20
KINETIC ENERGY OF ELECTRICITY IN MOTION [I]
Multiplying this expression by 2n, we find the mutual induct-
ance of the two layers to be
ет
+8Sne
If now one of them be displaced laterally through a dis-
tance q the inductance obviously becomes
Eπ
- 8Sne!
For all intermediate positions the inductance has a value
between these two extremes. Hence, if we neglect altogether
the effect of the different layers on each other, the error for
each pair of layers to be considered is less than 8Sne-/q.
But any two contiguous layers may be altogether left out of
account, for the induction between them is in fact zero to a
high degree of approximation. By substituting values of q, e,
R, such as occur in ordinary cases, we easily convince ourselves
that the error considered amounts to less than the part
of the self-inductance of the layer. In so far as we neglect
it we get the self-inductance of the whole spiral by adding the
self-inductances of the individual layers. Hence, if I denote
the whole length of wire contained in the spiral, we have
finally
4n
P = 21 { $
• 21 + + 10g 24 √57773m)
log
For the spirals used in our case
Rπ
l=130032 mm., n = 34,
R=0·465 mm.,
q=1·087 mm., P = 178,500 mm.
A calculation of the error possibly committed on the above
principle gave it as less than 1200 mm.
Determination of P.-The mutual inductance P' of the
two branches of the spiral, as has been already remarked, was
determined by comparison with the inductance of straight
wires. The arrangement of the experiment is shown in Fig. 4.
A and B are rectilinear systems of wires of the dimensions
marked on the figure, and were stretched out on the floor of