Telephone Circuits. 677 



is the value of h if the minus sign be taken and the value 

 of g if the plus sign be taken. The following formula lor 

 the current c is useful — 



° = V /+ t "// 2 ^ 6 " fasin (?-9 x + tan_1 f " tan_1 f )' ( 3) 



I showed in tables how good signalling was affected by 

 changes in the values of the constants and specially by 

 alterations in / and s. There was nothing very new in my 

 paper, but it enabled the non-mathematical man to under- 

 stand some of the discoveries of Mr. Heaviside. At that 

 time I saw no easy way of calculating how the introduction 

 of detached equidistant contrivances caused discrepance 

 from the idea of continuously distributed properties. 



In much that follows, Iq will be so large compared with r 

 that, taking s = 0, we have 



h = \ V r 9 = 9 x/kL 



If s is small but not negligible, g is as before, but 



As for other uniform distribution of properties, it is only 

 necessary here to speak of those which may immediately be 

 put in the above shape. For example, besides having merely 

 r and I in series in the line, we may have something of the 

 nature (mathematically) of k x farads per mile, so that instead 

 of r + Iqi we have 



r -f Iqi + -. — or r + qi 1 1 — -. — A 

 This is as if we had merely the resistance r and an inductance 



Again, instead of the leakance s which is the reciprocal 

 of a resistance R, let us have also something of the nature of 

 an inductance L, say, and assume R to be small relatively 

 to hq. Then instead of s we have 



1 R J_ 



R + Lqi ~ L 2 (/ 2 hq ' 



