406 BELL SYSTEM TECHNICAL JOURNAL 



the action of several resonant elements to produce a device with a uniform 

 transmission over a wide frequency range; and second, the dissipationless 

 lilter, with matched impedance terminations, is a device which delivers 

 to its output all of the energy impressed upon it over the widest possible 

 frequency range consistent with the elements composing it. These prop- 

 erties of the filter have been made use of in purely electrical networks to 

 determine the largest band width a vacuum tube with known character- 

 istics can have and still deliver a specified gain at a specified impedance 

 level. Applied to electro-mechanical transducer systems, the filter theory 

 shows how to combine resonant mechanical or electro-mechanical elements 

 to produce a uniform conversion of electrical to mechanical energy, or vice 

 versa, over a wide frequency range. Also, it is able to determine the greatest 

 band width that can be obtained without loss of efificiency for any type of 

 conversion element. 



This transfer of knowledge from one branch of science, electrical network 

 theory, to another branch of science deaUng with mechanical and electro- 

 mechanical structures is one example of a long line of such interchanges that 

 have been going on for over a hundred years. These interchanges are 

 made possible by the fundamental analogies which exist between electrical 

 and mechanical systems and which rest finally on the fact that electrical 

 motions and mechanical motions satisfy the same type of differential equa- 

 tions. Since such analogies have been very productive in the past and are 

 likely to continue to be so in the future, it seems worthwhile to examine 

 their foundation and development. 



Early Borrowings of Electrical from Mechanical Theory 

 The equations of motion of mechanical bodies and mechanical media were 

 developed and studied long before the equations for electrical wave propaga- 

 tion were derived. Under these circumstances it is natural that attempts 

 should have been made to explain electrical wave propagation as a mechani- 

 cal phenomenon. The view that electrical actions are ultimately dynamic 

 was one whose development in the hands of Maxwell led to notable advances 

 in the science, and it was the view toward which most of the early authorities 

 leaned. In support of this point of view Maxwell showed that the forces 

 on any system of charged bodies could be attributed to a system of stresses 

 in the medium in which they are embedded. Since magnetic energy is 

 associated with the presence of charge in motion while electro-static energy 

 is present for charges at rest, an identification was made between kinetic 

 and magnetic energy and between electro-static and potential energy. Ap- 

 plied to a concentrated system, this point of view indicates that an induct- 

 ance is the analogue of a mass, while a capacitance is the analogue of a spring. 

 A case for which this point of view bore useful results was the case of 



