Define Grand Lunar Canals (Moscow Phys-Tech)?

In one of his book, H. G. Wells illustrate an encounter of amateur earthling astronauts with a lunar civilization living in very deep caverns beneath the surface of the Moon. The caverns are attached to the surface by long channels filled with air.

The channel is dug among points A and B on the surface of the Moon so that the angle AOB=90^o suppose that the air pressure in the middle of a channel is P_o = 1 atm. calculate approximately the air pressure in the channel near the surface of the Moon. The radius of the Moon a ≈ 1750.  The hastening due to gravity on the surface of the Moon g_m≈ g/6  , where g is the hastening due to gravity on the surface of the Earth.