I wrote;
'That means getting only 1/4 the previous power every time the distance
from the transmitter doubles."

That`s true, but it`s only part of the story. A receiving antenna can
only deliver 50% of the power it receives and that can happen only when
it is perfectly matched to its receiver. Otherwise, it reradiates more
than 50% of its received power.

There is another fly in the ointment. A former colleague of mine, Peter
N. Saveskie compiled an interesting book, "Radio Propagation Handbook".
On page 826 Pete writes:
"Most of the attenuation of "free-space" loss occurs close-in to the
adiating antenna. The loss between two isotropic antennae separated by
one wavelength is 22.0 dB, thereafter increasing by 6.0 dB for each
doubling of the inter-antenna distance.'

This sort of loss in the first wavelength is one problem in trying to
use antennas back to back as passive repeaters. Enormous receiver
sensitivity makes the passive repeater practical sometimes in spite of
the path loss.

Pete`s path loss formula has worked well for me.

Best regards, Richard Harrison, KB5WZI