178 Mr. 0. Heaviside on the Resistance 



neglecting a vanishing term. The amplitude of the current- 

 waves is thus reduced from 



E 



R 

 (what it would be were there no retardation) to 



IT 



r= 7w+m?' (2) 



where V signifies the maximum current. Or the current is 

 the same as if the resistance were increased in the ratio of 



'\A+<$? 



If L?n is large compared with R, then T is small compared 

 with ~j or the diminution of current-strength is large. 

 Let T be the time of a complete reversal. Then 



With the Morse code, when T=Jq second, or m — 807r, an 

 automatic transmitter produces 100 words per minute, or a 



little more. Let ^ be between y^ and -jfe second, then -^ 

 ■t* R 



o7T 



is between ^ an0 ^ ^7r, or (say) between 2*5 and 25 ; therefore 



the current will be reduced from 2*5 to 25 times. 



On telephonic circuits, owing to the great rapidity of the 

 reversals, the reduction in current-strength is great, and is 

 nearly inversely proportional to the pitch of the tone, thus 

 rendering it impossible to reproduce at the receiving end the 

 same quality of sound as is emitted at the sending end, irre- 

 spective of mechanical or acoustical difficulties. The second 

 partial tone of any continuous sound will be weakened twice 

 as much as the first, the third thrice as much as the first, 

 and so on, thus producing a general deadness or want of 

 brilliancy. 



It also appears from (2) that the resistance of the circuit 



becomes quite subordinate when -=- is large ; and it may then 



be greatly increased without much weakening the current. 

 This is remarkably evident on telephonic circuits. On auto- 

 matic circuits it has sometimes been found beneficial to intro- 

 duce resistance-coils at the receiving end. The irregular 

 effects of leakage from neighbouring wires, which mutilate 



