226 Prof. J. A. Fleming on Propagation of a 
Hence we have for the abscissa of half voltage 2’ and the 
potential wave-velocity w the values 
0:7033 Loo 
fe = / i. e . ° e € 
a VKR° w=, ef L (23) 
Both these quantities are independent of the periodicity, 
and hence for this cable all potential waves travel at the same 
rate and are attenuated in the same ratio. 
If, therefore, such a cable could be practically constructed 
with a small enough value for / KR, telephonic speech would 
be possible through it with results not possible in the case of 
non-distortionless cables. 
The model shows clearly that the attenuation of the simple 
periodic wave depends on the value of a, that is on the varia- 
tion of eccentricity of the wheels, and that the wave-length 
is determined by the value of 8. 
It is not then difficult even for a non-mathematician to 
comprehend that if a complex periodic electromotive force 
acts at one end, which may be resolved into the sum of a 
number of simple periodic electromotive forces, the result in 
general will be to produce corresponding simple periodic 
waves which travel at different speeds and degrade at various 
rates. Hence, in a comparatively short distance the initial 
complex wave form is so altered that it becomes unrecog- 
nizable. Herein, therefore, resides the cause of the practical 
limitations of telephony. The remedy for it rests in the 
alteration of the primary constants of the cable so as to 
bring about the necessary changes in the secondary constants. 
There are, however. necessary practical limits to these 
changes. In overhead lines where capacity is relatively 
small, it is not difficult to introduce sufficient inductance (as 
Prof. Pupin has done) in the form of separated inductance- 
coils, and provided these are sufficiently close together within 
the limits of a wave-length the result is equivalent practically 
to continuous inductance. The same remedy for distortion 
could no doubt be applied to underground telephone trunk- 
lines, although the writer is not aware that it has been tried. 
On the other hand, an addition to the inductance is not 
easily made in the case of a submarine cable. Any inter- 
ference with the continuity of size or great increase in bulk 
or weight would hardly be permitted. 
Hence, in the case of cables the favourite prescription for 
the defect has been that of creating a large dielectric con- 
ductance by artificial leaks. The effect of any such proposed 
added leakage can easily be foretold. 5 
Taking the expressions for 2a’ and 2@? in (13) and (14) 
