The conformation of the backbone in the side chain liquid crystal polymer poly\[omega (4-methoxybiphenyl-4-yloxy)butyl methacrylate] has been studied in the smectic C and nematic phases. Small angle neutron scattering experiments were performed on mixtures of molecules with perdeuteriated backbones and unlabelled molecules. The polymer is found to adopt an oblate conformation in the smectic C phase. The components of the radius of gyration parallel and perpendicular to the director are determined as a function of temperature from Guinier plots of the SANS data. The radii of gyration do not vary across the smectic phase and are found to be Rg,||=(27+/-1)A, Rg, =(42+/-1)A. These results are compared with recent SANS results for other side chain liquid crystal polymers.