1889. ] Alternating Currents and on the Telephone. 323 
In the case we are considering we shall assume that 47rpa’/o 
is so small that c/47pa’/o is large. We must remark that c cannot 
be made to fall below a not very small fraction, for that even when 
there is no conductor at less than an infinite distance from the 
wire, the wire will behave (see Proc. Lond. Math. Soc. p. 315) as if 
ale 1 
Saag) log pay’/aV*’ 
where log y = ‘577 — log 2. 
Since in this case the second term in the bracket on the 
left-hand side of equation (2) is much larger than the first, we 
have : 
feet (08 
ie V? 2ara*p ’ 
Lol (ep le 7a} 
MV \Qnra®| \y2 V2)’ 
this represents a disturbance, propagated with the velocity 
V et 
cop 
and fading away to 1/e of its original value after traversing a 
distance 
V oe 
cop 
Thus in this case both the velocity of propagation of disturb- 
ances and the rate at which they die away depends upon the 
period, the quicker the rate of propagation, the faster the disturb- 
ances die away. Both these effects would be very detrimental 
to the distinct propagation of messages over a long wire. 
Case II. When 4rp/a’o is moderately small, say between 
1/10 and 4, but large enough to make co/47rpa’ a smallish fraction. 
In this case by equation (2), we have 
Ee a cae 
deg : , ca} ‘ 
this represents a disturbance propagated with the velocity V, and 
fading away to 1/e of its value after travelling over a distance 
4rra’/Veo, thus in this case both the velocity of propagation and 
the rate at which the vibrations die away are independent of the 
period, and therefore a wire fulfilling the conditions of this case will 
be able to transmit telephonic messages under the most favourable 
circumstances. 
24—2 
