422 Prof. J. A. Fleming on the Propagation of 
We have then to consider how the velocity of an electric 
wave along such a long helix can be determined. The point 
of view here adopted is to consider the closely wound helix as 
if it were a linear cylindrical conductor having a certain mean 
capacity and inductance per unit of length; these values 
being obtained from the quotient of the measured values of 
the total capacity and inductance, by the known length of 
the spiral. We then proceed to treat the problem as one 
of electric-wave propagation along a linear conductor in the 
usual manner. 
Let C be the capacity, L the inductance, R the resistance, 
and K the dielectric conductance, all per unit of length of an 
infinitely long helix considered as a simple linear conductor 
immersed in a dielectric. Then, considering any element 
dz of the length of the helix, if we call v the potential and 7 
the current at the beginning of this element, at any instant 
we have the well-known equations : 
di eee 
L dt + R2 a ay 5 te (1) 
dv dt ; 
CC. + Kv= dx’ . . ° o . . (2) 
expressing the current 2 and potential v at any point in 
terms of the constants. If we consider 2 and v to vary ina 
simple harmonic manner with frequency n=27/p and to 
have maximum values I and V (an assumption legitimate in 
the case of electrical oscillations), then the above equations 
can be written 
dV . 
qe (R+pl)L . . . 2.» B) 
di ° 1 ip 
Fg tO) Ss) ee 
where j= ~—1. Hence writing P for 
VR+jpL .V7K+7pC 
we can put (3) and (4) in the form 
av : 
ney — iP2ye . . . . ° . . (5) 
dT 
dx == PJ, . ° . . ° e od (6) 
A solution of (5) applicable in the present case is 
ve get bee 2h il atecente 
where a and 6 are constants. 
a ’ 
hie SSS ee 
