For isotope 1, we measured the value of a. If we look at the expression for a, we can see that the only unknowns are B_J and J. We can thus deduce a value for the ratio B_J/J.
Both values will not differ if we are working with a different isotope of the same element as J is a property of the electrons. If we now measure the value of a for isotope 2, we can rewrite the expression for a to an expression for the nuclear magnetic moment where all the variables are known because we deduced the value of B_J/J be first measuring for a isotope with known nuclear magnetic moment.