Lilies in Telephonic Transmission. 323 



Inspection of the diagram shows that at co = 1 the character 

 of the propagation changes ; that at this point reflexion, 

 per se, introduces attenuation. With perfect conductivity 

 (3 = 0) there is no attenuation below oi=l, but there is 

 attenuation above this value, and this is due, necessarily, to 

 reflexion. Below o> = l the attenuation is proportional to the 

 resistance so long as the resistance remains small, while above 

 co = l the attenuation is almost independent of the resistances 

 (or may even decrease with an increase in resistance), but 

 increases rapidly with the value of co. Consequent on this 

 change in the character of the propagation there is an 

 accompanying change in the line impedance from pure 

 resistance below <o=l to pure reactance for higher values 

 of co. The velocity curve also changes its direction and 

 character abruptly at co—1 ; there are two coils per actual 

 wave-length for o>=l, i.e., the disturbance is in opposite 

 phases at consecutive coils. The critical value co=l fur- 

 nishes the first essential condition for an efficient loaded 

 line, viz. : — 



tpd\/I7C<l, (36) 



i. e., there must be more than two coils per actual wave- 

 length, or approximately, ir coils per wave-length with the 

 load uniformly distributed. This has long been known for 

 loaded strings *. 



I have made use of these results by employing artificial 

 loaded lines for cutting out harmonics in generator currents. 

 The harmonics may all be~cut down as far as desired by the 

 use of a sufficient number of sections, while the attenuation 

 of the fundamental can be reduced at pleasure by decreasing 

 the resistance. The line does not require tuning, and with a 

 small value of p the action would be quite independent of the 

 frequency throughout a considerable range. The curves for 

 p = a correspond to the case of an artificial line. Combining 

 condensers and inductances, we may make a system which 

 will not only cut out higher frequencies, but also all frequencies 

 below a certain limit, as suggested at the beginning of this 

 article. This system will be an inversion of a model of 

 J. H. Vincent's t. 



The velocity and impedance are approximately independent 

 of the resistances. The attenuation below co — 1 is nor only 

 approximately proportional to the total resistance, but the 

 curves also show that the attenuation is reduced by trans- 



* Routh, Advanced Rigid Dynamics, p. 260, § 411 : Rayleigh, Theory 

 -of Sound, i., $ 148, pp. :?:«, 234. 

 t Phil. Mag-, xlvi. p. 557 (1898). 



