More accurate equations than previously used to describe a non-perfect spherical reference system are given, and experiments to confirm them described. When such a system is used to measure chemical shifts, there should be a correction due to the magnetic susceptibility of the material from which the sphere is made, as well as corrections due to the susceptibilities of the solutions. It is also shown that the change in magnetic field strength, caused by insertion of a sample into the pole gap of a magnet, may be significant in certain circumstances. The ‘substitution’ method of external referencing must therefore be used with care.