In the first experiment you measure a_1 = mu_1*B / (I_1 * J). In the second experiment you measure a_2 = mu_2*B / (I_2 * J). Assuming B and J originating from the electron cloud of the same element do not change, you can do: B/J = a_1 * I_1 / mu_1 = a_2* I_2 / mu_2. You now know everything (a_1 and a_2 were measured and I_1, I_2 and mu_1 known) except mu_2, so you can get this from these equations by doing: mu_2 = (a_2 * I_2 * mu_1) / (a_1 * I_1).