gareth wrote:

If short antennae radiate all the power that is fed to them, then why
would anyone use long antennae,

Because there may be factors other than power efficiecny that are important
to the designer. For example, radiation pattern.


because the first part of such an antenna,
the short
part, would radiate all the power, and then there'd be nothing left for
the extra bit, making up the rest of the long antenna, to do?


Unfortunately, only you belive that is the case. Your position conflicts
with what is understood about antennas.

The answer is, of course, because it is more difficult to feed a short
antenna
because of its reactance.


That may be one reason for using a longer antenna. It is not the only
reason, nor may it be the primary reason.

So, whence does this reactance arise?

Simple.

It is the power that has NOT been all radiated by the short antenna
arriving back at
the feed point with an awkward phase relationship with the incident power.

What happens to that power that has not ALL been radiated when it arrives
back
at the feed point?

Simple.

It passes back into the matching network, which, together with the short
bit, form
the resonant artefact, where much of it disappears as heat in the matching
network
before being fed back to the short antenna to start all over again.

If it is so simple, where are the equations and models that describe it?