  Thus the set of all arbitrary conformal transformations of the metric induces an equivalence class \(K\) of conformally related  symmetric linear connections. This equivalence class \(K\)  constitutes a second-order conformal structure on the manifold and  the difference between any two connections in the equivalence class  is given by (29). Weyl shows that a conformal transformation (29)  preserves the projective structure and hence is a projective  transformation (that is, a conformal transformation which also  satisfies (7)), if and only if \(\theta_{j} = 0\), in  which case the conformal and projective structures are compatible.  Weyl remarks after the proof: 