*"I agree that this paper has inacuracies in the equations. it appears they hid some 'Cooks Variable Constants' in their work so that the numbers worked out. However, they did attempt to create an equation to describe the relationships." - jgdpeng*

They should have been more up-front about how horrible their mutual C equation is. It's all plausibility and hand waving, and it's total crap for true linearity studies (i.e. if you're looking for a way to mathematically linearize the field).

*"The objective of the paper was to prove that the relationship between hand proximity and musical notation is approximately linear and sharping my pencil and correcting errors in the document will only make the result a little more linear, which is only a moot point." *

The simple algebraic C between two plates equation is actually pretty close, particularly in the far field. I think I would use that and work it back through the LC resonance equation. The linearity differences between a plate and a rod antenna aren't that great, and the hand behaves a lot like a plate.