Isotope and trace-element ratios

Let us consider two reactive species i and j (ions, elements, or isotopes) in a reservoir and their rate of change governed by the equations 

Using the rule of ratio differentiation, the rate of change of the ratio R — C /CJ can be written 

Let agr be the common value of the reactivity coefficients for both isotopes. Replacing the subscripts liq by SW , in by runoff and evaluating, we get the rate of change of 87Sr/86Sr as 

The magma residence time can be estimated by recasting equation (7.2.23) as 

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