This is the way we normally think about air at or around sea level: effectively as an incompressible
fluid. The mathematics leading to equation (7) is not terribly complicated and could be developed within the context of a university level physics course, possibly forming the basis of an assigned problem. It is the interpretation that we see as necessary. Weight is a confusing topic in any case and for solids it is intimately connected to the contact forces that simul- taneously act: an object is ‘weightless’ if only the force of gravity acts on it. For liquids much of the same can be said, but both for solids and liquids weight can be associated with a downward force alone. In the case of a gas this is not true, and the scale reading that we associate with weight is really a measure of differences in density, however slight, which result from gravitational effects. We show in the next section how these differences can be understood as a statistical bias rather than any direct effect of a downward force alone on the weighing apparatus