Periodic Electric Current in a Telephone Cable. 227 
‘we may write them in the following form: 
R? \2 K2 \2 : 
: 9 = bee 2 X K 2 2, \ ¢ 
29 ea) pC(1+ a) —(RK—p°LC). (25) 
If we employ any such frequency as 100 tv 200, then p is 
a number of the order of 1000. In all actual well-insulated 
submarine or underground cables, the quantity K?/C? per 
mile is a small quantity of the order of 10~4, whilst R*/L? is 
a large number of the order of 10* or 10°. Hence, if the 
frequency employed is anything of the order of that of the 
waves of the speaking voice, the quantity K?*/p?C? can be 
neglected, whilst the value of R?/p*L’ may approximate to 
unity, or say to a number such as 2, 3, or 4 near to unity. 
Accordingly, in practice we might have for the value of 
3 EE 
(2 ages -, reckoned per mile or per knot, a number of the 
order of, say, 2. 
Hence, in this case, the values of 2 and 8 per mile would 
reduce to :— 
ei Re nl) a (26) 
Pereop UO RR sk (27) 
Again, in the case of all well-instlated cables the value of RK 
is very small compared with p?LC for such frequencies as above 
mentioned, and hence as a first rough approximation we can 
ealeulate the values of a and £# for most actual submarine 
ables from the expressions 
ee, Rapa / Be. 
In this case 2 is a function of the frequency, but the wave- 
velocity p/® is independent of the frequency. Accordingly 
there is attenuation depending on frequency. For any well- 
insulated cable, however, we have the value of @ nearly given 
by the equation, 
2aP=pLC (1+ 1 )+RK—/LC;. (28) 
2 
pL? 
and from this equation combined with (19) we can always 
calculate the distance for drop to half initial voltage or 
current, which may be roughly said to represent the limiting 
distance of good telephony. 
Suppose, for instance, that we consider as an example any 
Q 2 
