flying fields 

 where it was expected to be used. The cost of such testing was extremely high. 

 A mathematical study of steady flight performance has, however, identified the 

 basic parameters and established their relations to one another. This has made 

 possible a scientific interpretation of flight test data taken at any suitable location 

 convenient to the aircraft factory, and a reliable conclusion therefrom as to the 

 performance to be expected under other conditions. This has greatly reduced 

 both the cost and the time necessary to establish performance figures." 



Fiflh: Sometimes experiments are virtually impossible and mathematics 

 must fill the breach. An example comes to me from Mr. Hall C. Hibbard, 

 Vice President and Chief Engineer of the Lockheed Aircraft Corporation: 



(/) "An unfortunate phenomenon that must be dealt with in aircraft design is a 

 type of violent vibration which may be set up in the wings if the plane is flown 

 too fast. It is known as flutter, and is highly dangerous, since the vibrations 

 may be of such intense character as to cause loss of control or even structural 

 failure. The technical problem is therefore to be sure that the critical speed at 

 which flutter would occur is higher than any at which the craft would ever be 

 flown. It is a phenomenon with respect to which wind tunnel experimentation 

 is difficult, and flight testing very dangerous. It has been the subject of a number 

 of mathematical investigations, the results of which have reached a sufficiently 

 advanced stage that they are now being used to predict the critical speeds and 

 flutter frequencies of aircraft while still in the design stage. Even more im- 

 portant, the mathematical investigation of this problem points the way to modifi- 

 cations of design which will insure that flutter cannot occur in the usable speed 

 range." 



Telephony provides a second example: 



(m) The equipment in an automatic telephone exchange must be capable of 

 connecting any calling subscriber with any called subscriber. It consists of several 

 stages of switches, each of which can be caused to make connection with a number 

 of trunks which lead in turn to switches in the next succeeding stage. Enough 

 switches must be provided so that only a very small proportion of subscribers' 

 calls will fail to be served immediately. Since the demands made by the sub- 



