CHAPTER I. 

INTRODUCTION. 

1. The preceding sections deal with transient phenomena in 
time, that is, phenomena occurring during the time when a 
change or transition takes place between one condition of a cir- 
cuit and .another. The time, t, then is the independent variable, 
electric quantities as current, e.m.f., etc., the dependent variables. 

Similar transient phenomena also occur in space, that is, with 
space, distance, length, etc., as independent variable. Such 
transient phenomena then connect the conditions of the electric 
quantities at one point in space with the electric quantities at 
another point in space, as, for instance, current and potential 
difference at the generator end of a transmission line with those 
at the receiving end of the line, or current density at the surface 
of a solid conductor carrying alternating current, as the rail 
return of a single-phase railway, with the current density at the 
center or in general inside of the conductor, or the distribution 
of alternating magnetism inside of a solid iron, as a lamina of an 
alternating-current transformer, etc. In such transient phenom- 
ena in space, the electric quantities, which appear as functions 
of space or distance, are not the instantaneous values, as in the 
preceding chapters, but are alternating currents, e.m.fs., etc., 
characterized by intensity and phase, that is, they are periodic 
functions of time, and the analytical method of dealing with 
such phenomena therefore introduces two independent variables, 
time t and distance I, that is, the electric quantities are periodic 
functions of time and transient functions of space. 

The introduction of the complex quantities, as representing the 
alternating wave by a constant algebraic number, eliminates 

277 


278 TRANSIENT PHENOMENA 

the time t as variable, so that, in the denotation by complex 
quantities, the transient phenomena in space are functions of 
one independent variable only, distance Z, and thus lead to the 
same equations as the previously discussed phenomena, with 
the difference, however, that here, in dealing with space phenom- 
ena, the dependent variables, current, e.m.f., etc., are complex 
quantities, while in the previous discussion they appeared as 
instantaneous values, that is, real quantities. 

Otherwise the method of treatment and the general form of 
the equations are the same as with transient functions of time. 

2. Some of the cases in which transient phenomena in space 
are of importance in electrical engineering are : 

(a) Circuits containing distributed capacity and self-induc- 
tance, as long-distance energy transmission lines, long-distance 
telephone circuits, multiple spark-gaps, as used in some forms 
of high potential lightning arresters (multi-gap arrester), etc. 

(b) The distribution of alternating current in solid conductors 
and the increase of effective resistance and decrease of effective 
inductance resulting therefrom. 

(c) The distribution of alternating magnetic flux in solid iron, 
or the screening effect of eddy currents produced in the iron, and 
the apparent decrease of permeability and increase of power 
consumption resulting therefrom. 

(d) The distribution of the electric field of a conductor 
through space, resulting from the finite velocity of propagation 
of the electric field, and the variation of self-inductance and 
mutual inductance and of capacity of a conductor without 
return, as function of the frequency, in its effect on wireless 
telegraphy. 

(e) Conductors conveying very high frequency currents, as 
lightning discharges.