676 Prof. J. Perry on 



greater than 1000 per second, the most important being 800, 

 good transmission of such currents is found to mean good 

 transmission of speech. 



6. It is quite a u^ual thing to find that experimenters are 

 using transmitting and receiving devices which are not the 

 best for a particular cable. For a receiving instrument, for 

 example, there is a best resistance and inductance (or com- 

 bination of inductance, capacity, back E.M.F., &c). In 

 every case yet studied by me (but I can imagine others) the 

 most suitable receiver causes the current and voltage near 

 that end of the line to be different from what they would be 

 if the line were infinitely long. Thus, for example, with 

 simply periodic currents in the standard cable it will be 

 found that at any place far from the ends, voltage divided 

 by current is of the form r( — 45 c ) or oc — ai. If the telephone 

 or other receiving instrument has a resistance R and an 

 inductance L each of which is proportional to the square of 

 the number of turns of wire upon it, and if the effect on the 

 instrument (such as the deflexion of a coil, &c.) is propor- 

 tional to the current turns received, this effect is a maximum 

 if R = a and if L = a/g r , where q is 2ir times the frequency. 

 It is easy to show that if we wished the receiving instrument 

 to produce the same effect as an infinite prolongation of the 

 cable, it ought to have a resistance R and a negative induct- 

 ance L = — u/q, which is a capacity 1/a.q. It is then not 

 merely when unsuitable instruments are used, but also when 

 the most suitable instruments are used that we have end 

 effects. 



7. A line with equidistant similar contrivances when they 

 are not too far apart may be replaced (mathematically) by a 

 line whose properties (as to resistance, inductance, capacity, 

 leakance, &c.) are continuous, for many purposes of 

 calculation. 



The simplest case of uniform distribution of properties in 

 an infinite line was studied in my paper read before the 

 Physical Society in 1893. Let v and c be the voltage and 

 current at any place whose distance from the sending end 

 is x ; let v sin qt be the voltage when x is 0. If r, /, s, 

 and k are the resistance, inductance, leakance, and capacity 

 per unit length, we have 



v = v €~ hx sin (qt- gx), .... (1) 

 where 



Vt\J\A^W^S)H^ 



(2) 



