ELECTRICAL AA'D MECILWICAL ANALOGIES AW 



further sul)(livisi()n produces an inappreciahle improxemcnt only. This 

 point is reached wfien the cord thus loaded vil)rates very nearly like a uni- 

 form cord of the same mass, tension, and frictional resistance." 



Campbell, who first arrived at the design formulae for the coil loaded line, 

 was guided by the solution, given by Lagrange over UK) years earlier, of 

 the propagation of a wave along a string loaded with masses at discrete 

 intervals, and a generalization of it made by Charles (Godfrey,* for he states'* 

 "For the method of treatment which I first employed I am indebted to an 

 interesting article by Mr. C. (iodfrey on the 'Discontinuities of Wave Mo- 

 tion Along a Periodically Loaded String.' " The spacing of the coils arrived 

 at is the same as the spacing of the massive beads along a string, namely, 

 that TT coils or beads occur per actual wave-length of the highest frequency 

 to be transmitted. The added result not given in the mechanical case was 

 that the addition of such coils reduced the attenuation and decreased the 

 distortion. 



The different points of view of the two inventors are well illustrated by 

 the quotations. Pupin was attempting to obtain a system which ap- 

 proached a uniform line while Campbell was investigating the propagation 

 characteristics of the structure without particular regard as to whether the 

 transmission was the same as that which would be provided by an equal 

 amount of inductance uniformly distributed along the line. It was the 

 broader point of view of Campbell which proved of wide significance and 

 which in particular led to the invention of the electrical wave filter. 



Development of Electrical Network Theory 



The first structures capable of transmitting bands of frequencies and 

 attenuating all other frequencies were mechanical structures, although this 

 was not generally realized at the time or made use of. The first structure 

 of this sort was the string loaded with massive beads, which was first studied 

 by Lagrange. Introducing the approximation that the mass of the string 

 could be neglected, Lagrange showed that all of the natural frequencies of 

 the device came below a certain critical frequency fc. Routh^ after dis- 

 cussing Lagrange's solution, points out that there may be a period of excita- 

 tion of the string which is ''so short that no motion of the nature of a wave 

 is transmitted along the string.'"' An acoustic forerunner of the wave filter 

 was the combination of two tubes of dififerent lengths first proposed by 



^ Phil Mag. 45, 456 (1898). 



* See "Collected Papers of George A. Canipliell," page 16. 



3 "Advanced Rigid Dynamics," p. 260, Paragraph 411 (1892). 



^ It should be noted that all mechanical filter theor\ of this time had to do with the 

 natural resonances of untcrminatcd filters or the transmission through misterminated 

 sections. The idea of matched impedance terminations to introduce power into and ab- 

 sorb power from a filter is a de\elopment of electrical network theor_\'. 



