Elemental fractionation during basalt differentiation

From equation (1.5.7), change in the concentration of an element i with the differentiation index (FeO/MgO)liq, written in lieu of (CFe0/CMg0)Hq, is calculated as 

Even for a constant KD, calculating the evolution of a species i in the residual melt requires that both Dt and Z)Mg0 are known for each value of (FeO/MgO)Hq. 

The Baffin Bay picrites (Francis, 1985) show a very good covariation of FeO, MgO, and Ni. Defined from the twelve XRF data listed in Table 1.12, the variables x = ln(FeO/MgO) and y = ln(Ni/MgO) have been fitted by the parabolic equation 

Assess the variations of Mg0Ni by assuming that DMgOFeO=KD=0.3. 

Taking the derivative dy/dx, we obtain the slope of the curve and, from equation (1.5.10), we write 

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