Right just checking my diving manuals and Stephen is right. It isn't double the compression at each 10 meters.
The measurements are (and WG's pool is really deep he could confirm this with the experiment I mentioned to him
)
at the surface the pressure is 1 bar and any container (lung, pop bottle or whatever) is full of air.
At 10 meters pressure is 2 bar and the container will be half full of air.
At 20 meters pressure is 3 bar and the container will one third full of air
At 30 meters pressure is 4 bar and the container will one quarter full of air
And so on. So yes you are right.
Mike