What is the basis for the unit "chow" for pearls?

by Rane
(Ann Arbor, MI)

The formula for calculating the "chows" per carat involves squaring the carat weight (multiplying the carat weight by itself), and multiplying that by 0.6518. This makes a 1 carat pearl 0.6518 "chow", but a 2 carat pearl 2.6072 "chow": four times, not just twice.

What is the rationale for this? It appears to be a way of considering both the mass and the size of the pearl in establishing a value, but does it really do that? That is, do the experts rely upon the "chow" value in any significant way in buying and selling pearls?

I would also be interested in knowing a source for learning the history of the "chow", because I am an engineer and engineers are always dealing with the "units" of (often obscure) measures, and their interconversion.