Richard Harrison wrote:
. . .
Richard Clark also says Bailey is "naively assuming a 3 dB gain with
each doubling of elements."

It seems to me that the 2nd, 4th, and 8th element may have the same
flaws as the first. No matter how good or bad they are, if they are all
similar, wouldn`t (n) elements abstract nX the energy in one element?
. . .

Yes, but the amount extracted by one element is affected by the presence
of the others. So adding or removing an element changes the amount
extracted by all the other elements. The effect is known as "mutual
coupling", and it explains why, for example, a 2 element Yagi or other
two element array can have gain greater than (or less than) 3 dB
relative to a single element.

Roy Lewallen, W7EL