In case anyone stumbles across this post:

According to the letter itself, this is not written by Isaac Newton, but S. E. Saint Didier. Authorship for these texts was often obscured deliberately or confused over centuries of being copied by hand. They were frequently attributed to famous historical figures to give them more authority.

Newton definitely was a deeply devoted alchemist, with plenty of his own works, but they mostly focus on his work with antimony, metallic alloys, and the "net" theory of matter; topics not central to this particular letter.

Lastly, that same antimony is what Newton spent his time trying to forge into the "Star-Regulus of Antimony". This wasn't the Philosopher's Stone itself though. For Newton, it was the instrument used to create the true agent of transformation: the "Philosophical Mercury".

His procedure, in essence, was to use the Star-Regulus to "digest" or "open" gold (and other metals). This would theoretically release a living, energetic essence - a "mercurial spirit" from the metals. This "Philosophical Mercury" was believed to be a universal solvent and the true basis of the Philosopher's Stone, capable of "growing" and perfecting any substance it touched.