It appears that Cecil is back with many postings, but he seems to be
ignoring answering my question. Perhaps he's unable to do so. Just so
the lurkers understand that indeed it is possible to work through the
phasor math, here goes. Here's exactly the scenario Cecil set up,
quoted from his posting:

==========

"So to be perfectly clear, here is my statement re-worded using
a 45 degree phase shift through the coil.

The forward current magnitude is equal at both ends of the coil.
The reflected current magnitude is equal at both ends of the coil.

At the bottom of the coil, the forward current is 1 amp at zero deg.
At the bottom of the coil, the reflected current is 1 amp at zero deg.
At the bottom of the coil, the standing wave current is 2 amps at
zero deg.

At the top of the coil, the forward current is 1 amp at -45 deg.
At the top of the coil, the reflected current is 1 amp at +45 deg.
At the bottom of the coil, the standing wave current is 1.4 amp at
zero deg."

==========

OK, so the difference in "FORWARD" current from the bottom to the top
is:
fwd.bottom.current - fwd.top.current
= 1A at 0 degrees - 1 amp at -45 degrees
= 1+j0 - sqrt(.5)-j*sqrt(.5)
= 1-sqrt(.5) + j*sqrt(.5)
(about 0.765 at 67.5 degrees)


The difference in "REFLECTED" current from the bottom to the top is:
refl.bottom.current - refl.top.current
= 1A at 0 degrees - 1 amp at +45 degrees
= 1+j0 - sqrt(.5)-j*sqrt(.5)
= 1-sqrt(.5) - j*sqrt(.5)

The SUM of these two differences is:
[1-sqrt(.5) + j*sqrt(.5)] + [1-sqrt(.5) - j*sqrt(.5)]
= 2 - 2*sqrt(.5) + j0
= 2 - sqrt(2) + j0
= 2 - sqrt(2) at zero degrees

The standing wave current at the bottom of the coil is 2 amps just as
Cecil suggests at one point: It's the sum of the "forward" and
"reflected":
net current at the bottom = sw.bottom.current
= 1+j0 + 1+j0
= 2+j0
= 2 at zero degrees

Presumably Cecil meant that the standing wave current at the TOP
(not the BOTTOM) of the coil is 1.4 amps at 0 degrees. That's close,
but more exactly, it's
net current at the top = sw.top.current
= sqrt(.5)-j*sqrt(.5) = sqrt(.5)+j*sqrt(.5)
= 2*sqrt(.5)
= sqrt(2)
= sqrt(2) at zero degrees.

So the difference in net current (that is, the difference in the
standing wave current) between the top and the bottom of the coil
in this example is exactly:

sw.bottom.current - sw.top.current
= 2 at zero degrees - sqrt(2) at zero degrees
= 2 - sqrt(2) at zero degrees

So, we see that the difference in current between the bottom and
the top is exactly the same, independent of whether we just use
the standing-wave currents, or the currents in the "forward"
travelling wave plus the currents in the "reflected" wave. That it's
also
exactly the same answer you get by looking at a full cycle of
instantaneous currents is left as an exercise (fairly simple) for the
reader.

Either way, there is a difference, and that current must go
somewhere. It should be pretty easy to account for it. In
fact, it's not even very hard to predict fairly accurately in
the case of a loading coil in an antenna perpendicular to a ground
plane or equivalently in a symmetrical doublet.

Cheers,
Tom