152 Dr. E. H. Barton on the Attenuation of Electric Waves 



theory applied to the case of reflexion from a terminal 

 arrangement prior to its publication *. 



On Heaviside's theory developed originally for long waves, 

 say of telephonic frequency, we have for the reflexion co- 

 efficient 



Z — Lu ._. 



"=Z + L? < 7 > 



where Z is the resistance operator, L is the inductance per 

 unit length of the line, and v is the speed of light. 



Now the resistance operator in the case of condensers, 

 secondary and primary coils is given by 



Z "5 + (B,+Itf) -T^? • • • (8) 



where S is the capacity of the condenser, the R's are the 

 resistances and the L's the inductances of the coils, M their 

 mutual inductance, and p the time differentiator. 



Of the three terms on the right-hand side of (8), the first 

 only is to be used if the arrangement is short-circuited at 

 the spark-gap, G (tig. 1), the first and second only if the 

 primary circuit of the induction-coil is open, but all three if 

 the primary is closed. 



Now in the actual experimental case the sparks at the 

 primary oscillator are started by the break of the primary 

 circuit of the induction-coil, the interruptor remaining open 

 during the greater part of its period (say the g\} of a second) . 

 But the time required for the wave-train to pass to the end 

 of the longest line used and back again, say a dozen times 

 (which practically extinguishes it), is only of the order 

 14 millionths of a second. Hence the form of (8) to be 

 adopted as applicable to the present case is 



Z=i+R 2 + L 2i >, (9) 



if indeed the long-wave theory holds at all for waves so short 

 as 8 or 9 m. 



But, on working from equation (9) the value of p, we 

 obtain a result differing from unity by less than 1 in 10 10 . 



It would appear therefore that the long-wave theory fails to 

 apply to the present case of high-frequency waves and their 

 reflexion from condensers and coils of high inductance, each 

 of which involves of course the time-differentiator. 



In the case of a resistance practically devoid of inductance, 



* 'Electromagnetic Theory,' pp. 78(3-9; 'The Electrician,' April 9, 

 1897. 



