1914] on Improvements in Long-Distance Telephony 87 



wave lengths in the ratio 1, 2, 3, etc., and of suitable amplitude and 

 phase difference. 



In virtue of the properties of certain mathematical functions, the 

 process of analysing a curve into its component harmonics is easily 

 reduced to arithmetic and can be even carried out by a machine. 

 Hence any complex periodic curve depicting an aerial or an electrical 

 vibration can be resolved into the sum of a number of simple 

 harmonic constituents. 



In the case of a complex electrical or aerial vibration this analysis 

 is not merely a mathematical fiction, but can be performed physically, 

 in the sense that we can separate out and extricate the harmonic 

 constituents from such a complex electric or aerial vibration by means 

 of devices called resonators. 



Thus I have in my laboratory at University College a dynamo 

 machine which gives an alternating or periodic electric current of a 

 complex form, having a frequency of 1000. I can, however, by 

 suitable electric resonators extract from it practically three electric 

 currents of simple harmonic form which have frequencies respectively 

 of 1000, 8000 and 5000. This process is analogous to that in which 

 a complex musical sound, such as a chord, can be analysed into its 

 component simple tones by acoustic resonators, and the ear enabled 

 to pick out and hear the components separately when the complex 

 sound is created. 



Hence, when we apply to the end of a telephonic cable such a 

 very complex electromotive force as that produced by speaking to a 

 telephone transmitter attached to it, we are entitled to assume that 

 the cable is being acted upon simultaneously by a number of simple 

 harmonic electromotive forces having frequencies in the ratio of 

 1, 2, 3, 4, etc., these harmonic constituents having various amph- 

 tudes and phase differences. 



We have, in the next place, to consider how the cable acts towards 

 these alternating electromotive forces or vibratory currents of different 

 frequencies. 



Every electric line, whether overhead, aerial, underground or sub- 

 marine cable, possesses four qualities, which are called its primary 

 constants. In virtue of two of these it stores up energy in two 

 forms, electrostatic and electromagnetic, and in virtue of the other 

 two it dissipates these energies as heat. 



The conservative qualities are called its capacity (C) and its 

 inductance (L), and its dissipative ones are called its conductor 

 resistance (E) and its dielectric leakance (S). 



Every telephonic wire or cable is a sort of Leyden jar. It 

 consists of a copper or bronze wire covered with gutta-percha, paper, 

 or other insulator. This again is covered with a metal sheath or 

 coating. 



The insulator or dielectric, when acted upon by electromotive 

 force, stores up energy electrostatically because it possesses capacity. 



