My thanks to previous correspondents.
What intrigues me is the progression between a completely closed box and and an open cage. No doubt a sealed box includes the normal weight of the cararies, flying or not. When, flying the mass cannot "disappear": If small holes are drilled round/through the top (and only top) of the box then eventually under equilibrium the pressure just under the top can only be atmospheric at that height. So the excess over atmospheric pressure just above the base must be just enough to account for the weight (the air being "forced down by the bird's wings"). Conversely. with holes at the bottom, the pressure just under the top will be less than atmospheric and the total pressure difference on the top surfaces will "support" the canaries.
With holes top and bottom, there will be over and under pressures balanced to "support" the mass of the canaries while at the same time causing equal volumes of air to flow in through the top holes and out through the bottom holes (no matter what their relative and absolute sizes) keeping the whole system balanced and stable.
Do you agree ?
We are told that, counter-intuitively, aeroplanes are held up by a lower pressure on the top of the wings than on the bottom (venturi) : - not because the under surface drives the air down. If the canaries were gliders, how would the excess pressure on the base be generated ?The question seems to be - with an aerofoil moving through air with streamline flow where is the weight "taken" , eventually.