1877.] Telegraph Beceiving Instrument. 185 



of very long and highly insulated lines, the question assumes a different 

 phase and becomes one o£ great importance. 



Now the best resistance for an electromagnet to be employed as a 

 receiving instrument on any line has to be considered from two aspects, 

 which may fitly be referred to as the " static" and the " kinetic." 



Considered under the first aspect the problem is a purely statical one : 

 it is to find the resistance of the receiving instrument, which will make its 

 magnetic force a maximum, when a steady current is flowing from the 

 sending to the receiving station. By a steady curi:.ent is meant one which 

 does not varj^ in strength with respect to time. This problem is complete- 

 ly solved and thoroughly understood. 



It can be shewn* that the magnetic force is a maximum for 



fk Ik 



s/ki{\ — ^^ +/(1 + ,) 



= ^/ ki 





Where r = resistance of receiving instrument. 

 / = „ „ battery. 



kf = „ „ conduction per unit of length. 



**t = „ „ insulation „ „ „ „ 



and I = length „ line. 



If the resistance / of the battery may be neglected, 

 — 2l\/i 



_ 1 — € Jk 



r = \/ ki — ^ I isl i 



= measured resistance of line with its distant end to earth. 



* Blavier, Annales Telegraphiques, 1858, p. 234. 

 f Let A = measured insulation of line : distant end insulated. 

 And B= „ conduction,, „ : „ ,, to earth. 





And % = -7-. 



