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Alchemy

One can convert Earth and Fire gems into gold using spells in Alteration.

Alteration 1: Distill Gold (F1) 

Alteration 2: Alchemical Transmutation (E1)  Alteration 5: Transmute Fire (F2)  Alteration 6: Earth Gem Alchemy (E2)

All the spells cost 1 gem of their respective types, and you can pile on additional gems to boost the ritual, like normal. The spell has a conversion rate which is boosted by the mage's skill in that path and that conversion rate is applied against all the gems you spend boosting the ritual. That means that the 1 gem paid to start the ritual is simply lost (earning you no gold), and that if you don't boost the ritual at all you will get no money for your trouble.
Formulas

Distill Gold: (15 + Fire Skill - 1) x (# of extra gems)  Alchemical Transmutation: (10 + Earth Skill - 1) x (# of extra gems)  Transmute Fire: (20 + 2x(Fire Skill - 2)) x (# of extra gems)  Earth Gem Alchemy: (15 + 2x(Earth Skill - 2)) x (# of extra gems)

An alchemy bonus is a multiplier applied to the result (e.g. a result of 20gp with a 50% alchemy bonus becomes 20 x 1.5 = 30gp).
Here's a couple of benchmarks

F1 casting Distill Gold = 15gp/extra gem  F2 casting Distill Gold = 16gp/extra gem  F9 w/100% Alchemy Bonus casting Distill Gold = 46gp/extra gem

E1 casting Alchem. Trans. = 10gp/extra gem  E2 casting Alchem. Trans. = 11gp/extra gem  E9 w/100% Alchemy Bonus casting Distill Gold = 36gp/extra gem

F2 casting Transmute Fire = 20gp/extra gem  F3 casting Transmute Fire = 22gp/extra gem  F9 w/100% Alchemy Bonus casting Transmute Fire = 68gp/extra gem

E2 casting Earth Gem Alch. = 15gp/extra gem  E3 casting Earth Gem Alch. = 17gp/extra gem  E9 w/100% Alchemy Bonus casting Earth Gem Alch. = 58gp/extra gem

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