Where I can I find a free copy of the original paper in which
Earnshaw's Theorem was published, preferably in .pdf format?  I would
like the actual paper, not an explanation of it, or a restatement.   I
believe the paper was presented in 1839 and published in 1842.

OK, basically I've scoured the net and not found and pdf versions of
the research.  What I did find was some references to it as well as
the name of the title you are looking for. Here is a cite that is
repeated that might help you find it in a catalogue.

Earnshaw, S. (1842) ?On the Nature of the Molecular Forces which
regulate the Constitution of the Lunminiferous Ether?, Trans. Camb.
Phil. Soc. 7, 97?112.

I've pretty much run into the same deal, kajun-ga.  The thing is, it's
referenced in lots of papers, but I don't believe a reference means
anything if you can't actually read the source for yourself.  As a
student, I really can't afford to order a backissue from 1842 from the
Cambridge Philosophical Society.  I would like to be able to read the
actual paper.  I couldn't find it with a google search, a google
suggest (beta) search, or a google scholar search.

I was hoping someone else might have better luck in searching the sources.