The paper gives a simple theoretical treatment of the results that can be developed when air flows according to polytropic laws in shafts and airways. Polytropic relationships for related vertical and horizontal frictional components of flow are also developed, together with the static air column in the measuring tubes. The resulting polytropic law for the horizontal frictional component may be calculated. Equations are developed giving the relationship between temperature, absolute pressure, and specific weight (or density) with depth, both for static and frictional flowing columns. The resulting curves obtained for shaft flow are illustrated graphically.