324 Prof. J. J. Thomson, On the Transmission of [Jan. 28, 
Case III. When 47upa*/o is large. In this case 
J, (ina) = — J, (ina), 
and equation (1) becomes: 
Now consider the case when c {cu/mpa’}* is small, then this 
equation becomes 
ioss & [1+ aie | ae " ; 
VA (mpa*) 
and this represents a disturbance propagated with the velocity V 
and fading away to 1/e of its value after traversing a distance 
2V6 ( 7a" )2 
ce (omps- 
Thus in this case though the velocity of propagation is inde- 
pendent of the period, the rate at which the vibrations die away 
is not, so that if the distance telephoned over is long enough 
to make the disturbance die away appreciably, the message will 
get confused. 
Case IV. When 47ppa’/o is large, and c{op/mpa’} con- 
siderably greater than unity, 
ep Gi Nea al D 
it ane (aa (wat wal 
In this case the rapidity of transmission is 
Vee 
Ampa’) ’ 
and the distance traversed before the vibration sinks to 1/e of 
its initial value is 
in this both the velocity and rapidity of decay depend upon the 
period, the velocity varying less quickly with the period, and 
the rate of decay more quickly than Case I. 
Let us now consider some numerical cases; in what follows 
we shall suppose the period p to range from 27 x 100 to 27 x 400, 
and we shall suppose that c is of the same order as if the wire 
