ELECTRICAL AND MECHANICAL ANALOGIES 407 



anomalous dispersion in optics. It was found experimentally that when 

 light was sent through certain sul^stances the velocity of propagation de- 

 pended markedly on the frequency in the neighborhood of a certain critical 

 frequency. Below this critical frequency the velocity decreased as the 

 frequency approached it, going rapidly toward zero as the critical frequency 

 was approached. Above this critical frequenc\- the phase velocity was 

 greater than the velocity of light in the material and gradually approached 

 that value for high frequencies. At the critical frequency a large absorp- 

 tion of light occurred. This was tirst explained by Sellmeier as being due to 

 some element in tlie medium lun-ing a resonant frequency at the critical 

 frequency In obtaining his equations he used a mechanical model in which 

 the resonant elements were spaced at equal intervals and excited by waves 

 jiropagated by virtue of the mass and elasticity of the substance. 



The case of greatest interest from the communication viewpoint is the 

 influence of mechanical theory on the theory of the loaded transmission line. 

 Wave propagation in a mechanical bar or stretched string has similar char- 

 acteristics to that of a dissipationless electrical line, but when the effect of 

 series resistances and shunt leakanceswere taken account of, effects appeared 

 for the electric line which had not previously been studied in mechanical 

 systems. These were high attenuation, which cut down the amount of 

 power delivered to the output, and distortion, which caused the shape of the 

 signal received at the end of the line to be different from that sent into the 

 line. Heaviside showed that the distortion could be removed by having a 

 certain relationship between the inductance, capacitance, resistance and 

 leakance, and moreover that a smaller attenuation and a lower distortion 

 would result, if an inductance were uniformly distributed along the line. 



It was not a practical matter, however, to put in extra inductance at 

 every point of the line so Heaviside suggested and tested out the effect of 

 placing inductances at discrete points along the line, and found no beneticial 

 results. It was not until Campbell and Pupin independently showed that 

 the inductances had to have discrete values and be placed at definite separa- 

 tions that any progress was made in approaching the desired conditions. 



Pupin's method of arriving at the solution is well illustrated by the follow- 

 ing extract from his paper.- "The main features of the theory are extremely 

 simple and can be explained by a simple mechanical illustration. Consider 

 the arrangement of Fig. 1. A tuning fork has its handle C rigidly fixed. 

 To one of its prongs is attached a flexible inextensible cord BD. One ter- 

 minal of the cord is fixed at D. Let the fork vibrate steadily, the vibration 

 being maintained electromagnetically or otherwise. The motion of the 

 cord will be a wave motion If the frictional resistances opposing the motion 



^ "Wave Transmission Over Non-uniform Cables and l^ong Distance Air Lines," 

 M. I. Pupin, Trans. A. I.E. E., Vol. XVII, May 19, 1900. 



