We report measurements of and meson photoproduction from longitudinally spin-polarised protons by an energy tagged (0.73-2.3 GeV) and linearly polarised photon beam. A close to complete solid angle coverage for the reaction products was provided by the CEBAF Large Acceptance Spectrometer at Jefferson Laboratory. The double-polarisation observable is extracted from Maximum Likelihood fits to the data, enabling the first accurate determination for the reaction , while also significantly extending the kinematic coverage for . This large data set provides an important constraint on the properties and spectrum of excited nucleon states decaying to Nπ in the mass range from 1.4 to 2.2 GeV, as well as for background (non-resonant) photoproducti...