Equations of Gyrostatic Aether: McCullach & Kelvin

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I would be interested in the equations of a gyrostatic ether as brought up by McCullach and Lord Kelvin, best in a modern notation. Before people jump on me: I an not interested in questioning modern theories like SR but rather in the extensions of continuum mechanics these theories go in hand with.
 
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Sorry I can't help you with that, but perhaps someone else would, if you'd provide a little more background info...

For example, do you have a link or reference to such a model (is it really a theory?); and maybe you can clarify how you think that such a model/theory leads (or led) to an extension of continuum mechanics (in other words, what could be or what was the use of it?).