186 R. S. Brough — Best Besistance of a [AuausT, 



From tliis value of r a considerable reduction has to be made, on ac- 

 count of the thickness of the insulating covering of the wire in the receiv- 

 ing instrument, according to the formula : * 



Resistance of receiving instrument Diameter of bare wire 



External resistance Diameter of covered wire 



Considered under the second aspect the problem is a kinetic one. 

 Here the current is not assumed to be steady ; but the influence of the 

 resistance of the receiving instrument on the rapidity of the variation of 

 the potential of the line is considered, that is to say, its influence on the 

 speed of signalling, since signalling is simply causing the potential at the 

 receiving end of the line to vary in some preconcerted manner. This pro- 

 blem has never been completely solved. 



Sir William Thomson, however, has shewn that when the resistance of 

 the receiving instrument is not very great as compared with the resistance 

 of a perfectly insulated line, its effect is the same on the speed of signalling 

 as if the line had been lengthened by a piece whose resistance would be 

 equal to that of the receiving instrument. 



Sir William Thomson has further shewn that the speed of signalling 

 on any line depends on the value for that line of a certain constant, which 

 miay be called the " retardation characteristic" of the line, and the expres- 

 sion for which is 



Ic c l\ /4\ 



EC = 



where h is the resistance and c the capacity of the line per mile, and / is 

 the length of the line in miles. - 



Now we see that the value of the RC increases as the square of the 

 length of the line, and since by increasing the resistance of tlie receiving 

 instrument we virtually increase the length of the line, it is perfectly ob- 

 vious that if we make the resistance of the receiving instrument unduly 

 high we may increase the value of the RC to such an extent as to impair 

 the signalling speed of the line. 



It thus becomes clear that in the case of a very loJig and highly insu- 

 lated line the best resistance for the receiving instrument, as indicated by 

 the result obtained by examining the problem under the first aspect only, may 

 be so great as to retard the speed of signalling. 



I shall here consider only the case of a perfectly insulated line. 

 Let I = the length of the line in miles 



Jc = resistance per mile in ohms (supposed uniform) 



c = capacity per mile in farads ( ditto ) 

 and r = the resistance in ohms of the receiving instrument. 



* See Proceedings, Asiatic Society of Bengal, June, 1877. 



