We want to be able to derive the Hamiltonian. For the first isotope, the I1, mu_1 are already known and a_1 is to be measured. The only thing needed to calculate the magnetic field is J. This can be derived from the Landé factor and energy difference fraction. Now that everything about the Hamiltonian is known, and we get I_2, a_2 is to be measured. From this we can derive mu_2 by using the equation H = -mu_2 * B(0) = (1/2) a_2 C.