Air gages were first developed in France before World War II by a carburetor company that was looking for a more reliable method of measuring its carburetor jets.
Air gaging is based on the law of physics regarding flow and pressure. They are directly proportionate to the clearance and will react opposite to each other. In other words, if there is more clearance there will be more flow but less pressure and with less clearance there will be more pressure and less flow.