The motion of a charged particle in a multipole magnetic field has three adiabatic invariants associated with it. The first is that the magnetic flux through the particle's cyclotron orbit about a field line is constant. An equivalent statement is that the magnetic moment of the particle due to its cyclotron motion is constant. The second adiabatic invariant states that the integral of the particle's parallel momentum between its two mirror points is constant. The third adiabatic invariant says that the magnetic flux through a surface connected to the longitudinal invariant surface and passing through the magnetic axis is constant. In this thesis I have examined the relationship between the magnetic moments from the first and third invariants. For a particle in the equatorial plane of a dipole field, the ratio of the magnetic moment from the third invariant to that from the first invariant is 3/2.