In the first part of this note the stress-function approaches of Boussinesq and Timpe to the rotationally symmetric problem in the classical theory of elasticity are referred to general orthogonal axisymmetric curvilinear co-ordinates. Although the underlying computations are of a routine character, it is felt that the presentation of the final results may serve a useful purpose. In the second part of the note, a connection between the two stress-function approaches is established.