Electrical Signals on Land Lines, 41 1 



marine cables, and hitherto has been quite unknown for land 

 lines. 



The mathematical expression for the above curve will not be 

 found in that paper. The following series, for which the writer 

 is indebted to Mr. Charles Hockin, allows the curve to be easily- 

 constructed. 



Let C be the maximum current, and let a have the value given 

 above; then calling x the current at any time t, we have 



# At 9t \6t 25t 



*~^-HQj -&-&-& +&-**■}}■ 



The series for uniform imperfect insulation may also be found 

 interesting. 



Let n express the quotient of the number expressing resistance 

 to loss from one unit of length of the conductor, divided by the 

 resistance of the same unit of length to conduction along itself, 

 then for uniformly imperfect insulation (the case of a* sound sub- 

 marine cable) we have the current 



x=C J 1-2 



i + 



(!) 



4 nir 



l I 



t p 



9t 



/3V 1 



3 j_ x \' 



4t 



\ a 1 



) + 1 F- 



9 mr l 



w 1+X3- 



16 mr 1 



In the curve as thus drawn, the maximum current will, when 

 graphically represented, be equal to 10a. 



The object of the present paper is to show the application of 

 the theory to land or aerial lines, and especially to fix an ap- 

 proximate value for the quantity c. The investigation of this sub- 

 ject has hitherto been neglected, inasmuch as the effect of induc- 

 tion in aerial lines is absolutely insensible when any of the ordi- 

 nary methods of signalling are employed. The charge induced 

 on a conductor separated from all surrounding conductors by 

 many feet of air is exceedingly small, and the time required to 

 allow the received current to reach a maximum is correspond- 

 ingly short — so short, indeed, that the speed of transmission 

 appears to depend on the skill of the manipulator and the deli- 

 cacy of the receiving-instruments alone; but when automatic 

 signalling arrangements are employed capable of transmitting a 

 very greatly increased number of words in a given time, the re- 

 tardation due to lateral induction becomes of importance even on 

 moderate lengths of aerial lines. 



2E2 



