Boundary layer equations (partial differential equations) can be transformed to ordinary diffential equations with constant coeffieients in terms of similarity transformed to ordinary differential equations with constant coeffieients in terms of similarity transformations in the heat tranfer analysis on the surface of any axiaymmetric boiles. The azimuth functions can not be uniquely determined because of the singular behavior at the stagnation point(X=0.deg.).In spite of the azimuth functions behaving singularly, many of researchers have analyzed the heat transfer problem on a horizontal chlinder or a sphere, supposing the set of solutions( $H_{1}$ & G$_{1}$) of being yieled from the simple differential equation to be unique solution of therazimuth functions. In order to ascertain whether mathematical incompatibility as mentioned above can be admitted in the viewpoint of enginerring or not, condensation heat transfer coefficients on a sphere are computed for all azimuth functions( $H_{1}$ G$_{1}$ & $H_{2}$ G$_{2}$) and comparisons with the experimental result are discussed.