This proposal is part of our project to investigate the unusual physics of 5d transition metal oxides. In particular, we are studying two samples of the chemical composition Ca2Os2O7: One forming the pyrochlore and the other the weberite crystal structure. The key interest in these materials are unusual metal-insulator (possibly Slater or Lifshitz) transitions, concomitant with magnetic ordering. For both samples, we have already performed extensive bulk characterisation and neutron diffraction experiments (and, for the pyrochlore, a preliminary MuSR measurement). However, in both cases, the experimental evidence is ambiguous and we believe that muon spin rotation will yield the desired answers: (1) For the weberite, we want to determine whether the two osmium sites order simultaneously and (2) For the pyrochlore, we want to determine whether any long range order sets in above 40 m