I
19
KINETIC ENERGY OF ELECTRICITY IN MOTION [I]
=
-
log 2S - log e
-
1
- 2 log 2S+2 log√e²+q² +2
2S+2 log 2S — 2 log√e² + 4q² — 2
-
-
— log 2S+ log √e² + (2n + 1)²q² + 1
-
2S log
€(e² +2²q²)(e² +4²q²)... (e² +(2n)²q²)
(e² + q³) (e² + 3²q³)... √e²+(2n+1)²q²
2
2
1² + (:) * 3² + (:) * √(2n + 1 ) + ( ;)"
2
=
2S log
€
22+
1
€²+(2n)²q²
We get an approximate value in finite form of the expres-
sion behind the logarithm sign by dividing the equation
:
22
22
2
c'. ' - (1 - -—-) (1 - -—-) '(' - ·´)...
COS
1272
by this second equation,
sin z = z 1
322
1
522
--(1-,-) (1-1)...
122
by putting v-1 for z on both sides and dividing the result
1; thus we get the equation
by
1+e="
1
2
v
-
2
- limit (¹² + (#)" ³°³ + (=)*° √(2n+1) + (~)
π
2
22+
v
2n² +
π
π
2
v
-
π
2
and thus the above inductance becomes approximately for a
large value of n
=
2S log
1
1+ e
Eπ
-
e "
or, if we neglect terms of the order e-3″/4,
4Se
EπT
COMENDE ENCINCEDINA I 1: