Reg Edwards, G4FGQ wrote:
"It has a uniformly distributed radiation resistance according to the
length of the coil form."

That may be the case of "treating" radiation resistance as if uniformly
distributed. Radiation resistance may be defined as the resistance which
would take the same power as that radiated when placed at the
high-current point of the antenna.

While a transmission line of uniform cross section may have uniform
inductance and capacitance per unit length, it is unlikely that an
antenna has uniform capacitance per unit length. Electric field lines of
force have a varying concentration along equal small segments of wire
length. It`s usually a function of distance between wires and this
varies in an antenna because the antenna is meant to radiate.

Variation of capacitance along an antenna causes a variation in surge
impedance along the antenna, but a useful average can be used for
calculations. Straight wire or coiled as in a rubber ducky, an antenna
is subject to this variation in capacitance and surge impedance.

Best regards, Richard Harrison, KB5WZI