We consider a closed curve C in the projective plane and the projective involutions which map C into itself. Any such mapping γ, other than the identity, is a harmonic homology whose axis η we call a projective axis of C and whose centre p we call an interior or exterior projective centre according as it is inside or outside C. The involutions are the generators of a group Γ, and the set of centres and the set of axes are invariant under Γ. The present paper is concerned with the type of centre sets which can exist and with the relationship between the nature of C and its centre set.
If C is a conic, then every point which is not on C is a projective centre. Conversely, it was shown by Kojima (4) that if C has a chord of interior centres, or a full line of exterior centres, then C is a conic.