2
KINETIC ENERGY OF ELECTRICITY IN MOTION [I]
a term corresponding to the increase in the kinetic energy of
the current. This is proportional to the square of the current
and may therefore be put equal to mi², where m is a constant
depending on the form and size of the circuit. We thus get
in place of the above the following corrected equations
Aidt = i²rdt + d(Pi²)+d(mi²),
=
ir A-P
pdi
di
dt
m at
>
di
=A-(P+m).
dt
...
Analogous conclusions apply to the case of a system of circuits
in which electromotive forces A,, A₂ act. When the
correction for inertia is introduced, the well-known differential
equations which determine the currents take the form
-
¿‚”‚ − A¸ − (P¸¸ + m‚)di, — P,
= (P₁
dt
di,
12 dt
•
•
-
din
- Pin
at
din
di,
½"₂ = A, - P
di,
dt
(P22 + m₂)
dt
inn = An- Pin
di,
dt
-
P.
P₂n
at
- (Pan+m.) din
nn
dt
Thus the only alteration which the mass of the electricity
has produced in these equations consists in an increase of the
self-inductance, and it is at once obvious
1. That the electromotive force of the extra-currents is
independent of the induction-currents simultaneously generated
in other conductors, and of the mass of the electricity moving
in them.
2. That the complete time-integrals of the induction-
currents are not affected by the mass of the electricity moved,
whether in the inducing or induced conductors.
3. That, on the other hand, the integral flow of the extra-
currents becomes greater than that calculated from inductive
actions alone.¹
1 With reference to these simple deductions the philosophical faculty of the
Frederick-William University at Berlin in 1879 propounded to the students the