We present, so far as we know, the first solution to thecomplete set of conditions developed by scaled particle theory under the usual approximation that G() can be expressed as a Laurent series for 1/2 <>. The theory leads to a fourth virial coefficient accurate to 0.6% and fair values for the first derivative of the radial distribution function(1). The results are used to calculate both boundary tension and boundary adsorption in the hard sphere fluid, as well as the pressure of a dilute hard sphere mixture. It is probable that the nearly linear function we calculate deviates only slightly from the true G() at fluid densities. Some discussion of this point is presented.