Electric Waves along Sprral Wires. 423 
If we apply this to the case of a semi-infinite cable having 
a simple harmonic electromotive force of maximum value E 
acting at one end and reckon « in the direction in which V 
decreases, then, since in this instance V=0 when z=, we 
must have b=0, and therefore 
Sete ch 2 is} ve -- (8) 
or, since P can be written in the form «+78, we have the 
following vector equation for the potential at z: 
V= He “(cos Ba—jsin Br). . . . (9) 
Hence, it follows that the wave-length of the potential dis- 
ee along the conductor is 27/8 and the wave velocity 
is p/B*. 
In the above equations x is to be understood as a distance 
measured along the axis of the helix, not along the spiral 
path of the wire. 
If we may consider, as we may in this case, since p is very 
large, that R and K are negligible in comparison with pL 
and pC, then P? reduces to —p?CL; and it follows at once 
from (9) that the wave-length X of the motion expressed 
by these equations under these conditions is given by 
A=H/[n /CL. 
Hence the wave velocity W=1/ /Ch. 
We can therefore calculate the wave velocity along the 
spiral if we know by experiment the capacity per unit of 
length (C) and the inductance per unit of length (L) of the 
helix. 
The length of the helix is 206 centimetres and its total 
inductance 19°9 x 10° ems., and its total capacity is Cy micro- 
microfarads (m.mfds.) depending on the distance of the 
parallel earth-wire. Hence, the wave velocity along the 
helix is given by the equation 
200 x W102 
ten Capacity in m.mtds. x Inductance in cms. 
(10) 
* If we multiply this equation (9) by «/” and take the real part of the 
resulting expression, we have v= Ke _™ cos (pt—x), which gives us the 
ordinary algebraic expression for the potential at any point and time in 
the cable. See J. A. Fleming, ‘‘On a Model illustrating the Propagation 
of a Periodic Current in a Telephone Cable, and the Simple Theory of its 
Operation,” Phil. Mag. August 1904. 
