A connection of two adapter parts of a modularly-constructed supporting apparatus includes a first adapter part which has an end-side attachment with a partially spherical recess, a second adapter part which has an end-side spherical attachment for insertion into the partially spherical recess in the first adapter part and has a clamping ring which bears against the spherical attachment, on its half which is averted from the partially spherical recess, and a connecting clamp which engages behind the attachment and the clamping ring on sides which are averted from one another and also fixes the attachment and the clamping ring axially and radially in relation to one another, wherein the attachment and the clamping ring each have at least one weakening region for deforming the attachment and the clamping ring when the connecting clamp acts on the attachment and the clamping ring. The connection is secure when tools, workpieces or the like of a relatively high weight are held by the supporting apparatus.