As was shown in §21.4, we can fit an equation of state to the results of a parametric fit. You might think it better to build the equation of state into the model and then fit that equation of state directly to all the data. As an example of this, one could define an equation that fits the volume expansion as a function of temperature to straight line and then rather than fitting the individual lattice constants, the thermal expansion coefficients would be fit directly, as has been done with other software. Since all the lattice constants are reduced to two linear thermal expansion coefficients, such a fit will appear to have much less “jitter” in the individual fits. Nonetheless, I feel that building a parametric equation into the fit is a poor choice. First of all, the two-step process we use, where least-squares fitting is done to the results from least-squares has been demonstrated (by Ted Prince) to produce the exact same results as a single fit, provided that the full covariance matrix is taken from the first fit and used in place of weights in the second fit. Since each fit in a sequential fit is independent, the only covariance that needs to be considered is that for the parameters that are fit together, and this is done in parametric fitting. However, the more important reason is that when a parametric equation is “baked into” a model, it becomes a constraint. It becomes very difficult to see that the constraint is not correct. If one constrains linear expansion to be linear, then there will be no direct feedback that this is not the best choice to fit the results. By seeing the actual fitted volume values as a function of temperature, one can decide if a linear model is the best choice.