Why is the Conventional Concordia Plot Concave Down

Pb / U vs. Pb / U plot, where denotes the radiogenic portion of Pb isotopes. This diagram also finds wide applications in zircon U-Pb geochronology. For U-Pb zircon dating, the daughter-parent ratios are given by 

The first derivative of y with respect to time t from Eq. (12.9) is 

Similarly, the first derivative of x with respect to t from Eq. (12.10) is 

All terms on the right htuid side of Eq. (12.13) is positive and thus dy/dx 0 everywhere. It is not surprising that a positive relationship between and is displayed in the conventional 

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