The transformation to practical reference frames

So far, all of our calculations have been made relative to a reference frame fixed on a set of inert markers (Darken, 

1948 Brady, 1975). This frame corresponds most closely to our intuitive view of diffusive behavior, and is useful in theoretical work. But few metamorphic rocks contain suitable inert markers, cuid we are frequently forced to choose a more practical reference frame, such as one moving with the mean velocity of all components, or with the velocity of a single component. The conversion from one frame to another is simplest if we rewrite the flvixes in the form Ji i i v jre F represents any reference frame, and Vt is the velocity of i. Then, to convert from frame 1 to frame 2, 

Lj j depend on the concentrations of the components in the rock, and will therefore vary markedly from one zone to another. For 

All of the previous calculations could equally well have been carried out with these coefficients, and would have given the cycle of Fig. 7 directly. 

There are many possible choices of reference frame most of the common ones are reviewed by Kirkwood and others (1960) and by Brady (1975). It is obviously essential to use a reference frame which can be measured accurately, so it is often preferable to use a single easily-measured component, rather than using a frame which depends on all of the fluxes, some of which may be difficult to measure accurately. It is also convenient to select a frame which moves relatively slowly, in order to minimize the size of the cross-terms. 

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