A common mistake in introductory physics textbooks is the omission of the buoyant force exerted by
the air on an object floating in a liquid. One previous work (Lan 2000 Phys. Teach. 38 [http://
http://dx.doi.org/10.1119/1.880449] 125 ) includes that missing term but assumes that the air, like
the liquid, is incompressible. Here we account for the barometric variation in the density of air
with altitude. Although the numerical size of that correction is small, it is conceptually important
because it helps students better appreciate that buoyancy results from the variation in fluid
pressure across the surface of an object.