A theory is offered for the drag and heat transfer relations in the statistically steady, horizontally homogeneous, diabatic, barotropic planetary boundary layer. The boundary layer is divided into three regionsR_{1},R_{2}, andR_{3}, in which the heights are of the order of magnitude ofz_{0},L, andh, respectively, wherez_{0} is the roughness length for either momentum or temperature,L is the Obukhov length, andh is the height of the planetary boundary layer. A matching procedure is used in the overlap zones of regionsR_{1} andR_{2} and of regionsR_{2} andR_{3}, assuming thatz_{0} ≪L ≪h. The analysis yields the three similarity functionsA(μ),B(μ), andC(μ) of the stability parameter, μ = ϰu_{*}/fL, where ϰ is von Kármán's constant,u_{*} is the friction velocity at the ground andf is the Coriolis parameter. The results are in agreement with those previously found by Zilitinkevich (1975) for the unstable case, and differ from his results only by the addition of a universal constant for the stable case. Some recent data from atmospheric measurements lend support to the theory and permit the approximate evaluation of universal constants.