of a Telegraph Receiving-instrument. 451 



where r = resistance of receiving-instrument, 



/ = ,, ^ battery, 



k* = conduction per unit of length, 



i* = insulation, 

 and I = length of line. 



If the resistance / of the battery may be neglected, 



l-fe-^Vr 



= measured resistance of line with its distant end to 

 earth. 



From this value of r a considerable reduction has to be 

 made, on account of the thickness of the insulating covering 

 of the wire in the receiving-instrument, according to the 

 formulaf 



resistance of receiving-instrument _ diameter of bare mre 



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 consi- 

 dered — 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 

 problem has never been completely solved. 



Sir William Thomson, however, has shown 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 shown that the speed of 

 signalling on any line depends on the value for that line of a 



* Let 



A = measured insulation of line, distant end insulated, 



and 

 Then 



and 



B = „ conduction „ „ to earth. 



VAB Va+VB 



^.^ AB 



t See Proceedings of the Asiatic Society of Bengal, June 1877. 



2G2 



