If we know µ1 and I1, then with the experiment we determine a1=µ1Bj/I1J1, and we can identify Bj/J1.
Then when we perform the same experiment, assuming J2~J1 (ok, same isotope + free atoms experiment), we have a similar Bj/J2 and the only thing unknown will be µ2 = a2I2J2/Bj.